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50 | 55 | 56 |TopCorr is a small python library for constructing filtered correlation networks. Currently implemented so far:
38 |Minimum Spanning Tree
Planar Maximally Filtered Graph
Triangular Maximally Filtered Graph
Thresholding
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1); 283 | }, 284 | 285 | initOnKeyListeners: function() { 286 | $(document).keydown(function(event) { 287 | var activeElementType = document.activeElement.tagName; 288 | // don't navigate when in search box or textarea 289 | if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT' 290 | && !event.altKey && !event.ctrlKey && !event.metaKey && !event.shiftKey) { 291 | switch (event.keyCode) { 292 | case 37: // left 293 | var prevHref = $('link[rel="prev"]').prop('href'); 294 | if (prevHref) { 295 | window.location.href = prevHref; 296 | return false; 297 | } 298 | case 39: // right 299 | var nextHref = $('link[rel="next"]').prop('href'); 300 | if (nextHref) { 301 | window.location.href = nextHref; 302 | return false; 303 | } 304 | } 305 | } 306 | }); 307 | } 308 | }; 309 | 310 | // quick alias for translations 311 | _ = Documentation.gettext; 312 | 313 | $(document).ready(function() { 314 | Documentation.init(); 315 | }); 316 | -------------------------------------------------------------------------------- /tests/test_topcorr.py: -------------------------------------------------------------------------------- 1 | 2 | import unittest 3 | from sklearn.datasets import make_spd_matrix, make_sparse_spd_matrix 4 | import numpy as np 5 | import rpy2.robjects as robjects 6 | from rpy2.robjects.packages import importr 7 | import rpy2.robjects.numpy2ri 8 | import rpy2.rinterface as rinterface 9 | from numpy.testing import assert_array_almost_equal, assert_equal 10 | import topcorr 11 | import networkx as nx 12 | import planarity 13 | 14 | class TestTopCorr(unittest.TestCase): 15 | def _construct_tmfg_with_r(self, corr): 16 | """ 17 | Constructs a TMFG using the implementation provided 18 | by the authors 19 | """ 20 | rpy2.robjects.numpy2ri.activate() 21 | nt = importr('NetworkToolbox') 22 | tmfg_corr = nt.TMFG(corr) 23 | return np.array(tmfg_corr[0]) 24 | 25 | def _construct_dependency_network_with_r(self, X): 26 | """ 27 | Constructs a dependency network from the NetworkToolbox R 28 | package 29 | """ 30 | rpy2.robjects.numpy2ri.activate() 31 | nt = importr('NetworkToolbox') 32 | depend_corr = nt.depend(X, False, "none") 33 | return np.array(depend_corr) 34 | 35 | def test_tmfg(self): 36 | """ 37 | Compares out TMFG algorithm to the one in the Network Toolbox 38 | """ 39 | p = 50 40 | mean = np.zeros(p) 41 | 42 | M = make_spd_matrix(p) 43 | X = np.random.multivariate_normal(mean, M, 200) 44 | corr = np.corrcoef(X.T) 45 | #C = np.abs(corr) 46 | G = topcorr.tmfg(corr, absolute=True, threshold_mean=True) 47 | tmfg_r = self._construct_tmfg_with_r(corr) 48 | tmfg_r[np.abs(tmfg_r) > 0] = 1 49 | tmfg_me = nx.to_numpy_array(G, weight=None) 50 | np.fill_diagonal(tmfg_me, 1) 51 | assert_array_almost_equal(tmfg_r, tmfg_me) 52 | 53 | G = topcorr.tmfg(corr, threshold_mean=False) 54 | assert(nx.check_planarity(G)[0]) 55 | 56 | def test_pmfg(self): 57 | """ 58 | Tests the PMFG - the way we're going to do this is by generating a 59 | correlation matrix that is planar and see if the algorithm can pick it up. 60 | In this case we choose a goldner-harary graph https://en.wikipedia.org/wiki/Goldner%E2%80%93Harary_graph 61 | """ 62 | p = 11 63 | mean = np.zeros(p) 64 | 65 | e= [(1,2 ),( 1,3 ),( 1,4 ),( 1,5 ),( 1,7 ),( 1,8 ),( 1,10 ), 66 | ( 1,11 ),( 2,3 ),( 2,4 ),( 2,6 ),( 2,7 ),( 2,9 ),( 2,10 ), 67 | ( 2,11 ),( 3,4 ),( 4,5 ),( 4,6 ),( 4,7 ),( 5,7 ),( 6,7 ), 68 | ( 7,8 ),( 7,9 ),( 7,10 ),( 8,10 ),( 9,10 ),( 10,11)] 69 | true_G = nx.Graph(e) 70 | corr_true_binary = nx.to_numpy_array(true_G, weight=None) 71 | corr_true = corr_true_binary.copy() * 0.5 72 | np.fill_diagonal(corr_true, 1) 73 | 74 | X = np.random.multivariate_normal(mean, corr_true, 2000) 75 | corr = np.corrcoef(X.T) 76 | #corr[corr < 0.1] = 0 77 | corr_G = nx.from_numpy_array(corr) 78 | pmfg_G = topcorr.pmfg(corr) 79 | corr_pmfg = nx.to_numpy_array(pmfg_G, weight=None) 80 | assert_array_almost_equal(corr_pmfg, corr_true_binary) 81 | 82 | def test_mst(self): 83 | """ 84 | Tests the MST by comparing it to the networkx implementation 85 | """ 86 | p = 50 87 | mean = np.zeros(p) 88 | M = make_spd_matrix(p) 89 | X = np.random.multivariate_normal(mean, M, 200) 90 | corr = np.corrcoef(X.T) 91 | nodes = list(np.arange(p)) 92 | # For the networkx MST we have to convert the correlation graph 93 | # into a distance one 94 | D = np.sqrt(2 - 2*corr) 95 | G = nx.from_numpy_array(D) 96 | mst_G = nx.minimum_spanning_tree(G) 97 | 98 | topcorr_mst_G = topcorr.mst(corr) 99 | 100 | mst_nx_M = nx.to_numpy_array(mst_G, nodelist=nodes, weight=None) 101 | mst_topcorr_M = nx.to_numpy_array(topcorr_mst_G, nodelist=nodes, weight=None) 102 | 103 | assert_array_almost_equal(mst_nx_M, mst_topcorr_M) 104 | 105 | def test_prim(self): 106 | """ 107 | Tests the implementation of Prim's algorithm by comparing it to the networkx 108 | implementation 109 | """ 110 | p = 10 111 | mean = np.zeros(p) 112 | M = make_spd_matrix(p) 113 | X = np.random.multivariate_normal(mean, M, 200) 114 | corr = np.corrcoef(X.T) 115 | nodes = list(np.arange(p)) 116 | # For the networkx MST we have to convert the correlation graph 117 | # into a distance one 118 | D = np.sqrt(2 - 2*corr) 119 | G = nx.from_numpy_array(D) 120 | mst_G = nx.minimum_spanning_tree(G, algorithm="prim") 121 | 122 | topcorr_mst_G = topcorr.mst(corr, algorithm="prim") 123 | 124 | mst_nx_M = nx.to_numpy_array(mst_G, nodelist=nodes, weight=None) 125 | mst_topcorr_M = nx.to_numpy_array(topcorr_mst_G, nodelist=nodes, weight=None) 126 | 127 | assert_array_almost_equal(mst_nx_M, mst_topcorr_M) 128 | 129 | def test_threshold(self): 130 | """ 131 | Tests the thresholding of the correlation matrix - here we add a 132 | bit of noise to a generated sparse matrix and see if we can recover 133 | the non zeros 134 | """ 135 | p = 50 136 | mean = np.zeros(p) 137 | M = make_sparse_spd_matrix(p, alpha=0.95, norm_diag = True, smallest_coef=0.7) 138 | t = np.abs(M).min() 139 | noise = 0.5*t * np.random.rand(p, p) 140 | M_noise = noise + M 141 | threshold = topcorr.threshold(M_noise, t, binary=True) 142 | M[np.abs(M) > 0] = 1 143 | assert_array_almost_equal(M, threshold) 144 | 145 | def test_dependency(self): 146 | """ 147 | Tests the dependency network by comparing it to the NetworkToolbox method 148 | """ 149 | p = 50 150 | mean = np.zeros(p) 151 | M = make_sparse_spd_matrix(p, alpha=0.95, norm_diag = True, smallest_coef=0.7) 152 | 153 | X = np.random.multivariate_normal(mean, M, 200) 154 | corr = np.corrcoef(X.T) 155 | 156 | D_topcorr = topcorr.dependency_network(corr) 157 | D_networktoolbox = self._construct_dependency_network_with_r(X) 158 | 159 | assert_array_almost_equal(D_networktoolbox, D_topcorr) 160 | 161 | def test_knn(self): 162 | """ 163 | Tests the kNN network by ensuring the resulting network meets the constraints 164 | """ 165 | p = 5 166 | k = 2 167 | mean = np.zeros(p) 168 | M = make_sparse_spd_matrix(p, alpha=0.95, norm_diag = True, smallest_coef=0.7) 169 | 170 | X = np.random.multivariate_normal(mean, M, 200) 171 | corr = np.corrcoef(X.T) 172 | 173 | G = topcorr.knn(corr, k) 174 | corr_knn = nx.to_numpy_array(G) 175 | 176 | for i in range(p): 177 | assert(np.count_nonzero(corr_knn[:, i]) >= k) 178 | 179 | assert(np.count_nonzero(corr_knn) < 2*k*p) 180 | 181 | def test_partial_correlation(self): 182 | """ 183 | Tests the partial correlation network by ensuring the resulting partial correlation 184 | matrix correctly recovers the nonzeros from a sparse underlying precision matrix 185 | """ 186 | p = 10 187 | mean = np.zeros(p) 188 | K = make_sparse_spd_matrix(p, alpha=0.9, norm_diag = True, smallest_coef=0.7) 189 | C = np.linalg.inv(K) 190 | ind = np.nonzero(K) 191 | t = 0.8*np.abs(K[ind]).min() 192 | 193 | partial_correlation = topcorr.partial_correlation(C) 194 | 195 | threshold = topcorr.threshold(partial_correlation, t, binary=True) 196 | K[np.abs(K) > 0] = 1 197 | assert_array_almost_equal(K, threshold) 198 | 199 | def test_affintiy(self): 200 | """ 201 | Tests the affinity matrix method by ensuring that it runs. Currently a bit 202 | stumped for a good test. 203 | """ 204 | p = 10 205 | mean = np.zeros(p) 206 | M = make_spd_matrix(p) 207 | X = np.random.multivariate_normal(mean, M, 200) 208 | corr = np.corrcoef(X.T) 209 | 210 | A = topcorr.affinity(corr) 211 | 212 | def test_al_mst(self): 213 | """ 214 | Tests the average linkage MST by ensuring that it runs 215 | """ 216 | p = 200 217 | mean = np.zeros(p) 218 | M = make_spd_matrix(p) 219 | X = np.random.multivariate_normal(mean, M, 200) 220 | corr = np.corrcoef(X.T) 221 | nodes = list(np.arange(p)) 222 | # For the networkx MST we have to convert the correlation graph 223 | # into a distance one 224 | 225 | topcorr_mst_G = topcorr.almst(corr) 226 | 227 | mst_topcorr_M = nx.to_numpy_array(topcorr_mst_G, nodelist=nodes, weight=None) 228 | 229 | def test_forest(self): 230 | """ 231 | Tests the forest construction by firstly ensuring the MSTs are identical when 232 | the correlation matrix only has unique edges, and secondly when the correlation 233 | matrix is degenerate 234 | """ 235 | p = 10 236 | mean = np.zeros(p) 237 | M = make_spd_matrix(p) 238 | X = np.random.multivariate_normal(mean, M, 200) 239 | corr = np.corrcoef(X.T) 240 | nodes = list(np.arange(p)) 241 | mst = topcorr.mst(corr) 242 | forest = topcorr.mst_forest(corr) 243 | 244 | M_mst = nx.to_numpy_array(mst, nodes) 245 | M_forest = nx.to_numpy_array(forest, nodes) 246 | 247 | assert_array_almost_equal(M_mst, M_forest) 248 | 249 | example_mat = np.array([[0, 0.1, 0.3, 0.2, 0.1], [0.1, 0, 0.3, 0.4, 1.7], [0.3, 0.3, 0, 0.6, 0.5], [0.2, 0.4, 0.6, 0, 0.2], [0.1, 1.7, 0.5, 0.2, 0]]) 250 | example_corr = 1-np.power(example_mat,2)/2 251 | forest = topcorr.mst_forest(example_corr) 252 | mst = topcorr.mst(example_corr) 253 | forest_edges = len(forest.edges) 254 | mst_edges = len(mst.edges) 255 | 256 | assert(forest_edges > mst_edges) 257 | assert(nx.is_connected(forest)) 258 | 259 | def test_dcca(self): 260 | """ 261 | Tests the DCCA method using the data provided by https://gist.github.com/jaimeide/a9cba18192ee904307298bd110c28b14 262 | """ 263 | x1 = [-1.042061,-0.669056,-0.685977,-0.067925,0.808380,1.385235,1.455245,0.540762 ,0.139570,-1.038133,0.080121,-0.102159,-0.068675,0.515445,0.600459,0.655325,0.610604,0.482337,0.079108,-0.118951,-0.050178,0.007500,-0.200622] 264 | x2 = [-2.368030,-2.607095,-1.277660,0.301499,1.346982,1.885968,1.765950,1.242890,-0.464786,0.186658,-0.036450,-0.396513,-0.157115,-0.012962,0.378752,-0.151658,0.774253,0.646541,0.311877,-0.694177,-0.412918,-0.338630,0.276635] 265 | x3 = np.array(x1)+np.array(x2)**2 # ad hoc 266 | 267 | X = np.array([x1, x2, x3]).T 268 | 269 | result = np.array([[ 1. , 0.62664048, 0.62095623], \ 270 | [ 0.62664048, 1. , 0.1783183 ], \ 271 | [ 0.62095623, 0.1783183 , 1. ]]) 272 | 273 | dcca_corr = topcorr.dcca(X) 274 | 275 | assert_array_almost_equal(dcca_corr, result) 276 | 277 | 278 | 279 | 280 | 281 | 282 | -------------------------------------------------------------------------------- /docs/_build/html/_static/underscore.js: -------------------------------------------------------------------------------- 1 | // Underscore.js 1.3.1 2 | // (c) 2009-2012 Jeremy Ashkenas, DocumentCloud Inc. 3 | // Underscore is freely distributable under the MIT license. 4 | // Portions of Underscore are inspired or borrowed from Prototype, 5 | // Oliver Steele's Functional, and John Resig's Micro-Templating. 6 | // For all details and documentation: 7 | // http://documentcloud.github.com/underscore 8 | (function(){function q(a,c,d){if(a===c)return a!==0||1/a==1/c;if(a==null||c==null)return a===c;if(a._chain)a=a._wrapped;if(c._chain)c=c._wrapped;if(a.isEqual&&b.isFunction(a.isEqual))return a.isEqual(c);if(c.isEqual&&b.isFunction(c.isEqual))return c.isEqual(a);var e=l.call(a);if(e!=l.call(c))return false;switch(e){case "[object String]":return a==String(c);case "[object Number]":return a!=+a?c!=+c:a==0?1/a==1/c:a==+c;case "[object Date]":case "[object Boolean]":return+a==+c;case "[object RegExp]":return a.source== 9 | c.source&&a.global==c.global&&a.multiline==c.multiline&&a.ignoreCase==c.ignoreCase}if(typeof a!="object"||typeof c!="object")return false;for(var f=d.length;f--;)if(d[f]==a)return true;d.push(a);var f=0,g=true;if(e=="[object Array]"){if(f=a.length,g=f==c.length)for(;f--;)if(!(g=f in a==f in c&&q(a[f],c[f],d)))break}else{if("constructor"in a!="constructor"in c||a.constructor!=c.constructor)return false;for(var h in a)if(b.has(a,h)&&(f++,!(g=b.has(c,h)&&q(a[h],c[h],d))))break;if(g){for(h in c)if(b.has(c, 10 | h)&&!f--)break;g=!f}}d.pop();return g}var r=this,G=r._,n={},k=Array.prototype,o=Object.prototype,i=k.slice,H=k.unshift,l=o.toString,I=o.hasOwnProperty,w=k.forEach,x=k.map,y=k.reduce,z=k.reduceRight,A=k.filter,B=k.every,C=k.some,p=k.indexOf,D=k.lastIndexOf,o=Array.isArray,J=Object.keys,s=Function.prototype.bind,b=function(a){return new m(a)};if(typeof exports!=="undefined"){if(typeof module!=="undefined"&&module.exports)exports=module.exports=b;exports._=b}else r._=b;b.VERSION="1.3.1";var j=b.each= 11 | b.forEach=function(a,c,d){if(a!=null)if(w&&a.forEach===w)a.forEach(c,d);else if(a.length===+a.length)for(var e=0,f=a.length;e').appendTo(this.out); 139 | this.output = $('