├── TwoNN
    ├── __init__.py
    └── twonn_dimension.py
├── README.md
└── LICENSE


/TwoNN/__init__.py:
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1 | from TwoNN.twonn_dimension import twonn_dimension


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/README.md:
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 1 | # TWO-NN
 2 | 
 3 | Naive Python 3 implementation of TWO-NN algorithm for intrinsic dimension inference.
 4 | 
 5 | Dependencies
 6 | ---
 7 | * Python >= 3.6
 8 | * Numpy >= 1.17
 9 | 
10 | Usage
11 | ---
12 | ```python
13 | import numpy as np
14 | from TwoNN import twonn_dimension
15 | 
16 | #mock dataset - 1000 samples with 500 features
17 | data = np.random.uniform(0,1,size=(1000,500))
18 | 
19 | #calculate intrinsic dimension d
20 | d = twonn_dimension(data)
21 | ```
22 | 
23 | References
24 | ---
25 | E. Facco, M. d’Errico, A. Rodriguez & A. Laio, Estimating the intrinsic dimension of datasets by a minimal neighborhood information, *Scientific Reports*, 2017
26 | 
27 | (https://doi.org/10.1038/s41598-017-11873-y)
28 |     
29 | 


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/LICENSE:
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 1 | MIT License
 2 | 
 3 | Copyright (c) 2019 fmottes
 4 | 
 5 | Permission is hereby granted, free of charge, to any person obtaining a copy
 6 | of this software and associated documentation files (the "Software"), to deal
 7 | in the Software without restriction, including without limitation the rights
 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 | 
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 | 
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 | 


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/TwoNN/twonn_dimension.py:
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 1 | #Author: Francesco Mottes
 2 | #Date  : 15-Oct-2019
 3 | #-----------------------------
 4 | 
 5 | 
 6 | import numpy as np
 7 | 
 8 | 
 9 | def twonn_dimension(data, return_xy=False):
10 |     """
11 |     Calculates intrinsic dimension of the provided data points with the TWO-NN algorithm.
12 |     
13 |     -----------
14 |     Parameters:
15 |     
16 |     data : 2d array-like
17 |         2d data matrix. Samples on rows and features on columns.
18 | 
19 |     return_xy : bool (default=False)
20 |         Whether to return also the coordinate vectors used for the linear fit.
21 |         
22 |     -----------
23 |     Returns:
24 |     
25 |     d : int
26 |         Intrinsic dimension of the dataset according to TWO-NN.
27 | 
28 |     x : 1d array (optional)
29 |         Array with the -log(mu) values.
30 | 
31 |     y : 1d array (optional)
32 |         Array with the -log(F(mu_{sigma(i)})) values.
33 |         
34 |     -----------
35 |     References:
36 |     
37 |     [1] E. Facco, M. d’Errico, A. Rodriguez & A. Laio
38 |         Estimating the intrinsic dimension of datasets by a minimal neighborhood information (https://doi.org/10.1038/s41598-017-11873-y)
39 |     
40 |     
41 |     """
42 |     
43 |     
44 |     data = np.array(data)
45 |     
46 |     N = len(data)
47 |     
48 |     #mu = r2/r1 for each data point
49 |     mu = []
50 |     for i,x in enumerate(data):
51 |         
52 |         dist = np.sort(np.sqrt(np.sum((x-data)**2, axis=1)))
53 |         r1, r2 = dist[dist>0][:2]
54 | 
55 |         mu.append((i+1,r2/r1))
56 |         
57 | 
58 |     #permutation function
59 |     sigma_i = dict(zip(range(1,len(mu)+1), np.array(sorted(mu, key=lambda x: x[1]))[:,0].astype(int)))
60 | 
61 |     mu = dict(mu)
62 | 
63 |     #cdf F(mu_{sigma(i)})
64 |     F_i = {}
65 |     for i in mu:
66 |         F_i[sigma_i[i]] = i/N
67 | 
68 |     #fitting coordinates
69 |     x = np.log([mu[i] for i in sorted(mu.keys())])
70 |     y = np.array([1-F_i[i] for i in sorted(mu.keys())])
71 | 
72 |     #avoid having log(0)
73 |     x = x[y>0]
74 |     y = y[y>0]
75 | 
76 |     y = -1*np.log(y)
77 | 
78 |     #fit line through origin to get the dimension
79 |     d = np.linalg.lstsq(np.vstack([x, np.zeros(len(x))]).T, y, rcond=None)[0][0]
80 |         
81 |     if return_xy:
82 |         return d, x, y
83 |     else: 
84 |         return d


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