├── A simple basline algorithm for graph classification.ipynb
├── DATASETS
├── PTC_MR
│ ├── PTC_MR_A.txt
│ ├── PTC_MR_edge_labels.txt
│ ├── PTC_MR_graph_indicator.txt
│ ├── PTC_MR_graph_labels.txt
│ ├── PTC_MR_node_labels.txt
│ └── README.txt
└── README.md
├── README.md
└── images
├── README.md
├── additional_results.png
├── k_dependence.png
├── method_schema.png
└── results.png
/A simple basline algorithm for graph classification.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "metadata": {},
6 | "source": [
7 | "# A Simple Baseline Algorithm for Graph Classification"
8 | ]
9 | },
10 | {
11 | "cell_type": "markdown",
12 | "metadata": {},
13 | "source": [
14 | "##### Edouard Pineau, Nathan de Lara"
15 | ]
16 | },
17 | {
18 | "cell_type": "code",
19 | "execution_count": 1,
20 | "metadata": {
21 | "collapsed": true
22 | },
23 | "outputs": [],
24 | "source": [
25 | "import networkx as nx\n",
26 | "import numpy as np\n",
27 | "import pandas as pd\n",
28 | "\n",
29 | "from scipy import sparse\n",
30 | "\n",
31 | "from sklearn.preprocessing import LabelEncoder\n",
32 | "\n",
33 | "from sklearn.ensemble import RandomForestClassifier\n",
34 | "from sklearn.model_selection import StratifiedKFold\n",
35 | "\n",
36 | "from sklearn.model_selection import cross_val_score\n",
37 | "\n",
38 | "%matplotlib inline\n"
39 | ]
40 | },
41 | {
42 | "cell_type": "markdown",
43 | "metadata": {},
44 | "source": [
45 | "### Loading all datasets"
46 | ]
47 | },
48 | {
49 | "cell_type": "code",
50 | "execution_count": 2,
51 | "metadata": {
52 | "collapsed": true
53 | },
54 | "outputs": [],
55 | "source": [
56 | "class GraphDataset:\n",
57 | " def __init__(self, folder_path=''):\n",
58 | "\n",
59 | " G = nx.Graph()\n",
60 | " data_adj = np.loadtxt(folder_path + '_A.txt', delimiter=',').astype(int)\n",
61 | " data_graph_indicator = np.loadtxt(folder_path + '_graph_indicator.txt', delimiter=',').astype(int)\n",
62 | " labels = np.loadtxt(folder_path + '_graph_labels.txt', delimiter=',').astype(int)\n",
63 | "\n",
64 | " data_tuple = list(map(tuple, data_adj))\n",
65 | " G.add_edges_from(data_tuple)\n",
66 | " G.remove_nodes_from(list(nx.isolates(G)))\n",
67 | "\n",
68 | " # split into graphs\n",
69 | "\n",
70 | " le = LabelEncoder()\n",
71 | " self.labels_ = le.fit_transform(labels)\n",
72 | " self.n_classes_ = len(le.classes_)\n",
73 | " self.n_graphs_ = len(self.labels_)\n",
74 | "\n",
75 | " graph_num = data_graph_indicator.max()\n",
76 | " node_list = np.arange(data_graph_indicator.shape[0]) + 1\n",
77 | " self.graphs_ = []\n",
78 | "\n",
79 | " for i in range(graph_num):\n",
80 | "\n",
81 | " nodes = node_list[data_graph_indicator == i + 1]\n",
82 | " G_sub = G.subgraph(nodes).copy()\n",
83 | " \n",
84 | " max_cc = max(nx.connected_components(G_sub), key=len)\n",
85 | " G_sub = G_sub.subgraph(max_cc).copy()\n",
86 | " G_sub.graph['label'] = self.labels_ [i]\n",
87 | " nx.convert_node_labels_to_integers(G_sub)\n",
88 | " self.graphs_.append(G_sub) \n",
89 | "\n",
90 | " self.graphs_ = np.array(self.graphs_)\n",
91 | "\n",
92 | " print('Loaded')"
93 | ]
94 | },
95 | {
96 | "cell_type": "code",
97 | "execution_count": 3,
98 | "metadata": {
99 | "collapsed": true
100 | },
101 | "outputs": [],
102 | "source": [
103 | "graphs_name = ['MUTAG', 'PTC_MR', 'ENZYMES', 'PROTEINS_full', 'DD', 'NCI1']\n",
104 | "data_pwd = 'DATASETS/'"
105 | ]
106 | },
107 | {
108 | "cell_type": "code",
109 | "execution_count": 4,
110 | "metadata": {
111 | "scrolled": false
112 | },
113 | "outputs": [
114 | {
115 | "name": "stdout",
116 | "output_type": "stream",
117 | "text": [
118 | "Loaded\n",
119 | "Loaded\n",
120 | "Loaded\n",
121 | "Loaded\n",
122 | "Loaded\n",
123 | "Loaded\n"
124 | ]
125 | }
126 | ],
127 | "source": [
128 | "datasets = {}\n",
129 | "for gn in graphs_name:\n",
130 | " datasets[gn] = GraphDataset(folder_path=data_pwd + gn + '/' + gn)"
131 | ]
132 | },
133 | {
134 | "cell_type": "markdown",
135 | "metadata": {},
136 | "source": [
137 | "### Spectral embedding, reshaping and training"
138 | ]
139 | },
140 | {
141 | "cell_type": "markdown",
142 | "metadata": {},
143 | "source": [
144 | "Embedding of the nodes: creation of the spectral features"
145 | ]
146 | },
147 | {
148 | "cell_type": "code",
149 | "execution_count": 5,
150 | "metadata": {
151 | "collapsed": true
152 | },
153 | "outputs": [],
154 | "source": [
155 | "def padded_spectral(graph, embedding_dimension=16, normalized=True):\n",
156 | " \n",
157 | " # Padding with zeros\n",
158 | " embedding = np.zeros(embedding_dimension)\n",
159 | " \n",
160 | " # Usage of networkx graph objects\n",
161 | " adj_matrix = nx.adj_matrix(graph)\n",
162 | " n_nodes, m_nodes = adj_matrix.shape\n",
163 | " k = min(embedding_dimension + 1, n_nodes - 1)\n",
164 | "\n",
165 | " if normalized:\n",
166 | " laplacian = nx.normalized_laplacian_matrix(graph)\n",
167 | " else:\n",
168 | " laplacian = nx.laplacian_matrix(graph)\n",
169 | "\n",
170 | " # Minus the eigen decomposition of minus the Laplacian is more stable than directly\n",
171 | " # computing the eigen decomposition of the Laplacian\n",
172 | " \n",
173 | " v0 = np.random.uniform(-1, 1, laplacian.shape[0])\n",
174 | " eigenvalues = sparse.linalg.eigsh(-laplacian, k=k, sigma=1.0, which='LM', tol=1e-6, v0=v0, return_eigenvectors=False)\n",
175 | " embedding[:len(eigenvalues)-1] = sorted(-eigenvalues)[1:]\n",
176 | " \n",
177 | " return embedding"
178 | ]
179 | },
180 | {
181 | "cell_type": "code",
182 | "execution_count": 6,
183 | "metadata": {
184 | "collapsed": true
185 | },
186 | "outputs": [],
187 | "source": [
188 | "def dataset_embedding(dataset, embedding_dim, normalized=True):\n",
189 | "\n",
190 | " list_graphs = []\n",
191 | " for g in dataset.graphs_:\n",
192 | " x = padded_spectral(g, embedding_dim, normalized)\n",
193 | " y = g.graph['label']\n",
194 | "\n",
195 | " list_graphs.append((x, y))\n",
196 | "\n",
197 | " X = np.array([l[0] for l in list_graphs])\n",
198 | " labels = np.array([l[1] for l in list_graphs])\n",
199 | " \n",
200 | " return X, labels"
201 | ]
202 | },
203 | {
204 | "cell_type": "code",
205 | "execution_count": 7,
206 | "metadata": {
207 | "collapsed": true
208 | },
209 | "outputs": [],
210 | "source": [
211 | "# Mean number of nodes per dataset\n",
212 | "\n",
213 | "embedding_dims = {'MUTAG': 18, 'PTC_MR': 14, 'ENZYMES': 33, 'PROTEINS_full': 39, 'DD': 284, 'NCI1': 30}"
214 | ]
215 | },
216 | {
217 | "cell_type": "code",
218 | "execution_count": 8,
219 | "metadata": {
220 | "collapsed": true
221 | },
222 | "outputs": [],
223 | "source": [
224 | "embedded_datasets = {}\n",
225 | "\n",
226 | "for name, dataset in datasets.items():\n",
227 | " k = embedding_dims[name]\n",
228 | " X, y = dataset_embedding(dataset, k)\n",
229 | " embedded_datasets[name] = {'X': X, 'y': y}"
230 | ]
231 | },
232 | {
233 | "cell_type": "markdown",
234 | "metadata": {},
235 | "source": [
236 | "Training for all datasets and embedding dimensions"
237 | ]
238 | },
239 | {
240 | "cell_type": "code",
241 | "execution_count": 9,
242 | "metadata": {},
243 | "outputs": [
244 | {
245 | "name": "stdout",
246 | "output_type": "stream",
247 | "text": [
248 | "Dataset: MUTAG, Embedding dim: 18, Accuracy: 0.883918\n",
249 | "Dataset: PTC_MR, Embedding dim: 14, Accuracy: 0.627941\n",
250 | "Dataset: ENZYMES, Embedding dim: 33, Accuracy: 0.436667\n",
251 | "Dataset: PROTEINS_full, Embedding dim: 39, Accuracy: 0.732328\n",
252 | "Dataset: DD, Embedding dim: 284, Accuracy: 0.753799\n",
253 | "Dataset: NCI1, Embedding dim: 30, Accuracy: 0.752792\n"
254 | ]
255 | }
256 | ],
257 | "source": [
258 | "rf_parameters = {'n_estimators': 500, 'max_depth': 100}\n",
259 | "\n",
260 | "for name, dataset in datasets.items():\n",
261 | "\n",
262 | " X, y = embedded_datasets[name]['X'], embedded_datasets[name]['y']\n",
263 | "\n",
264 | " rf = RandomForestClassifier(**rf_parameters, random_state=1, class_weight='balanced') \n",
265 | " skf = StratifiedKFold(n_splits=10, shuffle=True, random_state=1)\n",
266 | "\n",
267 | " cv_results = cross_val_score(rf, X, y, n_jobs=1, cv=skf, scoring='accuracy')\n",
268 | " \n",
269 | " print('Dataset: {}, Embedding dim: {}, Accuracy: {:2f}'.format(name, X.shape[1], np.mean(cv_results)))"
270 | ]
271 | },
272 | {
273 | "cell_type": "markdown",
274 | "metadata": {},
275 | "source": [
276 | "Study on hyper-parametrization"
277 | ]
278 | },
279 | {
280 | "cell_type": "code",
281 | "execution_count": 10,
282 | "metadata": {
283 | "collapsed": true,
284 | "scrolled": true
285 | },
286 | "outputs": [],
287 | "source": [
288 | "import pandas as pd\n",
289 | "\n",
290 | "hp_test_means, hp_test_std = {}, {}\n",
291 | "\n",
292 | "rf_parameters_grid = {'n_estimators': [1, 10, 50, 100, 250, 750, 1000], \n",
293 | " 'min_samples_leaf': [2, 3, 4, 5, 6], \n",
294 | " 'max_depth': [1, 5, 10, 50, 250, 500, 750, 1000], \n",
295 | " 'bootstrap': [False]}\n",
296 | "\n",
297 | "\n",
298 | "rf_parameters_default = {'n_estimators': 500, 'min_samples_leaf': 1, 'max_depth': 100, \n",
299 | " 'bootstrap': True, 'class_weight': 'balanced'}\n",
300 | "\n",
301 | "# Non default parameters\n",
302 | "\n",
303 | "for para_name in rf_parameters_grid:\n",
304 | " \n",
305 | " parameters_index = rf_parameters_grid[para_name] + [rf_parameters_default[para_name]]\n",
306 | " parameters_index.sort()\n",
307 | " \n",
308 | " hp_test_means[para_name] = pd.DataFrame(index=parameters_index, columns=list(datasets.keys()))\n",
309 | " hp_test_std[para_name] = pd.DataFrame(index=parameters_index, columns=list(datasets.keys()))\n",
310 | " \n",
311 | " rf_parameters = rf_parameters_default.copy()\n",
312 | " \n",
313 | " for para_val in rf_parameters_grid[para_name]:\n",
314 | " \n",
315 | " rf_parameters[para_name] = para_val\n",
316 | " \n",
317 | " for name, dataset in datasets.items():\n",
318 | "\n",
319 | " X, y = embedded_datasets[name]['X'], embedded_datasets[name]['y']\n",
320 | "\n",
321 | " rf = RandomForestClassifier(**rf_parameters, random_state=1)\n",
322 | " skf = StratifiedKFold(n_splits=10, shuffle=True, random_state=1)\n",
323 | " \n",
324 | " cv_results = cross_val_score(rf, X, y, n_jobs=1, cv=skf, scoring='accuracy')\n",
325 | " hp_test_means[para_name][name][para_val] = np.mean(cv_results)\n",
326 | " hp_test_std[para_name][name][para_val] = np.std(cv_results)\n",
327 | " \n",
328 | "# Default parameters\n",
329 | "\n",
330 | "rf_parameters = rf_parameters_default.copy()\n",
331 | "\n",
332 | "for name, dataset in datasets.items():\n",
333 | "\n",
334 | " X, y = embedded_datasets[name]['X'], embedded_datasets[name]['y']\n",
335 | "\n",
336 | " rf = RandomForestClassifier(**rf_parameters, random_state=1) \n",
337 | " skf = StratifiedKFold(n_splits=10, shuffle=True, random_state=1)\n",
338 | "\n",
339 | " cv_results = cross_val_score(rf, X, y, n_jobs=1, cv=skf, scoring='accuracy')\n",
340 | " \n",
341 | " for para_name in rf_parameters_grid:\n",
342 | " hp_test_means[para_name][name][rf_parameters[para_name]] = np.mean(cv_results)\n",
343 | " hp_test_std[para_name][name][rf_parameters[para_name]] = np.std(cv_results) "
344 | ]
345 | },
346 | {
347 | "cell_type": "code",
348 | "execution_count": 11,
349 | "metadata": {},
350 | "outputs": [
351 | {
352 | "data": {
353 | "text/html": [
354 | "
\n",
355 | "\n",
368 | "
\n",
369 | " \n",
370 | " \n",
371 | " | \n",
372 | " MUTAG | \n",
373 | " PTC_MR | \n",
374 | " ENZYMES | \n",
375 | " PROTEINS_full | \n",
376 | " DD | \n",
377 | " NCI1 | \n",
378 | "
\n",
379 | " \n",
380 | " \n",
381 | " \n",
382 | " 1 | \n",
383 | " 0.836725 | \n",
384 | " 0.575163 | \n",
385 | " 0.303333 | \n",
386 | " 0.659548 | \n",
387 | " 0.69102 | \n",
388 | " 0.649894 | \n",
389 | "
\n",
390 | " \n",
391 | " 10 | \n",
392 | " 0.846725 | \n",
393 | " 0.610784 | \n",
394 | " 0.37 | \n",
395 | " 0.707143 | \n",
396 | " 0.743615 | \n",
397 | " 0.722135 | \n",
398 | "
\n",
399 | " \n",
400 | " 50 | \n",
401 | " 0.862836 | \n",
402 | " 0.59951 | \n",
403 | " 0.406667 | \n",
404 | " 0.726046 | \n",
405 | " 0.756298 | \n",
406 | " 0.739416 | \n",
407 | "
\n",
408 | " \n",
409 | " 100 | \n",
410 | " 0.873392 | \n",
411 | " 0.610784 | \n",
412 | " 0.423333 | \n",
413 | " 0.730542 | \n",
414 | " 0.756349 | \n",
415 | " 0.74428 | \n",
416 | "
\n",
417 | " \n",
418 | " 250 | \n",
419 | " 0.878655 | \n",
420 | " 0.628105 | \n",
421 | " 0.421667 | \n",
422 | " 0.730526 | \n",
423 | " 0.757182 | \n",
424 | " 0.752064 | \n",
425 | "
\n",
426 | " \n",
427 | " 500 | \n",
428 | " 0.883918 | \n",
429 | " 0.627941 | \n",
430 | " 0.436667 | \n",
431 | " 0.732328 | \n",
432 | " 0.753799 | \n",
433 | " 0.752792 | \n",
434 | "
\n",
435 | " \n",
436 | " 750 | \n",
437 | " 0.878918 | \n",
438 | " 0.624837 | \n",
439 | " 0.426667 | \n",
440 | " 0.730534 | \n",
441 | " 0.753842 | \n",
442 | " 0.752547 | \n",
443 | "
\n",
444 | " \n",
445 | " 1000 | \n",
446 | " 0.873655 | \n",
447 | " 0.622059 | \n",
448 | " 0.428333 | \n",
449 | " 0.732336 | \n",
450 | " 0.752126 | \n",
451 | " 0.751578 | \n",
452 | "
\n",
453 | " \n",
454 | "
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455 | "
"
456 | ],
457 | "text/plain": [
458 | " MUTAG PTC_MR ENZYMES PROTEINS_full DD NCI1\n",
459 | "1 0.836725 0.575163 0.303333 0.659548 0.69102 0.649894\n",
460 | "10 0.846725 0.610784 0.37 0.707143 0.743615 0.722135\n",
461 | "50 0.862836 0.59951 0.406667 0.726046 0.756298 0.739416\n",
462 | "100 0.873392 0.610784 0.423333 0.730542 0.756349 0.74428\n",
463 | "250 0.878655 0.628105 0.421667 0.730526 0.757182 0.752064\n",
464 | "500 0.883918 0.627941 0.436667 0.732328 0.753799 0.752792\n",
465 | "750 0.878918 0.624837 0.426667 0.730534 0.753842 0.752547\n",
466 | "1000 0.873655 0.622059 0.428333 0.732336 0.752126 0.751578"
467 | ]
468 | },
469 | "execution_count": 11,
470 | "metadata": {},
471 | "output_type": "execute_result"
472 | }
473 | ],
474 | "source": [
475 | "hp_test_means['n_estimators']"
476 | ]
477 | },
478 | {
479 | "cell_type": "code",
480 | "execution_count": 12,
481 | "metadata": {},
482 | "outputs": [
483 | {
484 | "data": {
485 | "text/html": [
486 | "\n",
487 | "\n",
500 | "
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501 | " \n",
502 | " \n",
503 | " | \n",
504 | " MUTAG | \n",
505 | " PTC_MR | \n",
506 | " ENZYMES | \n",
507 | " PROTEINS_full | \n",
508 | " DD | \n",
509 | " NCI1 | \n",
510 | "
\n",
511 | " \n",
512 | " \n",
513 | " \n",
514 | " 1 | \n",
515 | " 0.883918 | \n",
516 | " 0.627941 | \n",
517 | " 0.436667 | \n",
518 | " 0.732328 | \n",
519 | " 0.753799 | \n",
520 | " 0.752792 | \n",
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524 | " 0.878918 | \n",
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526 | " 0.406667 | \n",
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528 | " 0.757239 | \n",
529 | " 0.751095 | \n",
530 | "
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531 | " \n",
532 | " 3 | \n",
533 | " 0.883918 | \n",
534 | " 0.622059 | \n",
535 | " 0.395 | \n",
536 | " 0.736816 | \n",
537 | " 0.761498 | \n",
538 | " 0.745988 | \n",
539 | "
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540 | " \n",
541 | " 4 | \n",
542 | " 0.878918 | \n",
543 | " 0.627778 | \n",
544 | " 0.386667 | \n",
545 | " 0.734138 | \n",
546 | " 0.757268 | \n",
547 | " 0.742821 | \n",
548 | "
\n",
549 | " \n",
550 | " 5 | \n",
551 | " 0.873363 | \n",
552 | " 0.625163 | \n",
553 | " 0.385 | \n",
554 | " 0.736832 | \n",
555 | " 0.758087 | \n",
556 | " 0.739653 | \n",
557 | "
\n",
558 | " \n",
559 | " 6 | \n",
560 | " 0.851696 | \n",
561 | " 0.622222 | \n",
562 | " 0.37 | \n",
563 | " 0.741337 | \n",
564 | " 0.756385 | \n",
565 | " 0.73624 | \n",
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567 | " \n",
568 | "
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571 | "text/plain": [
572 | " MUTAG PTC_MR ENZYMES PROTEINS_full DD NCI1\n",
573 | "1 0.883918 0.627941 0.436667 0.732328 0.753799 0.752792\n",
574 | "2 0.878918 0.613562 0.406667 0.735923 0.757239 0.751095\n",
575 | "3 0.883918 0.622059 0.395 0.736816 0.761498 0.745988\n",
576 | "4 0.878918 0.627778 0.386667 0.734138 0.757268 0.742821\n",
577 | "5 0.873363 0.625163 0.385 0.736832 0.758087 0.739653\n",
578 | "6 0.851696 0.622222 0.37 0.741337 0.756385 0.73624"
579 | ]
580 | },
581 | "execution_count": 12,
582 | "metadata": {},
583 | "output_type": "execute_result"
584 | }
585 | ],
586 | "source": [
587 | "hp_test_means['min_samples_leaf']"
588 | ]
589 | },
590 | {
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592 | "execution_count": 13,
593 | "metadata": {},
594 | "outputs": [
595 | {
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597 | "text/html": [
598 | "\n",
599 | "\n",
612 | "
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613 | " \n",
614 | " \n",
615 | " | \n",
616 | " MUTAG | \n",
617 | " PTC_MR | \n",
618 | " ENZYMES | \n",
619 | " PROTEINS_full | \n",
620 | " DD | \n",
621 | " NCI1 | \n",
622 | "
\n",
623 | " \n",
624 | " \n",
625 | " \n",
626 | " 1 | \n",
627 | " 0.84614 | \n",
628 | " 0.593301 | \n",
629 | " 0.243333 | \n",
630 | " 0.71883 | \n",
631 | " 0.762303 | \n",
632 | " 0.617522 | \n",
633 | "
\n",
634 | " \n",
635 | " 5 | \n",
636 | " 0.878918 | \n",
637 | " 0.610621 | \n",
638 | " 0.358333 | \n",
639 | " 0.735931 | \n",
640 | " 0.75637 | \n",
641 | " 0.688065 | \n",
642 | "
\n",
643 | " \n",
644 | " 10 | \n",
645 | " 0.883918 | \n",
646 | " 0.610131 | \n",
647 | " 0.415 | \n",
648 | " 0.73684 | \n",
649 | " 0.754683 | \n",
650 | " 0.735029 | \n",
651 | "
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652 | " \n",
653 | " 50 | \n",
654 | " 0.883918 | \n",
655 | " 0.627941 | \n",
656 | " 0.436667 | \n",
657 | " 0.732328 | \n",
658 | " 0.753799 | \n",
659 | " 0.752792 | \n",
660 | "
\n",
661 | " \n",
662 | " 100 | \n",
663 | " 0.883918 | \n",
664 | " 0.627941 | \n",
665 | " 0.436667 | \n",
666 | " 0.732328 | \n",
667 | " 0.753799 | \n",
668 | " 0.752792 | \n",
669 | "
\n",
670 | " \n",
671 | " 250 | \n",
672 | " 0.883918 | \n",
673 | " 0.627941 | \n",
674 | " 0.436667 | \n",
675 | " 0.732328 | \n",
676 | " 0.753799 | \n",
677 | " 0.752792 | \n",
678 | "
\n",
679 | " \n",
680 | " 500 | \n",
681 | " 0.883918 | \n",
682 | " 0.627941 | \n",
683 | " 0.436667 | \n",
684 | " 0.732328 | \n",
685 | " 0.753799 | \n",
686 | " 0.752792 | \n",
687 | "
\n",
688 | " \n",
689 | " 750 | \n",
690 | " 0.883918 | \n",
691 | " 0.627941 | \n",
692 | " 0.436667 | \n",
693 | " 0.732328 | \n",
694 | " 0.753799 | \n",
695 | " 0.752792 | \n",
696 | "
\n",
697 | " \n",
698 | " 1000 | \n",
699 | " 0.883918 | \n",
700 | " 0.627941 | \n",
701 | " 0.436667 | \n",
702 | " 0.732328 | \n",
703 | " 0.753799 | \n",
704 | " 0.752792 | \n",
705 | "
\n",
706 | " \n",
707 | "
\n",
708 | "
"
709 | ],
710 | "text/plain": [
711 | " MUTAG PTC_MR ENZYMES PROTEINS_full DD NCI1\n",
712 | "1 0.84614 0.593301 0.243333 0.71883 0.762303 0.617522\n",
713 | "5 0.878918 0.610621 0.358333 0.735931 0.75637 0.688065\n",
714 | "10 0.883918 0.610131 0.415 0.73684 0.754683 0.735029\n",
715 | "50 0.883918 0.627941 0.436667 0.732328 0.753799 0.752792\n",
716 | "100 0.883918 0.627941 0.436667 0.732328 0.753799 0.752792\n",
717 | "250 0.883918 0.627941 0.436667 0.732328 0.753799 0.752792\n",
718 | "500 0.883918 0.627941 0.436667 0.732328 0.753799 0.752792\n",
719 | "750 0.883918 0.627941 0.436667 0.732328 0.753799 0.752792\n",
720 | "1000 0.883918 0.627941 0.436667 0.732328 0.753799 0.752792"
721 | ]
722 | },
723 | "execution_count": 13,
724 | "metadata": {},
725 | "output_type": "execute_result"
726 | }
727 | ],
728 | "source": [
729 | "hp_test_means['max_depth']"
730 | ]
731 | },
732 | {
733 | "cell_type": "code",
734 | "execution_count": 14,
735 | "metadata": {},
736 | "outputs": [
737 | {
738 | "data": {
739 | "text/html": [
740 | "\n",
741 | "\n",
754 | "
\n",
755 | " \n",
756 | " \n",
757 | " | \n",
758 | " MUTAG | \n",
759 | " PTC_MR | \n",
760 | " ENZYMES | \n",
761 | " PROTEINS_full | \n",
762 | " DD | \n",
763 | " NCI1 | \n",
764 | "
\n",
765 | " \n",
766 | " \n",
767 | " \n",
768 | " False | \n",
769 | " 0.868099 | \n",
770 | " 0.62451 | \n",
771 | " 0.43 | \n",
772 | " 0.721517 | \n",
773 | " 0.749562 | \n",
774 | " 0.751094 | \n",
775 | "
\n",
776 | " \n",
777 | " True | \n",
778 | " 0.883918 | \n",
779 | " 0.627941 | \n",
780 | " 0.436667 | \n",
781 | " 0.732328 | \n",
782 | " 0.753799 | \n",
783 | " 0.752792 | \n",
784 | "
\n",
785 | " \n",
786 | "
\n",
787 | "
"
788 | ],
789 | "text/plain": [
790 | " MUTAG PTC_MR ENZYMES PROTEINS_full DD NCI1\n",
791 | "False 0.868099 0.62451 0.43 0.721517 0.749562 0.751094\n",
792 | "True 0.883918 0.627941 0.436667 0.732328 0.753799 0.752792"
793 | ]
794 | },
795 | "execution_count": 14,
796 | "metadata": {},
797 | "output_type": "execute_result"
798 | }
799 | ],
800 | "source": [
801 | "hp_test_means['bootstrap']"
802 | ]
803 | },
804 | {
805 | "cell_type": "code",
806 | "execution_count": 15,
807 | "metadata": {},
808 | "outputs": [
809 | {
810 | "data": {
811 | "text/plain": [
812 | ""
813 | ]
814 | },
815 | "execution_count": 15,
816 | "metadata": {},
817 | "output_type": "execute_result"
818 | },
819 | {
820 | "data": {
821 | "image/png": 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A08zsWDMbDfSTtGpZumohGdT3gB8Bz+LnPGsg9gF2WpSBSJ7mRsBbwPtpnXBDeSPeBdy4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\n",
822 | "text/plain": [
823 | ""
824 | ]
825 | },
826 | "metadata": {},
827 | "output_type": "display_data"
828 | }
829 | ],
830 | "source": [
831 | "hp_test_means['bootstrap'].plot(kind='box', figsize=(4, 2), grid=True, title='bootstrap', rot=45)"
832 | ]
833 | },
834 | {
835 | "cell_type": "code",
836 | "execution_count": 16,
837 | "metadata": {},
838 | "outputs": [
839 | {
840 | "data": {
841 | "text/plain": [
842 | ""
843 | ]
844 | },
845 | "execution_count": 16,
846 | "metadata": {},
847 | "output_type": "execute_result"
848 | },
849 | {
850 | "data": {
851 | "image/png": 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pE/hw3yLgFtyj2R2fqPNG3E0/EH+EWyNkPm6Nl587y8x+kEZ23mVm16ZM007g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\n+X8Bb56jh8va/wAAAABJRU5ErkJggg==\n",
852 | "text/plain": [
853 | ""
854 | ]
855 | },
856 | "metadata": {},
857 | "output_type": "display_data"
858 | }
859 | ],
860 | "source": [
861 | "hp_test_means['n_estimators'].plot(kind='box', figsize=(4, 2), grid=True, title='n_estimators', rot=45)"
862 | ]
863 | },
864 | {
865 | "cell_type": "code",
866 | "execution_count": 17,
867 | "metadata": {},
868 | "outputs": [
869 | {
870 | "data": {
871 | "text/plain": [
872 | ""
873 | ]
874 | },
875 | "execution_count": 17,
876 | "metadata": {},
877 | "output_type": "execute_result"
878 | },
879 | {
880 | "data": {
881 | "image/png": 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np+Xt8CpEY1GZ3fBh6fbNW++a/pe7gBXE+I39ECliSwqs5aBjDPBe0fK2+CAi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\ngiCTMA5BEGQSxiEIgkzCOARBkMn/AxKDqQ+JqxT6AAAAAElFTkSuQmCC\n",
882 | "text/plain": [
883 | ""
884 | ]
885 | },
886 | "metadata": {},
887 | "output_type": "display_data"
888 | }
889 | ],
890 | "source": [
891 | "hp_test_means['min_samples_leaf'].plot(kind='box', figsize=(4, 2), grid=True, title='min_samples_leaf', rot=45)"
892 | ]
893 | },
894 | {
895 | "cell_type": "code",
896 | "execution_count": 18,
897 | "metadata": {},
898 | "outputs": [
899 | {
900 | "data": {
901 | "text/plain": [
902 | ""
903 | ]
904 | },
905 | "execution_count": 18,
906 | "metadata": {},
907 | "output_type": "execute_result"
908 | },
909 | {
910 | "data": {
911 | "image/png": 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ZRNQVknbB8zsCYGZ/wYOz3ifP8vwYHso9Eh+YRqZsNCVyJHeHZCFSpN+F+FgK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\ngqAgYRyCIChIGIcgCAry/+0up3tA1QOeAAAAAElFTkSuQmCC\n",
912 | "text/plain": [
913 | ""
914 | ]
915 | },
916 | "metadata": {},
917 | "output_type": "display_data"
918 | }
919 | ],
920 | "source": [
921 | "hp_test_means['max_depth'].plot(kind='box', figsize=(4, 2), grid=True, title='max_depth', rot=45)"
922 | ]
923 | }
924 | ],
925 | "metadata": {
926 | "kernelspec": {
927 | "display_name": "Python 3",
928 | "language": "python",
929 | "name": "python3"
930 | },
931 | "language_info": {
932 | "codemirror_mode": {
933 | "name": "ipython",
934 | "version": 3
935 | },
936 | "file_extension": ".py",
937 | "mimetype": "text/x-python",
938 | "name": "python",
939 | "nbconvert_exporter": "python",
940 | "pygments_lexer": "ipython3",
941 | "version": "3.6.3"
942 | }
943 | },
944 | "nbformat": 4,
945 | "nbformat_minor": 2
946 | }
947 |
--------------------------------------------------------------------------------
/DATASETS/PTC_MR/PTC_MR_graph_indicator.txt:
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/DATASETS/PTC_MR/PTC_MR_graph_labels.txt:
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/DATASETS/PTC_MR/PTC_MR_node_labels.txt:
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963 | 5
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1930 | 3
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1932 | 5
1933 | 5
1934 | 3
1935 | 5
1936 | 7
1937 | 5
1938 | 5
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1940 | 5
1941 | 5
1942 | 5
1943 | 3
1944 | 2
1945 | 3
1946 | 2
1947 | 5
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1952 | 3
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1968 | 3
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1970 | 5
1971 | 3
1972 | 3
1973 | 7
1974 | 2
1975 | 2
1976 | 2
1977 | 4
1978 | 2
1979 | 7
1980 | 2
1981 | 5
1982 | 5
1983 | 5
1984 | 5
1985 | 7
1986 | 1
1987 | 2
1988 | 5
1989 | 2
1990 | 5
1991 | 2
1992 | 5
1993 | 5
1994 | 5
1995 | 5
1996 | 7
1997 | 5
1998 | 5
1999 | 5
2000 | 5
2001 | 3
2002 | 5
2003 | 3
2004 | 5
2005 | 6
2006 | 3
2007 | 5
2008 | 6
2009 | 3
2010 | 5
2011 | 5
2012 | 5
2013 | 5
2014 | 5
2015 | 5
2016 | 6
2017 | 2
2018 | 5
2019 | 5
2020 | 5
2021 | 5
2022 | 5
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4916 |
--------------------------------------------------------------------------------
/DATASETS/PTC_MR/README.txt:
--------------------------------------------------------------------------------
1 | README for dataset PTC_MR
2 |
3 |
4 | === Usage ===
5 |
6 | This folder contains the following comma separated text files
7 | (replace DS by the name of the dataset):
8 |
9 | n = total number of nodes
10 | m = total number of edges
11 | N = number of graphs
12 |
13 | (1) DS_A.txt (m lines)
14 | sparse (block diagonal) adjacency matrix for all graphs,
15 | each line corresponds to (row, col) resp. (node_id, node_id)
16 |
17 | (2) DS_graph_indicator.txt (n lines)
18 | column vector of graph identifiers for all nodes of all graphs,
19 | the value in the i-th line is the graph_id of the node with node_id i
20 |
21 | (3) DS_graph_labels.txt (N lines)
22 | class labels for all graphs in the dataset,
23 | the value in the i-th line is the class label of the graph with graph_id i
24 |
25 | (4) DS_node_labels.txt (n lines)
26 | column vector of node labels,
27 | the value in the i-th line corresponds to the node with node_id i
28 |
29 | There are OPTIONAL files if the respective information is available:
30 |
31 | (5) DS_edge_labels.txt (m lines; same size as DS_A_sparse.txt)
32 | labels for the edges in DS_A_sparse.txt
33 |
34 | (6) DS_edge_attributes.txt (m lines; same size as DS_A.txt)
35 | attributes for the edges in DS_A.txt
36 |
37 | (7) DS_node_attributes.txt (n lines)
38 | matrix of node attributes,
39 | the comma seperated values in the i-th line is the attribute vector of the node with node_id i
40 |
41 | (8) DS_graph_attributes.txt (N lines)
42 | regression values for all graphs in the dataset,
43 | the value in the i-th line is the attribute of the graph with graph_id i
44 |
45 |
46 | === Description of the dataset ===
47 |
48 | The PTC dataset contains compounds labeled according to carcinogenicity
49 | on rodents divided into male mice (MM), male rats (MR), female mice (FM)
50 | and female rats (FR).
51 |
52 | The chemical data was obtained form http://www.predictive-toxicology.org/ptc/
53 | and converted to graphs, where vertices represent atoms and edges
54 | represent chemical bonds. Explicit hydrogen atoms have been removed and
55 | vertices are labeled by atom type and edges by bond type (single, double,
56 | triple or aromatic). Chemical data was processed using the Chemistry
57 | Development Kit (v1.4).
58 |
59 | Node labels:
60 |
61 | 0 In
62 | 1 P
63 | 2 O
64 | 3 N
65 | 4 Na
66 | 5 C
67 | 6 Cl
68 | 7 S
69 | 8 Br
70 | 9 F
71 | 10 K
72 | 11 Cu
73 | 12 Zn
74 | 13 I
75 | 14 Ba
76 | 15 Sn
77 | 16 Pb
78 | 17 Ca
79 |
80 | Edge labels:
81 |
82 | 0 triple
83 | 1 double
84 | 2 single
85 | 3 aromatic
86 |
87 |
88 | === Previous Use of the Dataset ===
89 |
90 | Kriege, N., Mutzel, P.: Subgraph matching kernels for attributed graphs. In: Proceedings
91 | of the 29th International Conference on Machine Learning (ICML-2012) (2012).
92 |
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1 | A single dataset is archived in the DATASETS file, others can be found here: https://ls11-www.cs.tu-dortmund.de/staff/morris/graphkerneldatasets
2 |
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/README.md:
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1 | # A simple baseline algorithm for graph classification
2 |
3 | This repository proposes an implementation of the work developped and presented in: https://arxiv.org/abs/1810.09155
4 |
5 | This work was presented at the NIPS 2018 workshop session [Relational Representation Learning](https://r2learning.github.io/).
6 |
7 | Theoretical explanation of the good behavior of this simple baseline is presented in a preprint paper [Using Laplacian Spectrum as Graph Feature Representation](https://arxiv.org/abs/1912.00735), whose code is [here](https://github.com/edouardpineau/Using-Laplacian-Spectrum-as-Graph-Feature-Representation).
8 |
9 | ### Abstract
10 |
11 | Graph classification has recently received a lot of attention from various fields of machine learning e.g. kernel methods, sequential modeling or graph embedding. All these approaches offer promising results with different respective strengths and weaknesses. However, most of them rely on complex mathematics and require heavy computational power to achieve their best performance. We propose a simple and fast algorithm based on the spectral decomposition of graph Laplacian to perform graph classification and get a first reference score for a dataset. We show that this method obtains competitive results compared to state-of-the-art algorithms.
12 |
13 | ### Method
14 |
15 | 
16 | Figure 1: Schematic view of our model. L denotes the normalized Laplacian of the graph, c the predicted class.
17 |
18 | ### Results
19 |
20 | 
21 | Table 1: Experimental accuracy (%) of different models plus ours over standard molecular datasets.
22 |
23 | ###
24 |
25 | As we can see, SF + RFC provides the best results for all datasets except DD. Our intuition to explain these good results is that the decision tree classifier, which is at the core of RFC, is an algorithm based on level thresholding. Our paper uses [1] to say that the spectral features represent a sequence of energy levels. With this intuition, being above or below a certain level is thus likely to be meaningful for classification.
26 |
27 | ### Additional results
28 |
29 | 
30 | Table 2: Accuracy (%) of different classifiers combined to the spectral features embedding.
31 |
32 | ###
33 |
34 | Several experiments has been done with adidtional classifiers: random forest classifier (RFC), k-nearest neighbors classifier (k-NNC), 2-layers perceptron with Relu non-linearity (MLP), support vector machine with *one versus one* classification (SVM) and ridge regression classifier (RRC).
35 |
36 | ###
37 |
38 | 
39 | Table 3: Accuracy (%) of RF combined to the spectral features embedding of different dimensions.
40 |
41 | ### Citing
42 |
43 | @article{de2018simple,
44 | title={A simple baseline algorithm for graph classification},
45 | author={de Lara, Nathan and Pineau, Edouard},
46 | journal={Relational Representation Learning Workshop, NIPS 2018},
47 | year={2018}
48 | }
49 |
50 | ###
51 |
52 | [1] Thomas Bonald, Alexandre Hollocou, and Marc Lelarge. Weighted spectral embedding of graphs. arXiv preprint arXiv:1809.11115, 2018.
53 |
54 | A single dataset is archived in the DATASETS file, others can be found here: https://ls11-www.cs.tu-dortmund.de/staff/morris/graphkerneldatasets
55 |
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