├── .gitignore
├── LICENSE
├── README.md
├── code
├── CRep.py
├── README.md
├── analyse_results.ipynb
├── cv_functions.py
├── generate_data.py
├── generative_model_reciprocity.py
├── main.py
├── main_cv.py
├── setting_CRep.yaml
├── setting_CRep0.yaml
├── setting_CRepnc.yaml
├── setting_syn_data.yaml
├── test.py
├── test_cv.py
└── tools.py
├── data
├── input
│ ├── setting111.yaml
│ ├── syn111.dat
│ └── theta_gt111.npz
└── output
│ ├── 5-fold_cv
│ ├── setting_CRep.yaml
│ ├── syn111_cv.csv
│ ├── theta_0K3_test.npz
│ ├── theta_1K3_test.npz
│ ├── theta_2K3_test.npz
│ ├── theta_3K3_test.npz
│ ├── theta_4K3_test.npz
│ ├── theta_CRep_0K3.npz
│ ├── theta_CRep_1K3.npz
│ ├── theta_CRep_2K3.npz
│ ├── theta_CRep_3K3.npz
│ └── theta_CRep_4K3.npz
│ ├── setting_CRep.yaml
│ ├── theta_CRep.npz
│ └── theta_test.npz
└── requirements.txt
/.gitignore:
--------------------------------------------------------------------------------
1 | # Byte-compiled / optimized / DLL files
2 | *__pycache__
3 | *.py[cod]
4 | *$py.class
5 | *pyc
6 | *.DS_Store*
7 | # Distribution / packaging
8 | .Python
9 | build/
10 | develop-eggs/
11 | dist/
12 | downloads/
13 | eggs/
14 | .eggs/
15 | lib/
16 | .idea
17 | # Jupyter Notebook
18 | .ipynb_checkpoints
19 |
--------------------------------------------------------------------------------
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--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
1 | # CRep: reciprocity and community detection in networks
2 | Python implementation of CRep algorithm described in:
3 |
4 | - [1] Safdari H., Contisciani M. & De Bacco C. (2021). *Generative model for reciprocity and community detection in networks*, Phys. Rev. Research 3, 023209.
5 |
6 | This is a new probabilistic generative model and efficient algorithm to model reciprocity in directed networks. It assigns latent variables as community memberships to nodes and a reciprocity parameter to the whole network and it formalizes the assumption that a directed interaction is more likely to occur if an individual has already observed an interaction towards her.
7 |
8 | If you use this code please cite [1].
9 |
10 | The paper can be found [here](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.023209) (_Published version, open access_) or [here](https://arxiv.org/abs/2012.08215) (_preprint_).
11 |
12 | Copyright (c) 2020 [Hadiseh Safdari](https://github.com/hds-safdari), [Martina Contisciani](https://www.is.mpg.de/person/mcontisciani) and [Caterina De Bacco](http://cdebacco.com).
13 |
14 | Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
15 |
16 | The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
17 |
18 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON INFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
19 |
20 | ## What's included
21 | - `code` : Contains the Python implementation of CRep algorithm, the code for performing the cross-validation procedure and the code for generating benchmark synthetic data with intrinsic community structure and given reciprocity value.
22 | - `data/input` : Contains an example of directed network having an intrinsic community structure and a given reciprocity value, and some example files to initialize the latent variables. They are synthetic data.
23 | - `data/output` : Contains some results to test the code.
24 |
25 | ## Requirements
26 | The project has been developed using Python 3.9 with the packages contained in *requirements.txt*. We suggest to create a virtual environment with
27 | `python3.9 -m venv --copies CRep`, activate it with `source CRep/bin/activate`, and install all the dependencies by running (inside `CRep` directory):
28 |
29 | `pip install -r requirements.txt`
30 |
31 | ## Test
32 | You can run tests to reproduce results contained in `data/output` by running (inside `code` directory):
33 |
34 | ```bash
35 | python -m unittest test.py
36 | python -m unittest test_cv.py
37 | ```
38 |
39 | ## Usage
40 | To test the program on the given example file, type:
41 |
42 | ```bash
43 | cd code
44 | python main.py
45 | ```
46 |
47 | It will use the sample network contained in `./data/input`. The adjacency matrix *syn111.dat* represents a directed, weighted network with **N=600** nodes, **K=3** equal-size unmixed communities with an **assortative** structure and reciprocity parameter **eta=0.5**.
48 |
49 | ### Parameters
50 | - **-a** : Model configuration to use (CRep, CRepnc, CRep0), *(default='CRep')*.
51 | - **-K** : Number of communities, *(default=3)*.
52 | - **-A** : Input file name of the adjacency matrix, *(default='syn111.dat')*.
53 | - **-f** : Path of the input folder, *(default='../data/input/')*.
54 | - **-e** : Name of the source of the edge, *(default='source')*.
55 | - **-t** : Name of the target of the edge, *(default='target')*.
56 | - **-d** : Flag to force a dense transformation of the adjacency matrix, *(default=False)*.
57 | - **-F** : Flag to choose the convergence method, *(default='log')*.
58 |
59 | You can find a list by running (inside `code` directory):
60 |
61 | ```bash
62 | python main.py --help
63 | ```
64 |
65 | ## Input format
66 | The network should be stored in a *.dat* file. An example of rows is
67 |
68 | `node1 node2 3`
69 | `node1 node3 1`
70 |
71 | where the first and second columns are the _source_ and _target_ nodes of the edge, respectively; the third column tells if there is an edge and the weight. In this example the edge node1 --> node2 exists with weight 3, and the edge node1 --> node3 exists with weight 1.
72 |
73 | Other configuration settings can be set by modifying the *setting\_\*_.yaml* files:
74 |
75 | - *setting\_syn_data.yaml* : contains the setting to generate synthetic data
76 | - *setting\_CRep.yaml* : contains the setting to run the algorithm CRep
77 | - *setting\_CRepnc.yaml* : contains the setting to run the algorithm CRep without normalization constraints on the membership parameters
78 | - *setting\_CRep0.yaml* : contains the setting to run the algorithm CRep without considering the reciprocity effect
79 |
80 | ## Output
81 | The algorithm returns a compressed file inside the `data/output` folder. To load and print the out-going membership matrix:
82 |
83 | ```bash
84 | import numpy as np
85 | theta = np.load('theta_Crep.npz')
86 | print(theta['u'])
87 | ```
88 |
89 | _theta_ contains the two $N\times K$ membership matrices **u** *('u')* and **v** *('v')*, the $1\times K \times K$ (or $1\times K$ if assortative=True) affinity tensor **w** *('w')*, the reciprocity coefficient **$\eta$** *('eta')*, the total number of iterations *('max_it')*, the value of the maximum pseudo log-likelihood *('maxPSL')* and the nodes of the network *('nodes')*.
90 |
91 | For an example `jupyter notebook` importing the data, see `code/analyse_results.ipynb`.
92 |
--------------------------------------------------------------------------------
/code/CRep.py:
--------------------------------------------------------------------------------
1 | """
2 | Class definition of CRep, the algorithm to perform inference in networks with reciprocity.
3 | The latent variables are related to community memberships and reciprocity value.
4 | """
5 |
6 | from __future__ import print_function
7 | import time
8 | import sys
9 | import sktensor as skt
10 | import numpy as np
11 | from termcolor import colored
12 |
13 |
14 | class CRep:
15 | def __init__(self, N=100, L=1, K=2, undirected=False, assortative=False,
16 | rseed=0, inf=1e10, err_max=1e-8, err=0.01, N_real=1, tolerance=0.0001, decision=10, max_iter=500,
17 | initialization=0, fix_eta=False, fix_communities=False, fix_w=False, constrained=True,
18 | eta0=None, files='../data/input/synthetic/theta.npz',
19 | verbose=False, out_inference=False, out_folder='../data/output/', end_file='.dat'):
20 | self.N = N # number of nodes
21 | self.L = L # number of layers
22 | self.K = K # number of communities
23 | self.undirected = undirected # flag to call the undirected network
24 | self.assortative = assortative # if True, the network is assortative
25 | self.rseed = rseed # random seed for the initialization
26 | self.inf = inf # initial value of the pseudo log-likelihood
27 | self.err_max = err_max # minimum value for the parameters
28 | self.err = err # noise for the initialization
29 | self.N_real = N_real # number of iterations with different random initialization
30 | self.tolerance = tolerance # tolerance parameter for convergence
31 | self.decision = decision # convergence parameter
32 | self.max_iter = max_iter # maximum number of EM steps before aborting
33 | self.fix_eta = fix_eta # if True, the eta parameter is fixed
34 | self.fix_communities = fix_communities # if True, keep the communities u and v fixed
35 | self.fix_w = fix_w # if True, keep the affinity tensor fixed
36 | self.constrained = constrained # if True, use the configuration with constraints on the updates
37 | self.files = files # path of the input files for u, v, w (when initialization>0)
38 | self.verbose = verbose # flag to print details
39 | self.out_inference = out_inference # flag for storing the inferred parameters
40 | self.out_folder = out_folder # path for storing the output
41 | self.end_file = end_file # output file suffix
42 | if initialization not in {0, 1, 2, 3}: # indicator for choosing how to initialize u, v and w
43 | raise ValueError('The initialization parameter can be either 0, 1, 2 or 3. It is used as an indicator to '
44 | 'initialize the membership matrices u and v and the affinity matrix w. If it is 0, they '
45 | 'will be generated randomly; 1 means only the affinity matrix w will be uploaded from '
46 | 'file; 2 implies the membership matrices u and v will be uploaded from file and 3 all u, '
47 | 'v and w will be initialized through an input file.')
48 | self.initialization = initialization
49 | if eta0 is not None:
50 | if (eta0 < 0) or (eta0 > 1):
51 | raise ValueError('The reciprocity coefficient eta0 has to be in [0, 1]!')
52 | self.eta0 = eta0 # initial value for the reciprocity coefficient
53 | if self.fix_eta:
54 | if self.eta0 is None:
55 | raise ValueError('If fix_eta=True, provide a value for eta0.')
56 | if self.fix_w:
57 | if self.initialization not in {1, 3}:
58 | raise ValueError('If fix_w=True, the initialization has to be either 1 or 3.')
59 | if self.fix_communities:
60 | if self.initialization not in {2, 3}:
61 | raise ValueError('If fix_communities=True, the initialization has to be either 2 or 3.')
62 |
63 | if self.initialization > 0:
64 | self.theta = np.load(self.files, allow_pickle=True)
65 | if self.initialization == 1:
66 | dfW = self.theta['w']
67 | self.L = dfW.shape[0]
68 | self.K = dfW.shape[1]
69 | elif self.initialization == 2:
70 | dfU = self.theta['u']
71 | self.N, self.K = dfU.shape
72 | else:
73 | dfW = self.theta['w']
74 | dfU = self.theta['u']
75 | self.L = dfW.shape[0]
76 | self.K = dfW.shape[1]
77 | self.N = dfU.shape[0]
78 | assert self.K == dfU.shape[1]
79 |
80 | if self.undirected:
81 | if not (self.fix_eta and self.eta0 == 0):
82 | raise ValueError('If undirected=True, the parameter eta has to be fixed equal to 0.')
83 |
84 | # values of the parameters used during the update
85 | self.u = np.zeros((self.N, self.K), dtype=float) # out-going membership
86 | self.v = np.zeros((self.N, self.K), dtype=float) # in-going membership
87 | self.eta = 0. # reciprocity coefficient
88 |
89 | # values of the parameters in the previous iteration
90 | self.u_old = np.zeros((self.N, self.K), dtype=float) # out-going membership
91 | self.v_old = np.zeros((self.N, self.K), dtype=float) # in-going membership
92 | self.eta_old = 0. # reciprocity coefficient
93 |
94 | # final values after convergence --> the ones that maximize the pseudo log-likelihood
95 | self.u_f = np.zeros((self.N, self.K), dtype=float) # out-going membership
96 | self.v_f = np.zeros((self.N, self.K), dtype=float) # in-going membership
97 | self.eta_f = 0. # reciprocity coefficient
98 |
99 | # values of the affinity tensor
100 | if self.assortative: # purely diagonal matrix
101 | self.w = np.zeros((self.L, self.K), dtype=float)
102 | self.w_old = np.zeros((self.L, self.K), dtype=float)
103 | self.w_f = np.zeros((self.L, self.K), dtype=float)
104 | else:
105 | self.w = np.zeros((self.L, self.K, self.K), dtype=float)
106 | self.w_old = np.zeros((self.L, self.K, self.K), dtype=float)
107 | self.w_f = np.zeros((self.L, self.K, self.K), dtype=float)
108 |
109 | if self.fix_eta:
110 | self.eta = self.eta_old = self.eta_f = self.eta0
111 |
112 | def fit(self, data, data_T, data_T_vals, nodes, flag_conv, mask=None):
113 | """
114 | Model directed networks by using a probabilistic generative model that assume community parameters and
115 | reciprocity coefficient. The inference is performed via EM algorithm.
116 |
117 | Parameters
118 | ----------
119 | data : ndarray/sptensor
120 | Graph adjacency tensor.
121 | data_T: None/sptensor
122 | Graph adjacency tensor (transpose) - if sptensor.
123 | data_T_vals : None/ndarray
124 | Array with values of entries A[j, i] given non-zero entry (i, j) - if ndarray.
125 | nodes : list
126 | List of nodes IDs.
127 | flag_conv : str
128 | If 'log' the convergence is based on the log-likelihood values; if 'deltas' the convergence is
129 | based on the differences in the parameters values. The latter is suggested when the dataset
130 | is big (N > 1000 ca.).
131 | mask : ndarray
132 | Mask for selecting the held out set in the adjacency tensor in case of cross-validation.
133 |
134 | Returns
135 | -------
136 | u_f : ndarray
137 | Out-going membership matrix.
138 | v_f : ndarray
139 | In-coming membership matrix.
140 | w_f : ndarray
141 | Affinity tensor.
142 | eta_f : float
143 | Reciprocity coefficient.
144 | maxL : float
145 | Maximum pseudo log-likelihood.
146 | final_it : int
147 | Total number of iterations.
148 | """
149 |
150 | maxL = -self.inf # initialization of the maximum pseudo log-likelihood
151 |
152 | if data_T is None:
153 | E = np.sum(data) # weighted sum of edges (needed in the denominator of eta)
154 | data_T = np.einsum('aij->aji', data)
155 | data_T_vals = get_item_array_from_subs(data_T, data.nonzero())
156 | # pre-processing of the data to handle the sparsity
157 | data = preprocess(data)
158 | data_T = preprocess(data_T)
159 | else:
160 | E = np.sum(data.vals)
161 |
162 | # save the indexes of the nonzero entries
163 | if isinstance(data, skt.dtensor):
164 | subs_nz = data.nonzero()
165 | elif isinstance(data, skt.sptensor):
166 | subs_nz = data.subs
167 |
168 | rng = np.random.RandomState(self.rseed)
169 |
170 | for r in range(self.N_real):
171 |
172 | self._initialize(rng=rng, nodes=nodes)
173 |
174 | self._update_old_variables()
175 | self._update_cache(data, data_T_vals, subs_nz)
176 |
177 | # convergence local variables
178 | coincide, it = 0, 0
179 | convergence = False
180 | loglik = self.inf
181 |
182 | if self.verbose:
183 | print(f'Updating realization {r} ...')
184 | time_start = time.time()
185 | # --- single step iteration update ---
186 | while np.logical_and(not convergence, it < self.max_iter):
187 | # main EM update: updates memberships and calculates max difference new vs old
188 | delta_u, delta_v, delta_w, delta_eta = self._update_em(data, data_T_vals, subs_nz, denominator=E)
189 | if flag_conv == 'log':
190 | it, loglik, coincide, convergence = self._check_for_convergence(data, it, loglik, coincide,
191 | convergence, data_T=data_T,
192 | mask=mask)
193 | if self.verbose:
194 | if not it % 100:
195 | print(f'Nreal = {r} - Pseudo Log-likelihood = {loglik} - iterations = {it} - '
196 | f'time = {np.round(time.time() - time_start, 2)} seconds')
197 | elif flag_conv == 'deltas':
198 | it, coincide, convergence = self._check_for_convergence_delta(it, coincide, delta_u, delta_v,
199 | delta_w, delta_eta, convergence)
200 | if self.verbose:
201 | if not it % 100:
202 | print(f'Nreal = {r} - iterations = {it} - '
203 | f'time = {np.round(time.time() - time_start, 2)} seconds')
204 | else:
205 | raise ValueError('flag_conv can be either log or deltas!')
206 |
207 | if flag_conv == 'log':
208 | if maxL < loglik:
209 | self._update_optimal_parameters()
210 | maxL = loglik
211 | self.final_it = it
212 | conv = convergence
213 | elif flag_conv == 'deltas':
214 | loglik = self._PSLikelihood(data, data_T=data_T, mask=mask)
215 | if maxL < loglik:
216 | self._update_optimal_parameters()
217 | maxL = loglik
218 | self.final_it = it
219 | conv = convergence
220 | if self.verbose:
221 | print(f'Nreal = {r} - Pseudo Log-likelihood = {loglik} - iterations = {it} - '
222 | f'time = {np.round(time.time() - time_start, 2)} seconds\n')
223 |
224 | # end cycle over realizations
225 |
226 | self.maxPSL = maxL
227 | if np.logical_and(self.final_it == self.max_iter, not conv):
228 | # convergence not reaches
229 | try:
230 | print(colored('Solution failed to converge in {0} EM steps!'.format(self.max_iter), 'blue'))
231 | except:
232 | print('Solution failed to converge in {0} EM steps!'.format(self.max_iter))
233 |
234 | if self.out_inference:
235 | self.output_results(nodes)
236 |
237 | return self.u_f, self.v_f, self.w_f, self.eta_f, maxL
238 |
239 | def _initialize(self, rng, nodes):
240 | """
241 | Random initialization of the parameters u, v, w, eta.
242 |
243 | Parameters
244 | ----------
245 | rng : RandomState
246 | Container for the Mersenne Twister pseudo-random number generator.
247 | nodes : list
248 | List of nodes IDs.
249 | """
250 |
251 | if rng is None:
252 | rng = np.random.RandomState(self.rseed)
253 |
254 | if self.eta0 is not None:
255 | self.eta = self.eta0
256 | else:
257 | if self.verbose:
258 | print('eta is initialized randomly.')
259 | self._randomize_eta(rng=rng)
260 |
261 | if self.initialization == 0:
262 | if self.verbose:
263 | print('u, v and w are initialized randomly.')
264 | self._randomize_w(rng=rng)
265 | self._randomize_u_v(rng=rng)
266 |
267 | elif self.initialization == 1:
268 | if self.verbose:
269 | print(f'w is initialized using the input file: {self.files}.')
270 | print('u and v are initialized randomly.')
271 | self._initialize_w(rng)
272 | self._randomize_u_v(rng=rng)
273 |
274 | elif self.initialization == 2:
275 | if self.verbose:
276 | print(f'u and v are initialized using the input file: {self.files}.')
277 | print('w is initialized randomly.')
278 | self._initialize_u(rng, nodes)
279 | self._initialize_v(rng, nodes)
280 | self._randomize_w(rng=rng)
281 |
282 | elif self.initialization == 3:
283 | if self.verbose:
284 | print(f'u, v and w are initialized using the input file: {self.files}.')
285 | self._initialize_u(rng, nodes)
286 | self._initialize_v(rng, nodes)
287 | self._initialize_w(rng)
288 |
289 | def _randomize_eta(self, rng):
290 | """
291 | Generate a random number in (0, 1.).
292 |
293 | Parameters
294 | ----------
295 | rng : RandomState
296 | Container for the Mersenne Twister pseudo-random number generator.
297 | """
298 |
299 | if rng is None:
300 | rng = np.random.RandomState(self.rseed)
301 | self.eta = rng.random_sample(1)[0]
302 |
303 | def _randomize_w(self, rng):
304 | """
305 | Assign a random number in (0, 1.) to each entry of the affinity tensor w.
306 |
307 | Parameters
308 | ----------
309 | rng : RandomState
310 | Container for the Mersenne Twister pseudo-random number generator.
311 | """
312 |
313 | if rng is None:
314 | rng = np.random.RandomState(self.rseed)
315 | for i in range(self.L):
316 | for k in range(self.K):
317 | if self.assortative:
318 | self.w[i, k] = rng.random_sample(1)
319 | else:
320 | for q in range(k, self.K):
321 | if q == k:
322 | self.w[i, k, q] = rng.random_sample(1)
323 | else:
324 | self.w[i, k, q] = self.w[i, q, k] = self.err * rng.random_sample(1)
325 |
326 | def _randomize_u_v(self, rng):
327 | """
328 | Assign a random number in (0, 1.) to each entry of the membership matrices u and v, and normalize each row.
329 |
330 | Parameters
331 | ----------
332 | rng : RandomState
333 | Container for the Mersenne Twister pseudo-random number generator.
334 | """
335 |
336 | if rng is None:
337 | rng = np.random.RandomState(self.rseed)
338 | self.u = rng.random_sample(self.u.shape)
339 | row_sums = self.u.sum(axis=1)
340 | self.u[row_sums > 0] /= row_sums[row_sums > 0, np.newaxis]
341 |
342 | if not self.undirected:
343 | self.v = rng.random_sample(self.v.shape)
344 | row_sums = self.v.sum(axis=1)
345 | self.v[row_sums > 0] /= row_sums[row_sums > 0, np.newaxis]
346 | else:
347 | self.v = self.u
348 |
349 | def _initialize_u(self, rng, nodes):
350 | """
351 | Initialize out-going membership matrix u from file.
352 |
353 | Parameters
354 | ----------
355 | rng : RandomState
356 | Container for the Mersenne Twister pseudo-random number generator.
357 | nodes : list
358 | List of nodes IDs.
359 | """
360 |
361 | self.u = self.theta['u']
362 | assert np.array_equal(nodes, self.theta['nodes'])
363 |
364 | max_entry = np.max(self.u)
365 | self.u += max_entry * self.err * rng.random_sample(self.u.shape)
366 |
367 | def _initialize_v(self, rng, nodes):
368 | """
369 | Initialize in-coming membership matrix v from file.
370 |
371 | Parameters
372 | ----------
373 | rng : RandomState
374 | Container for the Mersenne Twister pseudo-random number generator.
375 | nodes : list
376 | List of nodes IDs.
377 | """
378 |
379 | if self.undirected:
380 | self.v = self.u
381 | else:
382 | self.v = self.theta['v']
383 | assert np.array_equal(nodes, self.theta['nodes'])
384 |
385 | max_entry = np.max(self.v)
386 | self.v += max_entry * self.err * rng.random_sample(self.v.shape)
387 |
388 | def _initialize_w(self, rng):
389 | """
390 | Initialize affinity tensor w from file.
391 |
392 | Parameters
393 | ----------
394 | rng : RandomState
395 | Container for the Mersenne Twister pseudo-random number generator.
396 | """
397 |
398 | if self.assortative:
399 | self.w = self.theta['w']
400 | assert self.w.shape == (self.L, self.K)
401 | else:
402 | self.w = self.theta['w']
403 |
404 | max_entry = np.max(self.w)
405 | self.w += max_entry * self.err * rng.random_sample(self.w.shape)
406 |
407 | def _update_old_variables(self):
408 | """
409 | Update values of the parameters in the previous iteration.
410 | """
411 |
412 | self.u_old[self.u > 0] = np.copy(self.u[self.u > 0])
413 | self.v_old[self.v > 0] = np.copy(self.v[self.v > 0])
414 | self.w_old[self.w > 0] = np.copy(self.w[self.w > 0])
415 | self.eta_old = np.copy(self.eta)
416 |
417 | def _update_cache(self, data, data_T_vals, subs_nz):
418 | """
419 | Update the cache used in the em_update.
420 |
421 | Parameters
422 | ----------
423 | data : sptensor/dtensor
424 | Graph adjacency tensor.
425 | data_T_vals : ndarray
426 | Array with values of entries A[j, i] given non-zero entry (i, j).
427 | subs_nz : tuple
428 | Indices of elements of data that are non-zero.
429 | """
430 |
431 | self.lambda0_nz = self._lambda0_nz(subs_nz)
432 | self.M_nz = self.lambda0_nz + self.eta * data_T_vals
433 | self.M_nz[self.M_nz == 0] = 1
434 | if isinstance(data, skt.dtensor):
435 | self.data_M_nz = data[subs_nz] / self.M_nz
436 | elif isinstance(data, skt.sptensor):
437 | self.data_M_nz = data.vals / self.M_nz
438 | self.data_M_nz[self.M_nz == 0] = 0
439 |
440 | def _lambda0_nz(self, subs_nz):
441 | """
442 | Compute the mean lambda0_ij for only non-zero entries.
443 |
444 | Parameters
445 | ----------
446 | subs_nz : tuple
447 | Indices of elements of data that are non-zero.
448 |
449 | Returns
450 | -------
451 | nz_recon_I : ndarray
452 | Mean lambda0_ij for only non-zero entries.
453 | """
454 |
455 | if not self.assortative:
456 | nz_recon_IQ = np.einsum('Ik,Ikq->Iq', self.u[subs_nz[1], :], self.w[subs_nz[0], :, :])
457 | else:
458 | nz_recon_IQ = np.einsum('Ik,Ik->Ik', self.u[subs_nz[1], :], self.w[subs_nz[0], :])
459 | nz_recon_I = np.einsum('Iq,Iq->I', nz_recon_IQ, self.v[subs_nz[2], :])
460 |
461 | return nz_recon_I
462 |
463 | def _update_em(self, data, data_T_vals, subs_nz, denominator=None):
464 | """
465 | Update parameters via EM procedure.
466 |
467 | Parameters
468 | ----------
469 | data : sptensor/dtensor
470 | Graph adjacency tensor.
471 | data_T_vals : ndarray
472 | Array with values of entries A[j, i] given non-zero entry (i, j).
473 | subs_nz : tuple
474 | Indices of elements of data that are non-zero.
475 | denominator : float
476 | Denominator used in the update of the eta parameter.
477 |
478 | Returns
479 | -------
480 | d_u : float
481 | Maximum distance between the old and the new membership matrix u.
482 | d_v : float
483 | Maximum distance between the old and the new membership matrix v.
484 | d_w : float
485 | Maximum distance between the old and the new affinity tensor w.
486 | d_eta : float
487 | Maximum distance between the old and the new reciprocity coefficient eta.
488 | """
489 |
490 | if not self.fix_eta:
491 | d_eta = self._update_eta(data, data_T_vals, denominator=denominator)
492 | else:
493 | d_eta = 0.
494 | self._update_cache(data, data_T_vals, subs_nz)
495 |
496 | if not self.fix_communities:
497 | d_u = self._update_U(subs_nz)
498 | self._update_cache(data, data_T_vals, subs_nz)
499 | else:
500 | d_u = 0.
501 |
502 | if self.undirected:
503 | self.v = self.u
504 | self.v_old = self.v
505 | d_v = d_u
506 | self._update_cache(data, data_T_vals, subs_nz)
507 | else:
508 | if not self.fix_communities:
509 | d_v = self._update_V(subs_nz)
510 | self._update_cache(data, data_T_vals, subs_nz)
511 | else:
512 | d_v = 0.
513 |
514 | if not self.fix_w:
515 | if not self.assortative:
516 | d_w = self._update_W(subs_nz)
517 | else:
518 | d_w = self._update_W_assortative(subs_nz)
519 | self._update_cache(data, data_T_vals, subs_nz)
520 | else:
521 | d_w = 0
522 |
523 | return d_u, d_v, d_w, d_eta
524 |
525 | def _update_eta(self, data, data_T_vals, denominator=None):
526 | """
527 | Update reciprocity coefficient eta.
528 |
529 | Parameters
530 | ----------
531 | data : sptensor/dtensor
532 | Graph adjacency tensor.
533 | data_T_vals : ndarray
534 | Array with values of entries A[j, i] given non-zero entry (i, j).
535 | denominator : float
536 | Denominator used in the update of the eta parameter.
537 |
538 | Returns
539 | -------
540 | dist_eta : float
541 | Maximum distance between the old and the new reciprocity coefficient eta.
542 | """
543 |
544 | if denominator is None:
545 | Deta = data.sum()
546 | else:
547 | Deta = denominator
548 |
549 | self.eta *= (self.data_M_nz * data_T_vals).sum() / Deta
550 |
551 | dist_eta = abs(self.eta - self.eta_old)
552 | self.eta_old = np.copy(self.eta)
553 |
554 | return dist_eta
555 |
556 | def _update_U(self, subs_nz):
557 | """
558 | Update out-going membership matrix.
559 |
560 | Parameters
561 | ----------
562 | subs_nz : tuple
563 | Indices of elements of data that are non-zero.
564 |
565 | Returns
566 | -------
567 | dist_u : float
568 | Maximum distance between the old and the new membership matrix u.
569 | """
570 |
571 | self.u = self.u_old * self._update_membership(subs_nz, 1)
572 |
573 | if not self.constrained:
574 | Du = np.einsum('iq->q', self.v)
575 | if not self.assortative:
576 | w_k = np.einsum('akq->kq', self.w)
577 | Z_uk = np.einsum('q,kq->k', Du, w_k)
578 | else:
579 | w_k = np.einsum('ak->k', self.w)
580 | Z_uk = np.einsum('k,k->k', Du, w_k)
581 | non_zeros = Z_uk > 0.
582 | self.u[:, Z_uk == 0] = 0.
583 | self.u[:, non_zeros] /= Z_uk[np.newaxis, non_zeros]
584 | else:
585 | row_sums = self.u.sum(axis=1)
586 | self.u[row_sums > 0] /= row_sums[row_sums > 0, np.newaxis]
587 |
588 | low_values_indices = self.u < self.err_max # values are too low
589 | self.u[low_values_indices] = 0. # and set to 0.
590 |
591 | dist_u = np.amax(abs(self.u - self.u_old))
592 | self.u_old = np.copy(self.u)
593 |
594 | return dist_u
595 |
596 | def _update_V(self, subs_nz):
597 | """
598 | Update in-coming membership matrix.
599 | Same as _update_U but with:
600 | data <-> data_T
601 | w <-> w_T
602 | u <-> v
603 |
604 | Parameters
605 | ----------
606 | subs_nz : tuple
607 | Indices of elements of data that are non-zero.
608 |
609 | Returns
610 | -------
611 | dist_v : float
612 | Maximum distance between the old and the new membership matrix v.
613 | """
614 |
615 | self.v *= self._update_membership(subs_nz, 2)
616 |
617 | if not self.constrained:
618 | Dv = np.einsum('iq->q', self.u)
619 | if not self.assortative:
620 | w_k = np.einsum('aqk->qk', self.w)
621 | Z_vk = np.einsum('q,qk->k', Dv, w_k)
622 | else:
623 | w_k = np.einsum('ak->k', self.w)
624 | Z_vk = np.einsum('k,k->k', Dv, w_k)
625 | non_zeros = Z_vk > 0
626 | self.v[:, Z_vk == 0] = 0.
627 | self.v[:, non_zeros] /= Z_vk[np.newaxis, non_zeros]
628 | else:
629 | row_sums = self.v.sum(axis=1)
630 | self.v[row_sums > 0] /= row_sums[row_sums > 0, np.newaxis]
631 |
632 | low_values_indices = self.v < self.err_max # values are too low
633 | self.v[low_values_indices] = 0. # and set to 0.
634 |
635 | dist_v = np.amax(abs(self.v - self.v_old))
636 | self.v_old = np.copy(self.v)
637 |
638 | return dist_v
639 |
640 | def _update_W(self, subs_nz):
641 | """
642 | Update affinity tensor.
643 |
644 | Parameters
645 | ----------
646 | subs_nz : tuple
647 | Indices of elements of data that are non-zero.
648 |
649 | Returns
650 | -------
651 | dist_w : float
652 | Maximum distance between the old and the new affinity tensor w.
653 | """
654 |
655 | uttkrp_DKQ = np.zeros_like(self.w)
656 |
657 | UV = np.einsum('Ik,Iq->Ikq', self.u[subs_nz[1], :], self.v[subs_nz[2], :])
658 | uttkrp_I = self.data_M_nz[:, np.newaxis, np.newaxis] * UV
659 | for k in range(self.K):
660 | for q in range(self.K):
661 | uttkrp_DKQ[:, k, q] += np.bincount(subs_nz[0], weights=uttkrp_I[:, k, q], minlength=self.L)
662 |
663 | self.w *= uttkrp_DKQ
664 |
665 | Z = np.einsum('k,q->kq', self.u.sum(axis=0), self.v.sum(axis=0))[np.newaxis, :, :]
666 | non_zeros = Z > 0
667 | self.w[non_zeros] /= Z[non_zeros]
668 |
669 | low_values_indices = self.w < self.err_max # values are too low
670 | self.w[low_values_indices] = 0. # and set to 0.
671 |
672 | dist_w = np.amax(abs(self.w - self.w_old))
673 | self.w_old = np.copy(self.w)
674 |
675 | return dist_w
676 |
677 | def _update_W_assortative(self, subs_nz):
678 | """
679 | Update affinity tensor (assuming assortativity).
680 |
681 | Parameters
682 | ----------
683 | subs_nz : tuple
684 | Indices of elements of data that are non-zero.
685 |
686 | Returns
687 | -------
688 | dist_w : float
689 | Maximum distance between the old and the new affinity tensor w.
690 | """
691 |
692 | uttkrp_DKQ = np.zeros_like(self.w)
693 |
694 | UV = np.einsum('Ik,Ik->Ik', self.u[subs_nz[1], :], self.v[subs_nz[2], :])
695 | uttkrp_I = self.data_M_nz[:, np.newaxis] * UV
696 | for k in range(self.K):
697 | uttkrp_DKQ[:, k] += np.bincount(subs_nz[0], weights=uttkrp_I[:, k], minlength=self.L)
698 |
699 | self.w *= uttkrp_DKQ
700 |
701 | Z = ((self.u_old.sum(axis=0)) * (self.v_old.sum(axis=0)))[np.newaxis, :]
702 | non_zeros = Z > 0
703 | self.w[non_zeros] /= Z[non_zeros]
704 |
705 | low_values_indices = self.w < self.err_max # values are too low
706 | self.w[low_values_indices] = 0. # and set to 0.
707 |
708 | dist_w = np.amax(abs(self.w - self.w_old))
709 | self.w_old = np.copy(self.w)
710 |
711 | return dist_w
712 |
713 | def _update_membership(self, subs_nz, m):
714 | """
715 | Return the Khatri-Rao product (sparse version) used in the update of the membership matrices.
716 |
717 | Parameters
718 | ----------
719 | subs_nz : tuple
720 | Indices of elements of data that are non-zero.
721 | m : int
722 | Mode in which the Khatri-Rao product of the membership matrix is multiplied with the tensor: if 1 it
723 | works with the matrix u; if 2 it works with v.
724 |
725 | Returns
726 | -------
727 | uttkrp_DK : ndarray
728 | Matrix which is the result of the matrix product of the unfolding of the tensor and the
729 | Khatri-Rao product of the membership matrix.
730 | """
731 |
732 | if not self.assortative:
733 | uttkrp_DK = sp_uttkrp(self.data_M_nz, subs_nz, m, self.u, self.v, self.w)
734 | else:
735 | uttkrp_DK = sp_uttkrp_assortative(self.data_M_nz, subs_nz, m, self.u, self.v, self.w)
736 |
737 | return uttkrp_DK
738 |
739 | def _check_for_convergence(self, data, it, loglik, coincide, convergence, data_T=None, mask=None):
740 | """
741 | Check for convergence by using the pseudo log-likelihood values.
742 |
743 | Parameters
744 | ----------
745 | data : sptensor/dtensor
746 | Graph adjacency tensor.
747 | it : int
748 | Number of iteration.
749 | loglik : float
750 | Pseudo log-likelihood value.
751 | coincide : int
752 | Number of time the update of the pseudo log-likelihood respects the tolerance.
753 | convergence : bool
754 | Flag for convergence.
755 | data_T : sptensor/dtensor
756 | Graph adjacency tensor (transpose).
757 | mask : ndarray
758 | Mask for selecting the held out set in the adjacency tensor in case of cross-validation.
759 |
760 | Returns
761 | -------
762 | it : int
763 | Number of iteration.
764 | loglik : float
765 | Pseudo log-likelihood value.
766 | coincide : int
767 | Number of time the update of the pseudo log-likelihood respects the tolerance.
768 | convergence : bool
769 | Flag for convergence.
770 | """
771 |
772 | if it % 10 == 0:
773 | old_L = loglik
774 | loglik = self._PSLikelihood(data, data_T=data_T, mask=mask)
775 | if abs(loglik - old_L) < self.tolerance:
776 | coincide += 1
777 | else:
778 | coincide = 0
779 | if coincide > self.decision:
780 | convergence = True
781 | it += 1
782 |
783 | return it, loglik, coincide, convergence
784 |
785 | def _check_for_convergence_delta(self, it, coincide, du, dv, dw, de, convergence):
786 | """
787 | Check for convergence by using the maximum distances between the old and the new parameters values.
788 |
789 | Parameters
790 | ----------
791 | it : int
792 | Number of iteration.
793 | coincide : int
794 | Number of time the update of the log-likelihood respects the tolerance.
795 | du : float
796 | Maximum distance between the old and the new membership matrix U.
797 | dv : float
798 | Maximum distance between the old and the new membership matrix V.
799 | dw : float
800 | Maximum distance between the old and the new affinity tensor W.
801 | de : float
802 | Maximum distance between the old and the new eta parameter.
803 | convergence : bool
804 | Flag for convergence.
805 |
806 | Returns
807 | -------
808 | it : int
809 | Number of iteration.
810 | coincide : int
811 | Number of time the update of the log-likelihood respects the tolerance.
812 | convergence : bool
813 | Flag for convergence.
814 | """
815 |
816 | if du < self.tolerance and dv < self.tolerance and dw < self.tolerance and de < self.tolerance:
817 | coincide += 1
818 | else:
819 | coincide = 0
820 | if coincide > self.decision:
821 | convergence = True
822 | it += 1
823 |
824 | return it, coincide, convergence
825 |
826 | def _PSLikelihood(self, data, data_T, mask=None):
827 | """
828 | Compute the pseudo log-likelihood of the data.
829 |
830 | Parameters
831 | ----------
832 | data : sptensor/dtensor
833 | Graph adjacency tensor.
834 | data_T : sptensor/dtensor
835 | Graph adjacency tensor (transpose).
836 | mask : ndarray
837 | Mask for selecting the held out set in the adjacency tensor in case of cross-validation.
838 |
839 | Returns
840 | -------
841 | l : float
842 | Pseudo log-likelihood value.
843 | """
844 |
845 | self.lambda0_ija = self._lambda0_full(self.u, self.v, self.w)
846 |
847 | if mask is not None:
848 | sub_mask_nz = mask.nonzero()
849 | if isinstance(data, skt.dtensor):
850 | l = -self.lambda0_ija[sub_mask_nz].sum() - self.eta * data_T[sub_mask_nz].sum()
851 | elif isinstance(data, skt.sptensor):
852 | l = -self.lambda0_ija[sub_mask_nz].sum() - self.eta * data_T.toarray()[sub_mask_nz].sum()
853 | else:
854 | if isinstance(data, skt.dtensor):
855 | l = -self.lambda0_ija.sum() - self.eta * data_T.sum()
856 | elif isinstance(data, skt.sptensor):
857 | l = -self.lambda0_ija.sum() - self.eta * data_T.vals.sum()
858 | logM = np.log(self.M_nz)
859 | if isinstance(data, skt.dtensor):
860 | Alog = data[data.nonzero()] * logM
861 | elif isinstance(data, skt.sptensor):
862 | Alog = data.vals * logM
863 |
864 | l += Alog.sum()
865 |
866 | if np.isnan(l):
867 | print("PSLikelihood is NaN!!!!")
868 | sys.exit(1)
869 | else:
870 | return l
871 |
872 | def _lambda0_full(self, u, v, w):
873 | """
874 | Compute the mean lambda0 for all entries.
875 |
876 | Parameters
877 | ----------
878 | u : ndarray
879 | Out-going membership matrix.
880 | v : ndarray
881 | In-coming membership matrix.
882 | w : ndarray
883 | Affinity tensor.
884 |
885 | Returns
886 | -------
887 | M : ndarray
888 | Mean lambda0 for all entries.
889 | """
890 |
891 | if w.ndim == 2:
892 | M = np.einsum('ik,jk->ijk', u, v)
893 | M = np.einsum('ijk,ak->aij', M, w)
894 | else:
895 | M = np.einsum('ik,jq->ijkq', u, v)
896 | M = np.einsum('ijkq,akq->aij', M, w)
897 | return M
898 |
899 | def _update_optimal_parameters(self):
900 | """
901 | Update values of the parameters after convergence.
902 | """
903 |
904 | self.u_f = np.copy(self.u)
905 | self.v_f = np.copy(self.v)
906 | self.w_f = np.copy(self.w)
907 | self.eta_f = np.copy(self.eta)
908 |
909 | def output_results(self, nodes):
910 | """
911 | Output results.
912 |
913 | Parameters
914 | ----------
915 | nodes : list
916 | List of nodes IDs.
917 | """
918 |
919 | outfile = self.out_folder + 'theta' + self.end_file
920 | np.savez_compressed(outfile + '.npz', u=self.u_f, v=self.v_f, w=self.w_f, eta=self.eta_f, max_it=self.final_it,
921 | maxPSL=self.maxPSL, nodes=nodes)
922 | print(f'\nInferred parameters saved in: {outfile + ".npz"}')
923 | print('To load: theta=np.load(filename), then e.g. theta["u"]')
924 |
925 |
926 | def sp_uttkrp(vals, subs, m, u, v, w):
927 | """
928 | Compute the Khatri-Rao product (sparse version).
929 |
930 | Parameters
931 | ----------
932 | vals : ndarray
933 | Values of the non-zero entries.
934 | subs : tuple
935 | Indices of elements that are non-zero. It is a n-tuple of array-likes and the length of tuple n must be
936 | equal to the dimension of tensor.
937 | m : int
938 | Mode in which the Khatri-Rao product of the membership matrix is multiplied with the tensor: if 1 it
939 | works with the matrix u; if 2 it works with v.
940 | u : ndarray
941 | Out-going membership matrix.
942 | v : ndarray
943 | In-coming membership matrix.
944 | w : ndarray
945 | Affinity tensor.
946 |
947 | Returns
948 | -------
949 | out : ndarray
950 | Matrix which is the result of the matrix product of the unfolding of the tensor and the Khatri-Rao product
951 | of the membership matrix.
952 | """
953 |
954 | if m == 1:
955 | D, K = u.shape
956 | out = np.zeros_like(u)
957 | elif m == 2:
958 | D, K = v.shape
959 | out = np.zeros_like(v)
960 |
961 | for k in range(K):
962 | tmp = vals.copy()
963 | if m == 1: # we are updating u
964 | tmp *= (w[subs[0], k, :].astype(tmp.dtype) * v[subs[2], :].astype(tmp.dtype)).sum(axis=1)
965 | elif m == 2: # we are updating v
966 | tmp *= (w[subs[0], :, k].astype(tmp.dtype) * u[subs[1], :].astype(tmp.dtype)).sum(axis=1)
967 | out[:, k] += np.bincount(subs[m], weights=tmp, minlength=D)
968 |
969 | return out
970 |
971 |
972 | def sp_uttkrp_assortative(vals, subs, m, u, v, w):
973 | """
974 | Compute the Khatri-Rao product (sparse version) with the assumption of assortativity.
975 |
976 | Parameters
977 | ----------
978 | vals : ndarray
979 | Values of the non-zero entries.
980 | subs : tuple
981 | Indices of elements that are non-zero. It is a n-tuple of array-likes and the length of tuple n must be
982 | equal to the dimension of tensor.
983 | m : int
984 | Mode in which the Khatri-Rao product of the membership matrix is multiplied with the tensor: if 1 it
985 | works with the matrix u; if 2 it works with v.
986 | u : ndarray
987 | Out-going membership matrix.
988 | v : ndarray
989 | In-coming membership matrix.
990 | w : ndarray
991 | Affinity tensor.
992 |
993 | Returns
994 | -------
995 | out : ndarray
996 | Matrix which is the result of the matrix product of the unfolding of the tensor and the Khatri-Rao product
997 | of the membership matrix.
998 | """
999 |
1000 | if m == 1:
1001 | D, K = u.shape
1002 | out = np.zeros_like(u)
1003 | elif m == 2:
1004 | D, K = v.shape
1005 | out = np.zeros_like(v)
1006 |
1007 | for k in range(K):
1008 | tmp = vals.copy()
1009 | if m == 1: # we are updating u
1010 | tmp *= w[subs[0], k].astype(tmp.dtype) * v[subs[2], k].astype(tmp.dtype)
1011 | elif m == 2: # we are updating v
1012 | tmp *= w[subs[0], k].astype(tmp.dtype) * u[subs[1], k].astype(tmp.dtype)
1013 | out[:, k] += np.bincount(subs[m], weights=tmp, minlength=D)
1014 |
1015 | return out
1016 |
1017 |
1018 | def get_item_array_from_subs(A, ref_subs):
1019 | """
1020 | Get values of ref_subs entries of a dense tensor.
1021 | Output is a 1-d array with dimension = number of non zero entries.
1022 | """
1023 |
1024 | return np.array([A[a, i, j] for a, i, j in zip(*ref_subs)])
1025 |
1026 |
1027 | def preprocess(A):
1028 | """
1029 | Pre-process input data tensor.
1030 | If the input is sparse, returns an int sptensor. Otherwise, returns an int dtensor.
1031 |
1032 | Parameters
1033 | ----------
1034 | A : ndarray
1035 | Input data (tensor).
1036 |
1037 | Returns
1038 | -------
1039 | A : sptensor/dtensor
1040 | Pre-processed data. If the input is sparse, returns an int sptensor. Otherwise, returns an int dtensor.
1041 | """
1042 |
1043 | if not A.dtype == np.dtype(int).type:
1044 | A = A.astype(int)
1045 | if np.logical_and(isinstance(A, np.ndarray), is_sparse(A)):
1046 | A = sptensor_from_dense_array(A)
1047 | else:
1048 | A = skt.dtensor(A)
1049 |
1050 | return A
1051 |
1052 |
1053 | def is_sparse(X):
1054 | """
1055 | Check whether the input tensor is sparse.
1056 | It implements a heuristic definition of sparsity. A tensor is considered sparse if:
1057 | given
1058 | M = number of modes
1059 | S = number of entries
1060 | I = number of non-zero entries
1061 | then
1062 | N > M(I + 1)
1063 |
1064 | Parameters
1065 | ----------
1066 | X : ndarray
1067 | Input data.
1068 |
1069 | Returns
1070 | -------
1071 | Boolean flag: true if the input tensor is sparse, false otherwise.
1072 | """
1073 |
1074 | M = X.ndim
1075 | S = X.size
1076 | I = X.nonzero()[0].size
1077 |
1078 | return S > (I + 1) * M
1079 |
1080 |
1081 | def sptensor_from_dense_array(X):
1082 | """
1083 | Create an sptensor from a ndarray or dtensor.
1084 | Parameters
1085 | ----------
1086 | X : ndarray
1087 | Input data.
1088 |
1089 | Returns
1090 | -------
1091 | sptensor from a ndarray or dtensor.
1092 | """
1093 |
1094 | subs = X.nonzero()
1095 | vals = X[subs]
1096 |
1097 | return skt.sptensor(subs, vals, shape=X.shape, dtype=X.dtype)
1098 |
--------------------------------------------------------------------------------
/code/README.md:
--------------------------------------------------------------------------------
1 | # CRep: Python code
2 | Copyright (c) 2020 [Hadiseh Safdari](https://github.com/hds-safdari), [Martina Contisciani](https://www.is.mpg.de/person/mcontisciani) and [Caterina De Bacco](http://cdebacco.com).
3 |
4 | Implements the algorithm described in:
5 |
6 | [1] Safdari H., Contisciani M. & De Bacco C. (2021). *Generative model for reciprocity and community detection in networks*, Phys. Rev. Research 3, 023209.
7 |
8 | If you use this code please cite this [article](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.023209) (_Published version, open access_).
9 |
10 | Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the 'Software'), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
11 |
12 | The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
13 |
14 | THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON INFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
15 |
16 |
17 | ## Files
18 | - `main.py` : General version of the algorithm. It performs the inference in the given single-layer directed network. It infers latent variables as community memberships to nodes and a reciprocity parameter to the whole network.
19 | - `CRep.py` : Class definition of CRep, the algorithm to perform inference in networks with reciprocity. The latent variables are related to community memberships and reciprocity value. This code is optimized to use sparse matrices.
20 | - `generate_data.py` : Code for generating the benchmark synthetic data with an intrinsic community structure and a given reciprocity value.
21 | - `generative_model_reciprocity.py` : Class definition of the reciprocity generative model with the member functions required. It builds a directed, possibly weighted, network. It contains functions to generate networks with an intrinsic community structure and a given reciprocity value, with reciprocity-only or without reciprocity.
22 | - `tools.py` : Contains non-class functions for handling the data.
23 | - `main_cv.py` : Code for performing a k-fold cross-validation procedure, in order to estimate the hyperparameter **K** (number of communities). It runs with a given K and returns a csv file summarizing the results over all folds. The output file contains the value of the pseudo log-likelihood, the regular AUC and the conditional AUC of the link prediction, both in the train and in test sets.
24 | - `cv_functions.py` : Contains functions for performing the k-fold cross-validation procedure.
25 | - `test.py` : Code for testing the main algorithm.
26 | - `test_cv.py` : Code for testing the cross-validation procedure.
27 | - `setting_syn_data.yaml` : Setting to generate synthetic data (input for *generate_data.py*).
28 | - `setting_CRep.yaml` : Setting to run the algorithm CRep (input for *main.py* and *main\_cv.py*).
29 | - `setting_CRepnc.yaml` : Setting to run the algorithm CRep without normalization constraints on the membership parameters (input for *main.py* and *main\_cv.py*).
30 | - `setting_CRep0.yaml` : Setting to run the algorithm CRep without considering the reciprocity effect (input for *main.py* and *main\_cv.py*).
31 | - `analyse_results.ipynb` : Example jupyter notebook to import the output results.
32 |
33 | ## Usage
34 | To test the program on the given example file, type
35 |
36 | ```bash
37 | python main.py
38 | ```
39 |
40 | It will use the sample network contained in `./data/input`. The adjacency matrix *syn111.dat* represents a directed, weighted network with **N=600** nodes, **K=3** equal-size unmixed communities with an **assortative** structure and reciprocity parameter **eta=0.5**.
41 |
42 | ### Parameters
43 | - **-a** : Model configuration to use (CRep, CRepnc, CRep0), *(default='CRep')*.
44 | - **-K** : Number of communities, *(default=3)*.
45 | - **-A** : Input file name of the adjacency matrix, *(default='syn111.dat')*.
46 | - **-f** : Path of the input folder, *(default='../data/input/')*.
47 | - **-e** : Name of the source of the edge, *(default='source')*.
48 | - **-t** : Name of the target of the edge, *(default='target')*.
49 | - **-d** : Flag to force a dense transformation of the adjacency matrix, *(default=False)*.
50 | - **-F** : Flag to choose the convergence method, *(default='log')*.
51 |
52 | You can find a list by running (inside `code` directory):
53 |
54 | ```bash
55 | python main.py --help
56 | ```
57 |
58 | ## Input format
59 | The network should be stored in a *.dat* file. An example of rows is
60 |
61 | `node1 node2 3`
62 | `node1 node3 1`
63 |
64 | where the first and second columns are the _source_ and _target_ nodes of the edge, respectively; the third column tells if there is an edge and the weight. In this example the edge node1 --> node2 exists with weight 3, and the edge node1 --> node3 exists with weight 1.
65 |
66 | ## Output
67 | The algorithm returns a compressed file inside the `./data/output` folder. To load and print the out-going membership matrix:
68 |
69 | ```bash
70 | import numpy as np
71 | theta = np.load('theta_Crep.npz')
72 | print(theta['u'])
73 | ```
74 |
75 | _theta_ contains the two NxK membership matrices **u** *('u')* and **v** *('v')*, the 1xKxK (or 1xK if assortative=True) affinity tensor **w** *('w')*, the reciprocity coefficient **$\eta$** *('eta')*, the total number of iterations *('max_it')*, the value of the maximum pseudo log-likelihood *('maxPSL')* and the nodes of the network *('nodes')*.
76 |
77 | For an example `jupyter notebook` importing the data, see *analyse_results.ipynb*.
78 |
--------------------------------------------------------------------------------
/code/analyse_results.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "### Analyse output results"
8 | ]
9 | },
10 | {
11 | "cell_type": "code",
12 | "execution_count": 1,
13 | "metadata": {},
14 | "outputs": [],
15 | "source": [
16 | "import numpy as np\n",
17 | "import matplotlib.pyplot as plt"
18 | ]
19 | },
20 | {
21 | "cell_type": "code",
22 | "execution_count": 2,
23 | "metadata": {},
24 | "outputs": [],
25 | "source": [
26 | "filename = '../data/output/theta_CRep.npz'\n",
27 | "theta = np.load(filename)"
28 | ]
29 | },
30 | {
31 | "cell_type": "code",
32 | "execution_count": 3,
33 | "metadata": {},
34 | "outputs": [],
35 | "source": [
36 | "u,v,w,eta = theta['u'],theta['v'],theta['w'],theta['eta']"
37 | ]
38 | },
39 | {
40 | "cell_type": "code",
41 | "execution_count": 4,
42 | "metadata": {},
43 | "outputs": [
44 | {
45 | "data": {
46 | "text/plain": [
47 | "array([[0. , 1. , 0. ],\n",
48 | " [0. , 0.66901078, 0.33098922],\n",
49 | " [0. , 0.73152525, 0.26847475],\n",
50 | " ...,\n",
51 | " [0.92174939, 0.07825061, 0. ],\n",
52 | " [1. , 0. , 0. ],\n",
53 | " [1. , 0. , 0. ]])"
54 | ]
55 | },
56 | "execution_count": 4,
57 | "metadata": {},
58 | "output_type": "execute_result"
59 | }
60 | ],
61 | "source": [
62 | "u"
63 | ]
64 | },
65 | {
66 | "cell_type": "code",
67 | "execution_count": 5,
68 | "metadata": {},
69 | "outputs": [
70 | {
71 | "data": {
72 | "text/plain": [
73 | "array([[0. , 0.68693478, 0.31306522],\n",
74 | " [0. , 1. , 0. ],\n",
75 | " [0. , 0. , 1. ],\n",
76 | " ...,\n",
77 | " [0. , 0. , 1. ],\n",
78 | " [1. , 0. , 0. ],\n",
79 | " [1. , 0. , 0. ]])"
80 | ]
81 | },
82 | "execution_count": 5,
83 | "metadata": {},
84 | "output_type": "execute_result"
85 | }
86 | ],
87 | "source": [
88 | "v"
89 | ]
90 | },
91 | {
92 | "cell_type": "code",
93 | "execution_count": 6,
94 | "metadata": {},
95 | "outputs": [
96 | {
97 | "data": {
98 | "text/plain": [
99 | "array([[0.0226852 , 0.02808736, 0.03392388]])"
100 | ]
101 | },
102 | "execution_count": 6,
103 | "metadata": {},
104 | "output_type": "execute_result"
105 | }
106 | ],
107 | "source": [
108 | "w"
109 | ]
110 | },
111 | {
112 | "cell_type": "code",
113 | "execution_count": 7,
114 | "metadata": {},
115 | "outputs": [
116 | {
117 | "data": {
118 | "text/plain": [
119 | "array(0.44088065)"
120 | ]
121 | },
122 | "execution_count": 7,
123 | "metadata": {},
124 | "output_type": "execute_result"
125 | }
126 | ],
127 | "source": [
128 | "eta"
129 | ]
130 | }
131 | ],
132 | "metadata": {
133 | "kernelspec": {
134 | "display_name": "Python 3",
135 | "language": "python",
136 | "name": "python3"
137 | },
138 | "language_info": {
139 | "codemirror_mode": {
140 | "name": "ipython",
141 | "version": 3
142 | },
143 | "file_extension": ".py",
144 | "mimetype": "text/x-python",
145 | "name": "python",
146 | "nbconvert_exporter": "python",
147 | "pygments_lexer": "ipython3",
148 | "version": "3.7.4"
149 | }
150 | },
151 | "nbformat": 4,
152 | "nbformat_minor": 4
153 | }
154 |
--------------------------------------------------------------------------------
/code/cv_functions.py:
--------------------------------------------------------------------------------
1 | """
2 | Functions used in the k-fold cross-validation procedure.
3 | """
4 |
5 | import CRep as CREP
6 | import numpy as np
7 | from sklearn import metrics
8 | import yaml
9 |
10 |
11 | def PSloglikelihood(B, u, v, w, eta, mask=None):
12 | """
13 | Compute the pseudo log-likelihood of the data.
14 |
15 | Parameters
16 | ----------
17 | B : ndarray
18 | Graph adjacency tensor.
19 | u : ndarray
20 | Out-going membership matrix.
21 | v : ndarray
22 | In-coming membership matrix.
23 | w : ndarray
24 | Affinity tensor.
25 | eta : float
26 | Reciprocity coefficient.
27 | mask : ndarray
28 | Mask for selecting the held out set in the adjacency tensor in case of cross-validation.
29 |
30 | Returns
31 | -------
32 | Pseudo log-likelihood value.
33 | """
34 |
35 | if mask is None:
36 | M = _lambda0_full(u, v, w)
37 | M += (eta * B[0, :, :].T)[np.newaxis, :, :]
38 | logM = np.zeros(M.shape)
39 | logM[M > 0] = np.log(M[M > 0])
40 | return (B * logM).sum() - M.sum()
41 | else:
42 | M = _lambda0_full(u, v, w)[mask > 0]
43 | M += (eta * B[0, :, :].T)[np.newaxis, :, :][mask > 0]
44 | logM = np.zeros(M.shape)
45 | logM[M > 0] = np.log(M[M > 0])
46 | return (B[mask > 0] * logM).sum() - M.sum()
47 |
48 |
49 | def _lambda0_full(u, v, w):
50 | """
51 | Compute the mean lambda0 for all entries.
52 |
53 | Parameters
54 | ----------
55 | u : ndarray
56 | Out-going membership matrix.
57 | v : ndarray
58 | In-coming membership matrix.
59 | w : ndarray
60 | Affinity tensor.
61 |
62 | Returns
63 | -------
64 | M : ndarray
65 | Mean lambda0 for all entries.
66 | """
67 |
68 | if w.ndim == 2:
69 | M = np.einsum('ik,jk->ijk', u, v)
70 | M = np.einsum('ijk,ak->aij', M, w)
71 | else:
72 | M = np.einsum('ik,jq->ijkq', u, v)
73 | M = np.einsum('ijkq,akq->aij', M, w)
74 |
75 | return M
76 |
77 |
78 | def transpose_ij(M):
79 | """
80 | Compute the transpose of a matrix.
81 |
82 | Parameters
83 | ----------
84 | M : ndarray
85 | Numpy matrix.
86 |
87 | Returns
88 | -------
89 | Transpose of the matrix.
90 | """
91 |
92 | return np.einsum('aij->aji', M)
93 |
94 |
95 | def calculate_expectation(u, v, w, eta=0.0):
96 | """
97 | Compute the expectations, e.g. the parameters of the marginal distribution m_{ij}.
98 |
99 | Parameters
100 | ----------
101 | u : ndarray
102 | Out-going membership matrix.
103 | v : ndarray
104 | In-coming membership matrix.
105 | w : ndarray
106 | Affinity tensor.
107 | eta : float
108 | Reciprocity coefficient.
109 |
110 | Returns
111 | -------
112 | M : ndarray
113 | Matrix whose elements are m_{ij}.
114 | """
115 |
116 | lambda0 = _lambda0_full(u, v, w)
117 | lambda0T = transpose_ij(lambda0)
118 | M = (lambda0 + eta * lambda0T) / (1. - eta * eta)
119 |
120 | return M
121 |
122 |
123 | def calculate_conditional_expectation(B, u, v, w, eta=0.0, mean=None):
124 | """
125 | Compute the conditional expectations, e.g. the parameters of the conditional distribution lambda_{ij}.
126 |
127 | Parameters
128 | ----------
129 | B : ndarray
130 | Graph adjacency tensor.
131 | u : ndarray
132 | Out-going membership matrix.
133 | v : ndarray
134 | In-coming membership matrix.
135 | w : ndarray
136 | Affinity tensor.
137 | eta : float
138 | Reciprocity coefficient.
139 | mean : ndarray
140 | Matrix with mean entries.
141 |
142 | Returns
143 | -------
144 | Matrix whose elements are lambda_{ij}.
145 | """
146 |
147 | if mean is None:
148 | return _lambda0_full(u, v, w) + eta * transpose_ij(B) # conditional expectation (knowing A_ji)
149 | else:
150 | return _lambda0_full(u, v, w) + eta * transpose_ij(mean)
151 |
152 |
153 | def calculate_AUC(pred, data0, mask=None):
154 | """
155 | Return the AUC of the link prediction. It represents the probability that a randomly chosen missing connection
156 | (true positive) is given a higher score by our method than a randomly chosen pair of unconnected vertices
157 | (true negative).
158 |
159 | Parameters
160 | ----------
161 | pred : ndarray
162 | Inferred values.
163 | data0 : ndarray
164 | Given values.
165 | mask : ndarray
166 | Mask for selecting a subset of the adjacency tensor.
167 |
168 | Returns
169 | -------
170 | AUC value.
171 | """
172 |
173 | data = (data0 > 0).astype('int')
174 | if mask is None:
175 | fpr, tpr, thresholds = metrics.roc_curve(data.flatten(), pred.flatten())
176 | else:
177 | fpr, tpr, thresholds = metrics.roc_curve(data[mask > 0], pred[mask > 0])
178 |
179 | return metrics.auc(fpr, tpr)
180 |
181 |
182 | def shuffle_indices_all_matrix(N, L, rseed=10):
183 | """
184 | Shuffle the indices of the adjacency tensor.
185 |
186 | Parameters
187 | ----------
188 | N : int
189 | Number of nodes.
190 | L : int
191 | Number of layers.
192 | rseed : int
193 | Random seed.
194 |
195 | Returns
196 | -------
197 | indices : ndarray
198 | Indices in a shuffled order.
199 | """
200 |
201 | n_samples = int(N * N)
202 | indices = [np.arange(n_samples) for _ in range(L)]
203 | rng = np.random.RandomState(rseed)
204 | for l in range(L):
205 | rng.shuffle(indices[l])
206 |
207 | return indices
208 |
209 |
210 | def extract_mask_kfold(indices, N, fold=0, NFold=5):
211 | """
212 | Extract a non-symmetric mask using KFold cross-validation. It contains pairs (i,j) but possibly not (j,i).
213 | KFold means no train/test sets intersect across the K folds.
214 |
215 | Parameters
216 | ----------
217 | indices : ndarray
218 | Indices of the adjacency tensor in a shuffled order.
219 | N : int
220 | Number of nodes.
221 | fold : int
222 | Current fold.
223 | NFold : int
224 | Number of total folds.
225 |
226 | Returns
227 | -------
228 | mask : ndarray
229 | Mask for selecting the held out set in the adjacency tensor.
230 | """
231 |
232 | L = len(indices)
233 | mask = np.zeros((L, N, N), dtype=bool)
234 | for l in range(L):
235 | n_samples = len(indices[l])
236 | test = indices[l][fold * (n_samples // NFold):(fold + 1) * (n_samples // NFold)]
237 | mask0 = np.zeros(n_samples, dtype=bool)
238 | mask0[test] = 1
239 | mask[l] = mask0.reshape((N, N))
240 |
241 | return mask
242 |
243 |
244 | def fit_model(B, B_T, data_T_vals, nodes, N, L, algo, K, flag_conv, **conf):
245 | """
246 | Model directed networks by using a probabilistic generative model that assume community parameters and
247 | reciprocity coefficient. The inference is performed via EM algorithm.
248 |
249 | Parameters
250 | ----------
251 | B : ndarray
252 | Graph adjacency tensor.
253 | B_T : None/sptensor
254 | Graph adjacency tensor (transpose).
255 | data_T_vals : None/ndarray
256 | Array with values of entries A[j, i] given non-zero entry (i, j).
257 | nodes : list
258 | List of nodes IDs.
259 | N : int
260 | Number of nodes.
261 | L : int
262 | Number of layers.
263 | algo : str
264 | Configuration to use (CRep, CRepnc, CRep0).
265 | K : int
266 | Number of communities.
267 | flag_conv : str
268 | If 'log' the convergence is based on the log-likelihood values; if 'deltas' the convergence is
269 | based on the differences in the parameters values. The latter is suggested when the dataset
270 | is big (N > 1000 ca.).
271 |
272 | Returns
273 | -------
274 | u_f : ndarray
275 | Out-going membership matrix.
276 | v_f : ndarray
277 | In-coming membership matrix.
278 | w_f : ndarray
279 | Affinity tensor.
280 | eta_f : float
281 | Reciprocity coefficient.
282 | maxPSL : float
283 | Maximum pseudo log-likelihood.
284 | mod : obj
285 | The CRep object.
286 | """
287 |
288 | # setting to run the algorithm
289 | with open(conf['out_folder'] + '/setting_' + algo + '.yaml', 'w') as f:
290 | yaml.dump(conf, f)
291 |
292 | mod = CREP.CRep(N=N, L=L, K=K, **conf)
293 | uf, vf, wf, nuf, maxPSL = mod.fit(data=B, data_T=B_T, data_T_vals=data_T_vals, flag_conv=flag_conv, nodes=nodes)
294 |
295 | return uf, vf, wf, nuf, maxPSL, mod
296 |
297 |
298 | def calculate_opt_func(B, algo_obj=None, mask=None, assortative=False):
299 | """
300 | Compute the optimal value for the pseudo log-likelihood with the inferred parameters.
301 |
302 | Parameters
303 | ----------
304 | B : ndarray
305 | Graph adjacency tensor.
306 | algo_obj : obj
307 | The CRep object.
308 | mask : ndarray
309 | Mask for selecting a subset of the adjacency tensor.
310 | assortative : bool
311 | Flag to use an assortative mode.
312 |
313 | Returns
314 | -------
315 | Maximum pseudo log-likelihood value
316 | """
317 |
318 | B_test = B.copy()
319 | if mask is not None:
320 | B_test[np.logical_not(mask)] = 0.
321 |
322 | if not assortative:
323 | return PSloglikelihood(B, algo_obj.u_f, algo_obj.v_f, algo_obj.w_f, algo_obj.eta_f, mask=mask)
324 | else:
325 | L = B.shape[0]
326 | K = algo_obj.w_f.shape[-1]
327 | w = np.zeros((L, K, K))
328 | for l in range(L):
329 | w1 = np.zeros((K, K))
330 | np.fill_diagonal(w1, algo_obj.w_f[l])
331 | w[l, :, :] = w1.copy()
332 | return PSloglikelihood(B, algo_obj.u_f, algo_obj.v_f, w, algo_obj.eta_f, mask=mask)
333 |
--------------------------------------------------------------------------------
/code/generate_data.py:
--------------------------------------------------------------------------------
1 | """
2 | It generates n synthetic samples of a network having an intrinsic community structure and a given reciprocity value.
3 | It uses the given yaml setting file.
4 | """
5 |
6 | import generative_model_reciprocity as gm
7 | import yaml
8 | import os
9 | from argparse import ArgumentParser
10 | import numpy as np
11 |
12 |
13 | def main_generate_data():
14 |
15 | p = ArgumentParser()
16 | p.add_argument('-s', '--setting', type=str, default='setting_syn_data.yaml') # file with the setting
17 | p.add_argument('-n', '--samples', type=int, default=1) # number of synthetic samples
18 | args = p.parse_args()
19 |
20 | prng = np.random.RandomState(seed=17) # set seed random number generator
21 |
22 | with open(args.setting) as f:
23 | conf = yaml.load(f, Loader=yaml.FullLoader)
24 |
25 | out_folder = conf['out_folder']
26 | if not os.path.exists(out_folder):
27 | os.makedirs(out_folder)
28 |
29 | for sn in range(args.samples):
30 | conf['seed'] += prng.randint(500)
31 | with open(out_folder + 'setting'+str(conf['seed'])+'.yaml', 'w') as f:
32 | yaml.dump(conf, f)
33 | conf['outfile_adj'] = 'syn' + str(conf['seed']) + '.dat'
34 | gen = gm.GM_reciprocity(**conf)
35 | _ = gen.reciprocity_planted_network()
36 |
37 |
38 | if __name__ == '__main__':
39 | main_generate_data()
40 |
--------------------------------------------------------------------------------
/code/generative_model_reciprocity.py:
--------------------------------------------------------------------------------
1 | """
2 | Class definition of the reciprocity generative model with the member functions required.
3 | It builds a directed, possibly weighted, network.
4 | """
5 |
6 | import numpy as np
7 | import networkx as nx
8 | import pandas as pd
9 | import scipy.sparse as sparse
10 | import math
11 | import tools as tl
12 |
13 |
14 | class GM_reciprocity:
15 | def __init__(self, N, K, eta=0.5, k=3, ExpM=None, over=0., corr=0., seed=0, alpha=0.1, ag=0.1, beta=0.1,
16 | Normalization=0, structure='assortative', end_file='', out_folder='../data/output/real_data/cv/',
17 | output_parameters=False, output_adj=False, outfile_adj='None', verbose=False):
18 | self.N = N # number of nodes
19 | self.K = K # number of communities
20 | self.k = k # average degree
21 | self.seed = seed # random seed
22 | self.alpha = alpha # parameter of the Dirichlet distribution
23 | self.ag = ag # alpha parameter of the Gamma distribution
24 | self.beta = beta # beta parameter of the Gamma distribution
25 | self.end_file = end_file # output file suffix
26 | self.out_folder = out_folder # path for storing the output
27 | self.output_parameters = output_parameters # flag for storing the parameters
28 | self.output_adj = output_adj # flag for storing the generated adjacency matrix
29 | self.outfile_adj = outfile_adj # name for saving the adjacency matrix
30 | self.verbose = verbose # flag to print details
31 | if (eta < 0) or (eta >= 1): # reciprocity coefficient
32 | raise ValueError('The reciprocity coefficient eta has to be in [0, 1)!')
33 | self.eta = eta
34 | if ExpM is None: # expected number of edges
35 | self.ExpM = int(self.N * self.k / 2.)
36 | else:
37 | self.ExpM = int(ExpM)
38 | self.k = 2 * self.ExpM / float(self.N)
39 | if (over < 0) or (over > 1): # fraction of nodes with mixed membership
40 | raise ValueError('The over parameter has to be in [0, 1]!')
41 | self.over = over
42 | if (corr < 0) or (corr > 1): # correlation between u and v synthetically generated
43 | raise ValueError('The correlation parameter corr has to be in [0, 1]!')
44 | self.corr = corr
45 | if Normalization not in {0, 1}: # indicator for choosing how to generate the latent variables
46 | raise ValueError('The Normalization parameter can be either 0 or 1! It is used as an indicator for '
47 | 'generating the membership matrices u and v from a Dirichlet or a Gamma distribution, '
48 | 'respectively. It is used when there is overlapping.')
49 | self.Normalization = Normalization
50 | if structure not in {'assortative', 'disassortative'}: # structure of the affinity matrix W
51 | raise ValueError('The structure of the affinity matrix w can be either assortative or disassortative!')
52 | self.structure = structure
53 |
54 | def reciprocity_planted_network(self, parameters=None):
55 | """
56 | Generate a directed, possibly weighted network by using the reciprocity generative model.
57 | Can be used to generate benchmarks for networks with reciprocity.
58 |
59 | Steps:
60 | 1. Generate the latent variables.
61 | 2. Extract A_ij entries (network edges) from a Poisson distribution;
62 | its mean depends on the latent variables.
63 |
64 | Parameters
65 | ----------
66 | parameters: object
67 | Latent variables u, v, w and eta.
68 |
69 | Returns
70 | -------
71 | G: MultiDigraph
72 | MultiDiGraph NetworkX object.
73 | """
74 |
75 | prng = np.random.RandomState(self.seed) # set seed random number generator
76 |
77 | '''
78 | Set latent variables u, v, w
79 | '''
80 |
81 | if parameters is not None:
82 | self.u, self.v, self.w, self.eta = parameters
83 | else:
84 | # equal-size unmixed group membership
85 | size = int(self.N / self.K)
86 | self.u = np.zeros((self.N, self.K))
87 | self.v = np.zeros((self.N, self.K))
88 | for i in range(self.N):
89 | q = int(math.floor(float(i) / float(size)))
90 | if q == self.K:
91 | self.u[i:, self.K - 1] = 1.
92 | self.v[i:, self.K - 1] = 1.
93 | else:
94 | for j in range(q * size, q * size + size):
95 | self.u[j, q] = 1.
96 | self.v[j, q] = 1.
97 | self.w = affinity_matrix(structure=self.structure, N=self.N, K=self.K, a=0.1, b=0.3)
98 |
99 | # in case of overlapping
100 | if self.over != 0.:
101 | overlapping = int(self.N * self.over) # number of nodes belonging to more communities
102 | ind_over = np.random.randint(len(self.u), size=overlapping)
103 | if self.Normalization == 0:
104 | # u and v from a Dirichlet distribution
105 | self.u[ind_over] = prng.dirichlet(self.alpha * np.ones(self.K), overlapping)
106 | self.v[ind_over] = self.corr * self.u[ind_over] + (1. - self.corr) * \
107 | prng.dirichlet(self.alpha * np.ones(self.K), overlapping)
108 | if self.corr == 1.:
109 | assert np.allclose(self.u, self.v)
110 | if self.corr > 0:
111 | self.v = tl.normalize_nonzero_membership(self.v)
112 | elif self.Normalization == 1:
113 | # u and v from a Gamma distribution
114 | self.u[ind_over] = prng.gamma(self.ag, 1. / self.beta, size=(overlapping, self.K))
115 | self.v[ind_over] = self.corr * self.u[ind_over] + (1. - self.corr) * \
116 | prng.gamma(self.ag, 1. / self.beta, size=(overlapping, self.K))
117 | self.u = tl.normalize_nonzero_membership(self.u)
118 | self.v = tl.normalize_nonzero_membership(self.v)
119 |
120 | M0 = Exp_ija_matrix(self.u, self.v, self.w) # whose elements are lambda0_{ij}
121 | np.fill_diagonal(M0, 0)
122 |
123 | c = (self.ExpM * (1. - self.eta)) / M0.sum() # constant to enforce sparsity
124 |
125 | MM = (M0 + self.eta * transpose_ij(M0)) / (1. - self.eta * self.eta) # whose elements are m_{ij}
126 | Mt = transpose_ij(MM)
127 | MM0 = M0.copy() # to be not influenced by c_lambda
128 |
129 | if parameters is None:
130 | self.w *= c # only w is impact by that, u and v have a constraint, their sum over k should sum to 1
131 | M0 *= c
132 | M0t = transpose_ij(M0) # whose elements are lambda0_{ji}
133 |
134 | M = (M0 + self.eta * M0t) / (1. - self.eta * self.eta) # whose elements are m_{ij}
135 | np.fill_diagonal(M, 0)
136 |
137 | rw = self.eta + ((MM0 * Mt + self.eta * Mt ** 2).sum() / MM.sum()) # expected reciprocity
138 |
139 | '''
140 | Generate network G (and adjacency matrix A) using the latent variables,
141 | with the generative model (A_ij,A_ji) ~ P(A_ij|u,v,w,eta) P(A_ji|A_ij,u,v,w,eta)
142 | '''
143 |
144 | G = nx.MultiDiGraph()
145 | for i in range(self.N):
146 | G.add_node(i)
147 |
148 | counter, totM = 0, 0,
149 | for i in range(self.N):
150 | for j in range(i + 1, self.N):
151 | r = prng.rand(1)[0]
152 | if r < 0.5:
153 | A_ij = prng.poisson(M[i, j], 1)[0] # draw A_ij from P(A_ij) = Poisson(m_ij)
154 | if A_ij > 0:
155 | G.add_edge(i, j, weight=A_ij)
156 | lambda_ji = M0[j, i] + self.eta * A_ij
157 | A_ji = prng.poisson(lambda_ji, 1)[0] # draw A_ji from P(A_ji|A_ij) = Poisson(lambda0_ji + eta*A_ij)
158 | if A_ji > 0:
159 | G.add_edge(j, i, weight=A_ji)
160 | else:
161 | A_ji = prng.poisson(M[j, i], 1)[0] # draw A_ij from P(A_ij) = Poisson(m_ij)
162 | if A_ji > 0:
163 | G.add_edge(j, i, weight=A_ji)
164 | lambda_ij = M0[i, j] + self.eta * A_ji
165 | A_ij = prng.poisson(lambda_ij, 1)[0] # draw A_ji from P(A_ji|A_ij) = Poisson(lambda0_ji + eta*A_ij)
166 | if A_ij > 0:
167 | G.add_edge(i, j, weight=A_ij)
168 | counter += 1
169 | totM += A_ij + A_ji
170 |
171 | # keep largest connected component
172 | Gc = max(nx.weakly_connected_components(G), key=len)
173 | nodes_to_remove = set(G.nodes()).difference(Gc)
174 | G.remove_nodes_from(list(nodes_to_remove))
175 |
176 | nodes = list(G.nodes())
177 | self.u = self.u[nodes]
178 | self.v = self.v[nodes]
179 | self.N = len(nodes)
180 |
181 | A = nx.to_scipy_sparse_matrix(G, nodelist=nodes, weight='weight')
182 |
183 | Sparsity_cof = np.round(2 * G.number_of_edges() / float(G.number_of_nodes()), 3)
184 |
185 | ave_w_deg = np.round(2 * totM / float(G.number_of_nodes()), 3)
186 |
187 | reciprocity_c = np.round(tl.reciprocal_edges(G), 3)
188 |
189 | if self.verbose:
190 | print(f'Number of links in the upper triangular matrix: {sparse.triu(A, k=1).nnz}\n'
191 | f'Number of links in the lower triangular matrix: {sparse.tril(A, k=-1).nnz}')
192 | print(f'Sum of weights in the upper triangular matrix: {np.round(sparse.triu(A, k=1).sum(), 2)}\n'
193 | f'Sum of weights in the lower triangular matrix: {np.round(sparse.tril(A, k=-1).sum(), 2)}\n'
194 | f'Number of possible unordered pairs: {counter}')
195 | print(f'Removed {len(nodes_to_remove)} nodes, because not part of the largest connected component')
196 | print(f'Number of nodes: {G.number_of_nodes()} \n'
197 | f'Number of edges: {G.number_of_edges()}')
198 | print(f'Average degree (2E/N): {Sparsity_cof}')
199 | print(f'Average weighted degree (2M/N): {ave_w_deg}')
200 | print(f'Expected reciprocity: {np.round(rw, 3)}')
201 | print(f'Reciprocity (intended as the proportion of bi-directional edges over the unordered pairs): '
202 | f'{reciprocity_c}\n')
203 |
204 | if self.output_parameters:
205 | self.output_results(nodes)
206 |
207 | if self.output_adj:
208 | self.output_adjacency(G, outfile=self.outfile_adj)
209 |
210 | return G
211 |
212 | def planted_network_cond_independent(self, parameters=None):
213 | """
214 | Generate a directed, possibly weighted network without using reciprocity.
215 | It uses conditionally independent A_ij from a Poisson | (u,v,w).
216 |
217 | Parameters
218 | ----------
219 | parameters: object
220 | Latent variables u, v and w.
221 |
222 | Returns
223 | -------
224 | G: MultiDigraph
225 | MultiDiGraph NetworkX object.
226 | """
227 |
228 | prng = np.random.RandomState(self.seed) # set seed random number generator
229 |
230 | '''
231 | Set latent variables u,v,w
232 | '''
233 |
234 | if parameters is not None:
235 | self.u, self.v, self.w = parameters
236 | else:
237 | # equal-size unmixed group membership
238 | size = int(self.N / self.K)
239 | self.u = np.zeros((self.N, self.K))
240 | self.v = np.zeros((self.N, self.K))
241 | for i in range(self.N):
242 | q = int(math.floor(float(i) / float(size)))
243 | if q == self.K:
244 | self.u[i:, self.K - 1] = 1.
245 | self.v[i:, self.K - 1] = 1.
246 | else:
247 | for j in range(q * size, q * size + size):
248 | self.u[j, q] = 1.
249 | self.v[j, q] = 1.
250 | self.w = affinity_matrix(structure=self.structure, N=self.N, K=self.K, a=0.1, b=0.3)
251 |
252 | # in case of overlapping
253 | if self.over != 0.:
254 | overlapping = int(self.N * self.over) # number of nodes belonging to more communities
255 | ind_over = np.random.randint(len(self.u), size=overlapping)
256 | if self.Normalization == 0:
257 | # u and v from a Dirichlet distribution
258 | self.u[ind_over] = prng.dirichlet(self.alpha * np.ones(self.K), overlapping)
259 | self.v[ind_over] = self.corr * self.u[ind_over] + (1. - self.corr) * \
260 | prng.dirichlet(self.alpha * np.ones(self.K), overlapping)
261 | if self.corr == 1.:
262 | assert np.allclose(self.u, self.v)
263 | if self.corr > 0:
264 | self.v = tl.normalize_nonzero_membership(self.v)
265 | elif self.Normalization == 1:
266 | # u and v from a Gamma distribution
267 | self.u[ind_over] = prng.gamma(self.ag, 1. / self.beta, size=(overlapping, self.K))
268 | self.v[ind_over] = self.corr * self.u[ind_over] + (1. - self.corr) * \
269 | prng.gamma(self.ag, 1. / self.beta, size=(overlapping, self.K))
270 | self.u = tl.normalize_nonzero_membership(self.u)
271 | self.v = tl.normalize_nonzero_membership(self.v)
272 |
273 | M0 = Exp_ija_matrix(self.u, self.v, self.w) # whose elements are lambda0_{ij}
274 | np.fill_diagonal(M0, 0)
275 | M0t = transpose_ij(M0) # whose elements are lambda0_{ji}
276 |
277 | rw = (M0 * M0t).sum() / M0.sum() # expected reciprocity
278 |
279 | c = self.ExpM / float(M0.sum()) # constant to enforce sparsity
280 | if parameters is None:
281 | self.w *= c # only w is impact by that, u and v have a constraint, their sum over k should sum to 1
282 |
283 | '''
284 | Generate network G (and adjacency matrix A) using the latent variable,
285 | with the generative model (A_ij) ~ P(A_ij|u,v,w)
286 | '''
287 |
288 | G = nx.MultiDiGraph()
289 | for i in range(self.N):
290 | G.add_node(i)
291 |
292 | totM = 0
293 | for i in range(self.N):
294 | for j in range(self.N):
295 | if i != j: # no self-loops
296 | A_ij = prng.poisson(c * M0[i, j], 1)[0] # draw A_ij from P(A_ij) = Poisson(c*m_ij)
297 | if A_ij > 0:
298 | G.add_edge(i, j, weight=A_ij)
299 | totM += A_ij
300 |
301 | nodes = list(G.nodes())
302 |
303 | # keep largest connected component
304 | Gc = max(nx.weakly_connected_components(G), key=len)
305 | nodes_to_remove = set(G.nodes()).difference(Gc)
306 | G.remove_nodes_from(list(nodes_to_remove))
307 |
308 | nodes = list(G.nodes())
309 | self.u = self.u[nodes]
310 | self.v = self.v[nodes]
311 | self.N = len(nodes)
312 |
313 | A = nx.to_scipy_sparse_matrix(G, nodelist=nodes, weight='weight')
314 |
315 | Sparsity_cof = np.round(2 * G.number_of_edges() / float(G.number_of_nodes()), 3)
316 |
317 | ave_w_deg = np.round(2 * totM / float(G.number_of_nodes()), 3)
318 |
319 | reciprocity_c = np.round(tl.reciprocal_edges(G), 3)
320 |
321 | if self.verbose:
322 | print(f'Number of links in the upper triangular matrix: {sparse.triu(A, k=1).nnz}\n'
323 | f'Number of links in the lower triangular matrix: {sparse.tril(A, k=-1).nnz}')
324 | print(f'Sum of weights in the upper triangular matrix: {np.round(sparse.triu(A, k=1).sum(), 2)}\n'
325 | f'Sum of weights in the lower triangular matrix: {np.round(sparse.tril(A, k=-1).sum(), 2)}')
326 | print(f'Removed {len(nodes_to_remove)} nodes, because not part of the largest connected component')
327 | print(f'Number of nodes: {G.number_of_nodes()} \n'
328 | f'Number of edges: {G.number_of_edges()}')
329 | print(f'Average degree (2E/N): {Sparsity_cof}')
330 | print(f'Average weighted degree (2M/N): {ave_w_deg}')
331 | print(f'Expected reciprocity: {np.round(rw, 3)}')
332 | print(f'Reciprocity (intended as the proportion of bi-directional edges over the unordered pairs): '
333 | f'{reciprocity_c}\n')
334 |
335 | if self.output_parameters:
336 | self.output_results(nodes)
337 |
338 | if self.output_adj:
339 | self.output_adjacency(G, outfile=self.outfile_adj)
340 |
341 | return G
342 |
343 | def planted_network_reciprocity_only(self, p=None):
344 | """
345 | Generate a directed, possibly weighted network using only reciprocity.
346 | One of the directed-edges is generated with probability p, the other with eta*A_ji,
347 | i.e. as in Erdos-Renyi reciprocity.
348 |
349 | Parameters
350 | ----------
351 | p: float
352 | Probability to generate one of the directed-edge.
353 |
354 | Returns
355 | -------
356 | G: MultiDigraph
357 | MultiDiGraph NetworkX object.
358 | """
359 |
360 | prng = np.random.RandomState(self.seed) # set seed random number generator
361 |
362 | if p is None:
363 | p = (1. - self.eta) * self.k * 0.5 / (self.N - 1.)
364 |
365 | '''
366 | Generate network G (and adjacency matrix A)
367 | '''
368 |
369 | G = nx.MultiDiGraph()
370 | for i in range(self.N):
371 | G.add_node(i)
372 |
373 | totM = 0
374 | for i in range(self.N):
375 | for j in range(i + 1, self.N):
376 | A0 = prng.poisson(p, 1)[0]
377 | A1 = prng.poisson(p + A0, 1)[0]
378 | r = prng.rand(1)[0]
379 | if r < 0.5:
380 | if A0 > 0:
381 | G.add_edge(i, j, weight=A0)
382 | if A1 > 0:
383 | G.add_edge(j, i, weight=A1)
384 | else:
385 | if A0 > 0:
386 | G.add_edge(j, i, weight=A0)
387 | if A1 > 0:
388 | G.add_edge(i, j, weight=A1)
389 | totM += A0 + A1
390 |
391 | # keep largest connected component
392 | Gc = max(nx.weakly_connected_components(G), key=len)
393 | nodes_to_remove = set(G.nodes()).difference(Gc)
394 | G.remove_nodes_from(list(nodes_to_remove))
395 |
396 | nodes = list(G.nodes())
397 | self.N = len(nodes)
398 |
399 | A = nx.to_scipy_sparse_matrix(G, nodelist=nodes, weight='weight')
400 |
401 | Sparsity_cof = np.round(2 * G.number_of_edges() / float(G.number_of_nodes()), 3)
402 |
403 | ave_w_deg = np.round(2 * totM / float(G.number_of_nodes()), 3)
404 |
405 | reciprocity_c = np.round(tl.reciprocal_edges(G), 3)
406 |
407 | if self.verbose:
408 | print(f'Number of links in the upper triangular matrix: {sparse.triu(A, k=1).nnz}\n'
409 | f'Number of links in the lower triangular matrix: {sparse.tril(A, k=-1).nnz}')
410 | print(f'Sum of weights in the upper triangular matrix: {np.round(sparse.triu(A, k=1).sum(), 2)}\n'
411 | f'Sum of weights in the lower triangular matrix: {np.round(sparse.tril(A, k=-1).sum(), 2)}')
412 | print(f'Removed {len(nodes_to_remove)} nodes, because not part of the largest connected component')
413 | print(f'Number of nodes: {G.number_of_nodes()} \n'
414 | f'Number of edges: {G.number_of_edges()}')
415 | print(f'Average degree (2E/N): {Sparsity_cof}')
416 | print(f'Average weighted degree (2M/N): {ave_w_deg}')
417 | print(f'Reciprocity (intended as the proportion of bi-directional edges over the unordered pairs): '
418 | f'{reciprocity_c}\n')
419 |
420 | if self.output_adjacency:
421 | self.output_adjacency(G, outfile=self.outfile_adj)
422 |
423 | return G
424 |
425 | def output_results(self, nodes):
426 | """
427 | Output results in a compressed file.
428 |
429 | Parameters
430 | ----------
431 | nodes : list
432 | List of nodes IDs.
433 | """
434 |
435 | output_parameters = self.out_folder + 'theta_gt' + str(self.seed) + self.end_file
436 | np.savez_compressed(output_parameters + '.npz', u=self.u, v=self.v, w=self.w, eta=self.eta, nodes=nodes)
437 | if self.verbose:
438 | print(f'Parameters saved in: {output_parameters}.npz')
439 | print('To load: theta=np.load(filename), then e.g. theta["u"]')
440 |
441 | def output_adjacency(self, G, outfile=None):
442 | """
443 | Output the adjacency matrix. Default format is space-separated .csv with 3 columns:
444 | node1 node2 weight
445 |
446 | Parameters
447 | ----------
448 | G: MultiDigraph
449 | MultiDiGraph NetworkX object.
450 | outfile: str
451 | Name of the adjacency matrix.
452 | """
453 |
454 | if outfile is None:
455 | outfile = 'syn' + str(self.seed) + '_k' + str(int(self.k)) + '.dat'
456 |
457 | edges = list(G.edges(data=True))
458 | try:
459 | data = [[u, v, d['weight']] for u, v, d in edges]
460 | except:
461 | data = [[u, v, 1] for u, v, d in edges]
462 |
463 | df = pd.DataFrame(data, columns=['source', 'target', 'w'], index=None)
464 | df.to_csv(self.out_folder + outfile, index=False, sep=' ')
465 | if self.verbose:
466 | print(f'Adjacency matrix saved in: {self.out_folder + outfile}')
467 |
468 |
469 | def Exp_ija_matrix(u, v, w):
470 | """
471 | Compute the mean lambda0_ij for all entries.
472 |
473 | Parameters
474 | ----------
475 | u : ndarray
476 | Out-going membership matrix.
477 | v : ndarray
478 | In-coming membership matrix.
479 | w : ndarray
480 | Affinity matrix.
481 |
482 | Returns
483 | -------
484 | M : ndarray
485 | Mean lambda0_ij for all entries.
486 | """
487 |
488 | M = np.einsum('ik,jq->ijkq', u, v)
489 | M = np.einsum('ijkq,kq->ij', M, w)
490 |
491 | return M
492 |
493 |
494 | def transpose_ij(M):
495 | """
496 | Compute the transpose of a matrix.
497 |
498 | Parameters
499 | ----------
500 | M : ndarray
501 | Numpy matrix.
502 |
503 | Returns
504 | -------
505 | Transpose of the matrix.
506 | """
507 |
508 | return np.einsum('ij->ji', M)
509 |
510 |
511 | def affinity_matrix(structure='assortative', N=100, K=2, a=0.1, b=0.3):
512 | """
513 | Return the KxK affinity matrix w with probabilities between and within groups.
514 |
515 | Parameters
516 | ----------
517 | structure : string
518 | Structure of the network, e.g. assortative, disassortative.
519 | N : int
520 | Number of nodes.
521 | K : int
522 | Number of communities.
523 | a : float
524 | Parameter for secondary probabilities.
525 | b : float
526 | Parameter for third probabilities.
527 |
528 | Returns
529 | -------
530 | p : ndarray
531 | Array with probabilities between and within groups. Element (k,q) gives the density of edges going from the
532 | nodes of group k to nodes of group q.
533 | """
534 |
535 | b *= a
536 | p1 = K / N
537 | if structure == 'assortative':
538 | p = p1 * a * np.ones((K, K)) # secondary-probabilities
539 | np.fill_diagonal(p, p1 * np.ones(K)) # primary-probabilities
540 |
541 | elif structure == 'disassortative':
542 | p = p1 * np.ones((K, K)) # primary-probabilities
543 | np.fill_diagonal(p, a * p1 * np.ones(K)) # secondary-probabilities
544 |
545 | # print(f'Affinity matrix w: \n{p}')
546 |
547 | return p
548 |
--------------------------------------------------------------------------------
/code/main.py:
--------------------------------------------------------------------------------
1 | """
2 | Performing the inference in the given single-layer directed network.
3 | Implementation of CRep algorithm.
4 | """
5 |
6 | import yaml
7 | import time
8 | import os
9 | import tools as tl
10 | import CRep as CREP
11 | import numpy as np
12 | import sktensor as skt
13 | from argparse import ArgumentParser
14 |
15 |
16 | def main():
17 | p = ArgumentParser()
18 | p.add_argument('-a', '--algorithm', type=str, choices=['Crep', 'Crepnc', 'Crep0'], default='CRep') # configuration
19 | p.add_argument('-K', '--K', type=int, default=3) # number of communities
20 | p.add_argument('-A', '--adj', type=str, default='syn111.dat') # name of the network
21 | p.add_argument('-f', '--in_folder', type=str, default='../data/input/') # path of the input network
22 | p.add_argument('-e', '--ego', type=str, default='source') # name of the source of the edge
23 | p.add_argument('-t', '--alter', type=str, default='target') # name of the target of the edge
24 | p.add_argument('-d', '--force_dense', type=bool, default=False) # flag to force a dense transformation in input
25 | p.add_argument('-F', '--flag_conv', type=str, choices=['log', 'deltas'], default='log') # flag for convergence
26 | args = p.parse_args()
27 |
28 | # setting to run the algorithm
29 | with open('setting_' + args.algorithm + '.yaml') as f:
30 | conf = yaml.load(f, Loader=yaml.FullLoader)
31 | if not os.path.exists(conf['out_folder']):
32 | os.makedirs(conf['out_folder'])
33 | with open(conf['out_folder'] + '/setting_' + args.algorithm + '.yaml', 'w') as f:
34 | yaml.dump(conf, f)
35 |
36 | '''
37 | Import data
38 | '''
39 | network = args.in_folder + args.adj # network complete path
40 | A, B, B_T, data_T_vals = tl.import_data(network, ego=args.ego, alter=args.alter,
41 | force_dense=args.force_dense, header=0)
42 | nodes = A[0].nodes()
43 |
44 | valid_types = [np.ndarray, skt.dtensor, skt.sptensor]
45 | assert any(isinstance(B, vt) for vt in valid_types)
46 |
47 | '''
48 | Run CRep
49 | '''
50 | print(f'\n### Run {args.algorithm} ###')
51 |
52 | time_start = time.time()
53 | model = CREP.CRep(N=A[0].number_of_nodes(), L=len(A), K=args.K, **conf)
54 | _ = model.fit(data=B, data_T=B_T, data_T_vals=data_T_vals, flag_conv=args.flag_conv, nodes=nodes)
55 |
56 | print(f'\nTime elapsed: {np.round(time.time() - time_start, 2)} seconds.')
57 |
58 |
59 | if __name__ == '__main__':
60 | main()
61 |
--------------------------------------------------------------------------------
/code/main_cv.py:
--------------------------------------------------------------------------------
1 | """
2 | Main function to implement cross-validation given a number of communities.
3 |
4 | - Hold-out part of the dataset (pairs of edges labeled by unordered pairs (i,j));
5 | - Infer parameters on the training set;
6 | - Calculate performance measures in the test set (AUC).
7 | """
8 |
9 | # TODO: optimize for big matrices (so when the input would be done with force_dense=False)
10 |
11 | import csv
12 | import os
13 | import pickle
14 | from argparse import ArgumentParser
15 | import cv_functions as cvfun
16 | import numpy as np
17 | import tools as tl
18 | import yaml
19 | import sktensor as skt
20 | import time
21 |
22 |
23 | def main():
24 | p = ArgumentParser()
25 | p.add_argument('-a', '--algorithm', type=str, choices=['Crep', 'Crepnc', 'Crep0'], default='CRep') # configuration
26 | p.add_argument('-K', '--K', type=int, default=3) # number of communities
27 | p.add_argument('-A', '--adj', type=str, default='syn111.dat') # name of the network
28 | p.add_argument('-f', '--in_folder', type=str, default='../data/input/') # path of the input network
29 | p.add_argument('-o', '--out_folder', type=str, default='../data/output/5-fold_cv/') # path to store outputs
30 | p.add_argument('-e', '--ego', type=str, default='source') # name of the source of the edge
31 | p.add_argument('-t', '--alter', type=str, default='target') # name of the target of the edge
32 | # p.add_argument('-d', '--force_dense', type=bool, default=True) # flag to force a dense transformation in input
33 | p.add_argument('-F', '--flag_conv', type=str, choices=['log', 'deltas'], default='log') # flag for convergence
34 | p.add_argument('-N', '--NFold', type=int, default=5) # number of fold to perform cross-validation
35 | p.add_argument('-m', '--out_mask', type=bool, default=False) # flag to output the masks
36 | p.add_argument('-r', '--out_results', type=bool, default=True) # flag to output the results in a csv file
37 | p.add_argument('-i', '--out_inference', type=bool, default=True) # flag to output the inferred parameters
38 | args = p.parse_args()
39 |
40 | prng = np.random.RandomState(seed=17) # set seed random number generator
41 |
42 | '''
43 | Cross validation parameters and set up output directory
44 | '''
45 | NFold = args.NFold
46 | out_mask = args.out_mask
47 | out_results = args.out_results
48 |
49 | out_folder = args.out_folder
50 | if not os.path.exists(out_folder):
51 | os.makedirs(out_folder)
52 |
53 | '''
54 | Model parameters
55 | '''
56 | K = args.K
57 | network = args.in_folder + args.adj # network complete path
58 | algorithm = args.algorithm # algorithm to use to generate the samples
59 | adjacency = args.adj.split('.dat')[0] # name of the network without extension
60 | with open('setting_' + algorithm + '.yaml') as f:
61 | conf = yaml.load(f, Loader=yaml.FullLoader)
62 | conf['out_folder'] = out_folder
63 | conf['out_inference'] = args.out_inference
64 |
65 | '''
66 | Import data
67 | '''
68 | A, B, B_T, data_T_vals = tl.import_data(network, ego=args.ego, alter=args.alter, force_dense=True, header=0)
69 | nodes = A[0].nodes()
70 | valid_types = [np.ndarray, skt.dtensor, skt.sptensor]
71 | assert any(isinstance(B, vt) for vt in valid_types)
72 |
73 | print('\n### CV procedure ###')
74 | comparison = [0 for _ in range(11)]
75 | comparison[0] = K
76 |
77 | # save the results
78 | if out_results:
79 | out_file = out_folder + adjacency + '_cv.csv'
80 | if not os.path.isfile(out_file): # write header
81 | with open(out_file, 'w') as outfile:
82 | wrtr = csv.writer(outfile, delimiter=',', quotechar='"')
83 | wrtr.writerow(['K', 'fold', 'rseed', 'eta', 'auc_train', 'auc_test', 'auc_cond_train', 'auc_cond_test',
84 | 'opt_func_train', 'opt_func_test', 'max_it'])
85 | outfile = open(out_file, 'a')
86 | wrtr = csv.writer(outfile, delimiter=',', quotechar='"')
87 | print(f'Results will be saved in: {out_file}')
88 |
89 | time_start = time.time()
90 | L = B.shape[0]
91 | N = B.shape[-1]
92 |
93 | rseed = prng.randint(1000)
94 | indices = cvfun.shuffle_indices_all_matrix(N, L, rseed=rseed)
95 | init_end_file = conf['end_file']
96 |
97 | for fold in range(NFold):
98 | print('\nFOLD ', fold)
99 | comparison[1], comparison[2] = fold, rseed
100 |
101 | mask = cvfun.extract_mask_kfold(indices, N, fold=fold, NFold=NFold)
102 | if out_mask:
103 | outmask = out_folder + 'mask_f' + str(fold) + '_' + adjacency + '.pkl'
104 | print(f'Mask saved in: {outmask}')
105 | with open(outmask, 'wb') as f:
106 | pickle.dump(np.where(mask > 0), f)
107 |
108 | '''
109 | Set up training dataset
110 | '''
111 | B_train = B.copy()
112 | B_train[mask > 0] = 0
113 |
114 | '''
115 | Run CRep on the training
116 | '''
117 | tic = time.time()
118 | conf['end_file'] = init_end_file + '_' + str(fold) + 'K' + str(K)
119 | u, v, w, eta, maxPSL, algo_obj = cvfun.fit_model(B_train, B_T, data_T_vals, nodes=nodes, N=N, L=L, K=K,
120 | algo=algorithm, flag_conv=args.flag_conv, **conf)
121 |
122 | '''
123 | Output performance results
124 | '''
125 | comparison[3] = eta
126 | M = cvfun.calculate_expectation(u, v, w, eta=eta)
127 | comparison[4] = cvfun.calculate_AUC(M, B, mask=np.logical_not(mask))
128 | comparison[5] = cvfun.calculate_AUC(M, B, mask=mask)
129 | M_cond = cvfun.calculate_conditional_expectation(B, u, v, w, eta=eta)
130 | comparison[6] = cvfun.calculate_AUC(M_cond, B, mask=np.logical_not(mask))
131 | comparison[7] = cvfun.calculate_AUC(M_cond, B, mask=mask)
132 | comparison[9] = cvfun.calculate_opt_func(B, algo_obj, mask=mask, assortative=conf['assortative'])
133 | comparison[8] = maxPSL
134 | comparison[10] = algo_obj.final_it
135 |
136 | print(f'Time elapsed: {np.round(time.time() - tic, 2)} seconds.')
137 |
138 | if out_results:
139 | wrtr.writerow(comparison)
140 | outfile.flush()
141 |
142 | if out_results:
143 | outfile.close()
144 |
145 | print(f'\nTime elapsed: {np.round(time.time() - time_start, 2)} seconds.')
146 |
147 |
148 | if __name__ == '__main__':
149 | main()
150 |
--------------------------------------------------------------------------------
/code/setting_CRep.yaml:
--------------------------------------------------------------------------------
1 | N_real: 5
2 | tolerance: 0.0001
3 | decision: 10
4 | max_iter: 1000
5 | rseed: 0
6 | inf: 10000000000.0
7 | err_max: 0.000000000001
8 | err: 0.1
9 | initialization: 0
10 | undirected: False
11 | verbose: False
12 | out_inference: True
13 | out_folder: "../data/output/"
14 | end_file: "_CRep"
15 | assortative: True
16 | eta0: null
17 | fix_eta: False
18 | constrained: True
19 | files: '../data/input/theta_gt111.npz'
20 |
--------------------------------------------------------------------------------
/code/setting_CRep0.yaml:
--------------------------------------------------------------------------------
1 | N_real: 5
2 | tolerance: 0.0001
3 | decision: 10
4 | max_iter: 1000
5 | rseed: 0
6 | inf: 10000000000.0
7 | err_max: 0.000000000001
8 | err: 0.1
9 | initialization: 0
10 | undirected: False
11 | verbose: False
12 | out_inference: True
13 | out_folder: "../data/output/"
14 | end_file: "_CRep0"
15 | assortative: True
16 | eta0: 0
17 | fix_eta: True
18 | constrained: True
19 | files: '../data/input/synthetic/theta.npz'
20 |
--------------------------------------------------------------------------------
/code/setting_CRepnc.yaml:
--------------------------------------------------------------------------------
1 | N_real: 5
2 | tolerance: 0.0001
3 | decision: 10
4 | max_iter: 1000
5 | rseed: 0
6 | inf: 10000000000.0
7 | err_max: 0.000000000001
8 | err: 0.1
9 | initialization: 0
10 | undirected: False
11 | verbose: False
12 | out_inference: True
13 | out_folder: "../data/output/"
14 | end_file: "_CRepnc"
15 | assortative: True
16 | eta0: null
17 | fix_eta: False
18 | constrained: False
19 | files: '../data/input/synthetic/theta.npz'
20 |
--------------------------------------------------------------------------------
/code/setting_syn_data.yaml:
--------------------------------------------------------------------------------
1 | N: 600
2 | K: 3
3 | eta: 0.5
4 | k: 20
5 | ExpM: null
6 | over: 0.
7 | corr: 0.
8 | seed: 0
9 | alpha: 0.1
10 | ag: 0.1
11 | beta: 0.1
12 | Normalization: 0
13 | structure: "assortative"
14 | end_file: ""
15 | out_folder: '../data/input/'
16 | output_parameters: True
17 | output_adj: True
18 | outfile_adj: null
19 | verbose: True
--------------------------------------------------------------------------------
/code/test.py:
--------------------------------------------------------------------------------
1 | import unittest
2 | import numpy as np
3 | import CRep as CREP
4 | import yaml
5 | import tools as tl
6 |
7 |
8 | class Test(unittest.TestCase):
9 | """
10 | The basic class that inherits unittest.TestCase
11 | """
12 | algorithm = 'CRep'
13 | K = 3
14 | in_folder = '../data/input/'
15 | out_folder = '../data/output/'
16 | end_file = '_test'
17 | adj = 'syn111.dat'
18 | ego = 'source'
19 | alter = 'target'
20 | force_dense = False
21 | flag_conv = 'log'
22 |
23 | '''
24 | Import data
25 | '''
26 | network = in_folder + adj # network complete path
27 | A, B, B_T, data_T_vals = tl.import_data(network, ego=ego, alter=alter, force_dense=force_dense, header=0)
28 | nodes = A[0].nodes()
29 |
30 | '''
31 | Setting to run the algorithm
32 | '''
33 | with open('setting_' + algorithm + '.yaml') as f:
34 | conf = yaml.load(f, Loader=yaml.FullLoader)
35 | conf['end_file'] = end_file
36 |
37 | model = CREP.CRep(N=A[0].number_of_nodes(), L=len(A), K=K, **conf)
38 |
39 | # test case function to check the crep.set_name function
40 | def test_import_data(self):
41 | print("Start import data test\n")
42 | if self.force_dense:
43 | self.assertTrue(self.B.sum() > 0)
44 | print('B has ', self.B.sum(), ' total weight.')
45 | else:
46 | self.assertTrue(self.B.vals.sum() > 0)
47 | print('B has ', self.B.vals.sum(), ' total weight.')
48 |
49 | # test case function to check the Person.get_name function
50 | def test_running_algorithm(self):
51 | print("\nStart running algorithm test\n")
52 |
53 | _ = self.model.fit(data=self.B, data_T=self.B_T, data_T_vals=self.data_T_vals, flag_conv=self.flag_conv,
54 | nodes=self.nodes)
55 |
56 | theta = np.load(self.model.out_folder+'theta'+self.model.end_file+'.npz')
57 | thetaGT = np.load(self.model.out_folder+'theta_'+self.algorithm+'.npz')
58 |
59 | print(np.where(thetaGT['u'] != theta['u']))
60 |
61 | self.assertTrue(np.array_equal(self.model.u_f, theta['u']))
62 | self.assertTrue(np.array_equal(self.model.v_f, theta['v']))
63 | self.assertTrue(np.array_equal(self.model.w_f, theta['w']))
64 | self.assertTrue(np.array_equal(self.model.eta_f, theta['eta']))
65 |
66 | self.assertTrue(np.array_equal(thetaGT['u'], theta['u']))
67 | self.assertTrue(np.array_equal(thetaGT['v'], theta['v']))
68 | self.assertTrue(np.array_equal(thetaGT['w'], theta['w']))
69 | self.assertTrue(np.array_equal(thetaGT['eta'], theta['eta']))
70 |
71 |
72 | if __name__ == '__main__':
73 | # begin the unittest.main()
74 | unittest.main()
75 |
--------------------------------------------------------------------------------
/code/test_cv.py:
--------------------------------------------------------------------------------
1 | import unittest
2 | import numpy as np
3 | import tools as tl
4 | import cv_functions as cvfun
5 | import yaml
6 |
7 |
8 | class Test(unittest.TestCase):
9 | """
10 | The basic class that inherits unittest.TestCase
11 | """
12 | algorithm = 'CRep'
13 | K = 3
14 | in_folder = '../data/input/'
15 | out_folder = '../data/output/5-fold_cv/'
16 | end_file = '_test'
17 | adj = 'syn111.dat'
18 | ego = 'source'
19 | alter = 'target'
20 | # force_dense = True
21 | flag_conv = 'log'
22 | NFold = 5
23 | out_mask = False
24 | out_results = True
25 | out_inference = True
26 |
27 | prng = np.random.RandomState(seed=17) # set seed random number generator
28 | rseed = prng.randint(1000)
29 |
30 | '''
31 | Setting to run the algorithm
32 | '''
33 | with open('setting_' + algorithm + '.yaml') as f:
34 | conf = yaml.load(f, Loader=yaml.FullLoader)
35 | conf['out_folder'] = out_folder
36 |
37 | '''
38 | Import data
39 | '''
40 | network = in_folder + adj # network complete path
41 | A, B, B_T, data_T_vals = tl.import_data(network, ego=ego, alter=alter, force_dense=True, header=0)
42 | nodes = A[0].nodes()
43 |
44 | def test_running_algorithm(self):
45 | print("\nStart running algorithm test\n")
46 |
47 | L = self.B.shape[0]
48 | N = self.B.shape[1]
49 |
50 | indices = cvfun.shuffle_indices_all_matrix(N, L, rseed=self.rseed)
51 |
52 | for fold in range(self.NFold):
53 | mask = cvfun.extract_mask_kfold(indices, N, fold=fold, NFold=self.NFold)
54 |
55 | '''
56 | Set up training dataset
57 | '''
58 | B_train = self.B.copy()
59 | print(B_train.shape, mask.shape)
60 | B_train[mask > 0] = 0
61 |
62 | self.conf['end_file'] = '_' + str(fold) + 'K' + str(self.K) + self.end_file
63 | u, v, w, eta, maxPSL, algo_obj = cvfun.fit_model(B_train, self.B_T, self.data_T_vals, nodes=self.nodes,
64 | N=N, L=L, K=self.K, algo=self.algorithm,
65 | flag_conv=self.flag_conv, **self.conf)
66 |
67 | '''
68 | Load parameters
69 | '''
70 | theta = np.load(self.out_folder+'theta_'+str(fold)+'K'+str(self.K)+self.end_file+'.npz')
71 | thetaGT = np.load(self.out_folder+'theta_'+str(self.algorithm)+'_'+str(fold)+'K'+str(self.K)+'.npz')
72 |
73 | self.assertTrue(np.array_equal(u, theta['u']))
74 | self.assertTrue(np.array_equal(v, theta['v']))
75 | self.assertTrue(np.array_equal(w, theta['w']))
76 | self.assertTrue(np.array_equal(algo_obj.eta_f, theta['eta']))
77 |
78 | self.assertTrue(np.array_equal(thetaGT['u'], theta['u']))
79 | self.assertTrue(np.array_equal(thetaGT['v'], theta['v']))
80 | self.assertTrue(np.array_equal(thetaGT['w'], theta['w']))
81 | self.assertTrue(np.array_equal(thetaGT['eta'], theta['eta']))
82 |
83 |
84 | if __name__ == '__main__':
85 | # begin the unittest.main()
86 | unittest.main()
87 |
--------------------------------------------------------------------------------
/code/tools.py:
--------------------------------------------------------------------------------
1 | """
2 | Functions for handling the data.
3 | """
4 |
5 | import networkx as nx
6 | import numpy as np
7 | import pandas as pd
8 | import sktensor as skt
9 |
10 |
11 | def import_data(dataset, ego='source', alter='target', force_dense=True, header=None):
12 | """
13 | Import data, i.e. the adjacency matrix, from a given folder.
14 |
15 | Return the NetworkX graph and its numpy adjacency matrix.
16 |
17 | Parameters
18 | ----------
19 | dataset : str
20 | Path of the input file.
21 | ego : str
22 | Name of the column to consider as source of the edge.
23 | alter : str
24 | Name of the column to consider as target of the edge.
25 | force_dense : bool
26 | If set to True, the algorithm is forced to consider a dense adjacency tensor.
27 | header : int
28 | Row number to use as the column names, and the start of the data.
29 |
30 | Returns
31 | -------
32 | A : list
33 | List of MultiDiGraph NetworkX objects.
34 | B : ndarray/sptensor
35 | Graph adjacency tensor.
36 | B_T : None/sptensor
37 | Graph adjacency tensor (transpose).
38 | data_T_vals : None/ndarray
39 | Array with values of entries A[j, i] given non-zero entry (i, j).
40 | """
41 |
42 | # read adjacency file
43 | df_adj = pd.read_csv(dataset, sep='\s+', header=header)
44 | print('{0} shape: {1}'.format(dataset, df_adj.shape))
45 |
46 | A = read_graph(df_adj=df_adj, ego=ego, alter=alter, noselfloop=True)
47 |
48 | nodes = list(A[0].nodes())
49 |
50 | # save the network in a tensor
51 | if force_dense:
52 | B, rw = build_B_from_A(A, nodes=nodes)
53 | B_T, data_T_vals = None, None
54 | else:
55 | B, B_T, data_T_vals, rw = build_sparse_B_from_A(A)
56 |
57 | print_graph_stat(A, rw)
58 |
59 | return A, B, B_T, data_T_vals
60 |
61 |
62 | def read_graph(df_adj, ego='source', alter='target', noselfloop=True):
63 | """
64 | Create the graph by adding edges and nodes.
65 | It assumes that columns of layers are from l+2 (included) onwards.
66 |
67 | Return the list MultiDiGraph NetworkX objects.
68 |
69 | Parameters
70 | ----------
71 | df_adj : DataFrame
72 | Pandas DataFrame object containing the edges of the graph.
73 | ego : str
74 | Name of the column to consider as source of the edge.
75 | alter : str
76 | Name of the column to consider as target of the edge.
77 | noselfloop : bool
78 | If set to True, the algorithm removes the self-loops.
79 |
80 | Returns
81 | -------
82 | A : list
83 | List of MultiDiGraph NetworkX objects.
84 | """
85 |
86 | # build nodes
87 | egoID = df_adj[ego].unique()
88 | alterID = df_adj[alter].unique()
89 | nodes = list(set(egoID).union(set(alterID)))
90 | nodes.sort()
91 |
92 | L = df_adj.shape[1] - 2 # number of layers
93 | # build the NetworkX graph: create a list of graphs, as many graphs as there are layers
94 | A = [nx.MultiDiGraph() for _ in range(L)]
95 | # set the same set of nodes and order over all layers
96 | for l in range(L):
97 | A[l].add_nodes_from(nodes)
98 |
99 | for index, row in df_adj.iterrows():
100 | v1 = row[ego]
101 | v2 = row[alter]
102 | for l in range(L):
103 | if row[l + 2] > 0:
104 | if A[l].has_edge(v1, v2):
105 | A[l][v1][v2][0]['weight'] += int(row[l + 2]) # the edge already exists -> no parallel edge created
106 | else:
107 | A[l].add_edge(v1, v2, weight=int(row[l + 2]))
108 |
109 | # remove self-loops
110 | if noselfloop:
111 | print('Removing self loops')
112 | for l in range(L):
113 | A[l].remove_edges_from(list(nx.selfloop_edges(A[l])))
114 |
115 | return A
116 |
117 |
118 | def print_graph_stat(A, rw):
119 | """
120 | Print the statistics of the graph A.
121 |
122 | Parameters
123 | ----------
124 | A : list
125 | List of MultiDiGraph NetworkX objects.
126 | rw : list
127 | List whose elements are reciprocity (considering the weights of the edges) values, one per each layer.
128 | """
129 |
130 | L = len(A)
131 | N = A[0].number_of_nodes()
132 | print('Number of nodes =', N)
133 | print('Number of layers =', L)
134 |
135 | print('Number of edges and average degree in each layer:')
136 | for l in range(L):
137 | E = A[l].number_of_edges()
138 | k = 2 * float(E) / float(N)
139 | M = np.sum([d['weight'] for u, v, d in list(A[l].edges(data=True))])
140 | kW = 2 * float(M) / float(N)
141 |
142 | print(f'E[{l}] = {E} - = {np.round(k, 3)}')
143 | print(f'M[{l}] = {M} - = {np.round(kW, 3)}')
144 | print(f'Reciprocity (networkX) = {np.round(nx.reciprocity(A[l]), 3)}')
145 | print(f'Reciprocity (intended as the proportion of bi-directional edges over the unordered pairs) = '
146 | f'{np.round(reciprocal_edges(A[l]), 3)}')
147 | print(f'Reciprocity (considering the weights of the edges) = {np.round(rw[l], 3)}')
148 |
149 |
150 | def build_B_from_A(A, nodes=None):
151 | """
152 | Create the numpy adjacency tensor of a networkX graph.
153 |
154 | Parameters
155 | ----------
156 | A : list
157 | List of MultiDiGraph NetworkX objects.
158 | nodes : list
159 | List of nodes IDs.
160 |
161 | Returns
162 | -------
163 | B : ndarray
164 | Graph adjacency tensor.
165 | rw : list
166 | List whose elements are reciprocity (considering the weights of the edges) values, one per each layer.
167 | """
168 |
169 | N = A[0].number_of_nodes()
170 | if nodes is None:
171 | nodes = list(A[0].nodes())
172 | B = np.empty(shape=[len(A), N, N])
173 | rw = []
174 | for l in range(len(A)):
175 | B[l, :, :] = nx.to_numpy_array(A[l], weight='weight', dtype=int, nodelist=nodes)
176 | rw.append(np.multiply(B[l], B[l].T).sum() / B[l].sum())
177 |
178 | return B, rw
179 |
180 |
181 | def build_sparse_B_from_A(A):
182 | """
183 | Create the sptensor adjacency tensor of a networkX graph.
184 |
185 | Parameters
186 | ----------
187 | A : list
188 | List of MultiDiGraph NetworkX objects.
189 |
190 | Returns
191 | -------
192 | data : sptensor
193 | Graph adjacency tensor.
194 | data_T : sptensor
195 | Graph adjacency tensor (transpose).
196 | v_T : ndarray
197 | Array with values of entries A[j, i] given non-zero entry (i, j).
198 | rw : list
199 | List whose elements are reciprocity (considering the weights of the edges) values, one per each layer.
200 | """
201 |
202 | N = A[0].number_of_nodes()
203 | L = len(A)
204 | rw = []
205 |
206 | d1 = np.array((), dtype='int64')
207 | d2, d2_T = np.array((), dtype='int64'), np.array((), dtype='int64')
208 | d3, d3_T = np.array((), dtype='int64'), np.array((), dtype='int64')
209 | v, vT, v_T = np.array(()), np.array(()), np.array(())
210 | for l in range(L):
211 | b = nx.to_scipy_sparse_array(A[l])
212 | b_T = nx.to_scipy_sparse_array(A[l]).transpose()
213 | rw.append(np.sum(b.multiply(b_T))/np.sum(b))
214 | nz = b.nonzero()
215 | nz_T = b_T.nonzero()
216 | d1 = np.hstack((d1, np.array([l] * len(nz[0]))))
217 | d2 = np.hstack((d2, nz[0]))
218 | d2_T = np.hstack((d2_T, nz_T[0]))
219 | d3 = np.hstack((d3, nz[1]))
220 | d3_T = np.hstack((d3_T, nz_T[1]))
221 | v = np.hstack((v, np.array([b[i, j] for i, j in zip(*nz)])))
222 | vT = np.hstack((vT, np.array([b_T[i, j] for i, j in zip(*nz_T)])))
223 | v_T = np.hstack((v_T, np.array([b[j, i] for i, j in zip(*nz)])))
224 | subs_ = (d1, d2, d3)
225 | subs_T_ = (d1, d2_T, d3_T)
226 | data = skt.sptensor(subs_, v, shape=(L, N, N), dtype=v.dtype)
227 | data_T = skt.sptensor(subs_T_, vT, shape=(L, N, N), dtype=vT.dtype)
228 |
229 | return data, data_T, v_T, rw
230 |
231 |
232 | def reciprocal_edges(G):
233 | """
234 | Compute the proportion of bi-directional edges, by considering the unordered pairs.
235 |
236 | Parameters
237 | ----------
238 | G: MultiDigraph
239 | MultiDiGraph NetworkX object.
240 |
241 | Returns
242 | -------
243 | reciprocity: float
244 | Reciprocity value, intended as the proportion of bi-directional edges over the unordered pairs.
245 | """
246 |
247 | n_all_edge = G.number_of_edges()
248 | n_undirected = G.to_undirected().number_of_edges() # unique pairs of edges, i.e. edges in the undirected graph
249 | n_overlap_edge = (n_all_edge - n_undirected) # number of undirected edges reciprocated in the directed network
250 |
251 | if n_all_edge == 0:
252 | raise nx.NetworkXError("Not defined for empty graphs.")
253 |
254 | reciprocity = float(n_overlap_edge) / float(n_undirected)
255 |
256 | return reciprocity
257 |
258 |
259 | def can_cast(string):
260 | """
261 | Verify if one object can be converted to integer object.
262 |
263 | Parameters
264 | ----------
265 | string : int or float or str
266 | Name of the node.
267 |
268 | Returns
269 | -------
270 | bool : bool
271 | If True, the input can be converted to integer object.
272 | """
273 |
274 | try:
275 | int(string)
276 | return True
277 | except ValueError:
278 | return False
279 |
280 |
281 | def normalize_nonzero_membership(u):
282 | """
283 | Given a matrix, it returns the same matrix normalized by row.
284 |
285 | Parameters
286 | ----------
287 | u: ndarray
288 | Numpy Matrix.
289 |
290 | Returns
291 | -------
292 | The matrix normalized by row.
293 | """
294 |
295 | den1 = u.sum(axis=1, keepdims=True)
296 | nzz = den1 == 0.
297 | den1[nzz] = 1.
298 |
299 | return u / den1
300 |
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/data/input/setting111.yaml:
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1 | ExpM: null
2 | K: 3
3 | N: 600
4 | Normalization: 0
5 | ag: 0.1
6 | alpha: 0.1
7 | beta: 0.1
8 | corr: 0.0
9 | end_file: ''
10 | eta: 0.5
11 | k: 20
12 | out_folder: ../data/input/
13 | outfile_adj: null
14 | output_adj: true
15 | output_parameters: true
16 | over: 0.0
17 | seed: 111
18 | structure: assortative
19 | verbose: true
20 |
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/data/output/5-fold_cv/setting_CRep.yaml:
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1 | N_real: 5
2 | assortative: true
3 | constrained: true
4 | decision: 10
5 | end_file: _4K3_test
6 | err: 0.1
7 | err_max: 1.0e-12
8 | eta0: null
9 | files: ../data/input/theta_gt111.npz
10 | fix_eta: false
11 | inf: 10000000000.0
12 | initialization: 0
13 | max_iter: 1000
14 | out_folder: ../data/output/5-fold_cv/
15 | out_inference: true
16 | rseed: 0
17 | tolerance: 0.0001
18 | undirected: false
19 | verbose: false
20 |
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/data/output/5-fold_cv/syn111_cv.csv:
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1 | K,fold,rseed,eta,auc_train,auc_test,auc_cond_train,auc_cond_test,opt_func_train,opt_func_test,max_it
2 | 3,0,623,0.34450780895354066,0.7357956061904156,0.6431951069025217,0.8644220192265917,0.7730123610462685,-18834.94381488201,-3438.707471119684,1000
3 | 3,1,623,0.34969550348108364,0.706802046864056,0.6064551644130902,0.8603468628767448,0.7346084232804233,-18875.0841499074,-3450.015939354893,651
4 | 3,2,623,0.3599626759523616,0.7060443755969068,0.5882220201581183,0.8601274876998479,0.7160829809919951,-18777.639870169412,-3480.266685876016,471
5 | 3,3,623,0.3563177533646485,0.7075971592020338,0.5894315176609548,0.860625257711535,0.732398520174079,-18725.337471532228,-3544.56033815658,521
6 | 3,4,623,0.35199272216813915,0.731800436164251,0.6443309676975304,0.8652655318514253,0.7729335828495194,-19055.316878897367,-3327.6275534005563,1000
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/data/output/setting_CRep.yaml:
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1 | N_real: 5
2 | assortative: true
3 | constrained: true
4 | decision: 10
5 | end_file: _CRep
6 | err: 0.1
7 | err_max: 1.0e-12
8 | eta0: null
9 | files: ../data/input/theta_gt111.npz
10 | fix_eta: false
11 | inf: 10000000000.0
12 | initialization: 0
13 | max_iter: 1000
14 | out_folder: ../data/output/
15 | out_inference: true
16 | rseed: 0
17 | tolerance: 0.0001
18 | undirected: false
19 | verbose: false
20 |
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/requirements.txt:
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1 | numpy==1.22.0
2 | pandas
3 | scikit-learn
4 | scikit-tensor-py3
5 | scipy==1.10.0
6 | networkx
7 | argparse
8 | termcolor
9 | pyyaml
10 | pytest
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