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annotate python/ml.py @ 968:32a34a143c27
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author | Nicolas Saunier <nicolas.saunier@polymtl.ca> |
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date | Thu, 07 Dec 2017 15:13:06 -0500 |
parents | ec1682ed999f |
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1 #! /usr/bin/env python |
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2 '''Libraries for machine learning algorithms''' |
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3 |
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4 from os import path |
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5 from random import shuffle |
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6 from copy import copy, deepcopy |
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7 |
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8 import numpy as np |
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9 from matplotlib.pylab import text |
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10 import matplotlib as mpl |
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11 import matplotlib.pyplot as plt |
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12 from scipy.cluster.vq import kmeans, whiten, vq |
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13 from sklearn import mixture |
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14 import cv2 |
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15 |
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16 import utils |
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17 |
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18 ##################### |
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19 # OpenCV ML models |
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20 ##################### |
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21 |
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22 def computeConfusionMatrix(model, samples, responses): |
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23 'computes the confusion matrix of the classifier (model)' |
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24 classifications = {} |
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25 for x,y in zip(samples, responses): |
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26 predicted = model.predict(x) |
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27 classifications[(y, predicted)] = classifications.get((y, predicted), 0)+1 |
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28 return classifications |
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29 |
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30 class StatModel(object): |
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31 '''Abstract class for loading/saving model''' |
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32 def load(self, filename): |
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33 if path.exists(filename): |
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34 self.model.load(filename) |
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35 else: |
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36 print('Provided filename {} does not exist: model not loaded!'.format(filename)) |
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38 def save(self, filename): |
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39 self.model.save(filename) |
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41 class SVM(StatModel): |
380 | 42 '''wrapper for OpenCV SimpleVectorMachine algorithm''' |
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43 def __init__(self, svmType = cv2.SVM_C_SVC, kernelType = cv2.SVM_RBF, degree = 0, gamma = 1, coef0 = 0, Cvalue = 1, nu = 0, p = 0): |
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44 self.model = cv2.SVM() |
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45 self.params = dict(svm_type = svmType, kernel_type = kernelType, degree = degree, gamma = gamma, coef0 = coef0, Cvalue = Cvalue, nu = nu, p = p) |
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46 # OpenCV3 |
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47 # self.model = cv2.SVM() |
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48 # self.model.setType(svmType) |
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49 # self.model.setKernel(kernelType) |
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50 # self.model.setDegree(degree) |
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51 # self.model.setGamma(gamma) |
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52 # self.model.setCoef0(coef0) |
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53 # self.model.setC(Cvalue) |
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54 # self.model.setNu(nu) |
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55 # self.model.setP(p) |
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57 def train(self, samples, responses, computePerformance = False): |
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58 self.model.train(samples, responses, params = self.params) |
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59 if computePerformance: |
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60 return computeConfusionMatrix(self, samples, responses) |
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62 def predict(self, hog): |
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63 return self.model.predict(hog) |
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65 | |
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66 ##################### |
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67 # Clustering |
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68 ##################### |
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69 |
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70 class Centroid(object): |
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71 'Wrapper around instances to add a counter' |
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72 |
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73 def __init__(self, instance, nInstances = 1): |
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74 self.instance = instance |
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75 self.nInstances = nInstances |
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76 |
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77 # def similar(instance2): |
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78 # return self.instance.similar(instance2) |
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79 |
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80 def add(self, instance2): |
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81 self.instance = self.instance.multiply(self.nInstances)+instance2 |
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82 self.nInstances += 1 |
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83 self.instance = self.instance.multiply(1/float(self.nInstances)) |
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84 |
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85 def average(c): |
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86 inst = self.instance.multiply(self.nInstances)+c.instance.multiply(instance.nInstances) |
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87 inst.multiply(1/(self.nInstances+instance.nInstances)) |
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88 return Centroid(inst, self.nInstances+instance.nInstances) |
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89 |
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90 def plot(self, options = ''): |
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91 self.instance.plot(options) |
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92 text(self.instance.position.x+1, self.instance.position.y+1, str(self.nInstances)) |
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93 |
386 | 94 def kMedoids(similarityMatrix, initialCentroids = None, k = None): |
95 '''Algorithm that clusters any dataset based on a similarity matrix | |
96 Either the initialCentroids or k are passed''' | |
97 pass | |
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98 |
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99 def assignCluster(data, similarFunc, initialCentroids = None, shuffleData = True): |
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100 '''k-means algorithm with similarity function |
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101 Two instances should be in the same cluster if the sameCluster function returns true for two instances. It is supposed that the average centroid of a set of instances can be computed, using the function. |
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102 The number of clusters will be determined accordingly |
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103 |
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104 data: list of instances |
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105 averageCentroid: ''' |
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106 localdata = copy(data) # shallow copy to avoid modifying data |
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107 if shuffleData: |
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108 shuffle(localdata) |
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109 if initialCentroids is None: |
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110 centroids = [Centroid(localdata[0])] |
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111 else: |
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112 centroids = deepcopy(initialCentroids) |
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113 for instance in localdata[1:]: |
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114 i = 0 |
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115 while i<len(centroids) and not similarFunc(centroids[i].instance, instance): |
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116 i += 1 |
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117 if i == len(centroids): |
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118 centroids.append(Centroid(instance)) |
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119 else: |
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120 centroids[i].add(instance) |
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121 |
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122 return centroids |
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123 |
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124 # TODO recompute centroids for each cluster: instance that minimizes some measure to all other elements |
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125 |
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126 def spectralClustering(similarityMatrix, k, iter=20): |
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127 '''Spectral Clustering algorithm''' |
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128 n = len(similarityMatrix) |
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129 # create Laplacian matrix |
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130 rowsum = np.sum(similarityMatrix,axis=0) |
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131 D = np.diag(1 / np.sqrt(rowsum)) |
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132 I = np.identity(n) |
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133 L = I - np.dot(D,np.dot(similarityMatrix,D)) |
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134 # compute eigenvectors of L |
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135 U,sigma,V = np.linalg.svd(L) |
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136 # create feature vector from k first eigenvectors |
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137 # by stacking eigenvectors as columns |
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138 features = np.array(V[:k]).T |
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139 # k-means |
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140 features = whiten(features) |
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141 centroids,distortion = kmeans(features,k, iter) |
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142 code,distance = vq(features,centroids) # code starting from 0 (represent first cluster) to k-1 (last cluster) |
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143 return code,sigma |
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144 |
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145 class Cluster: |
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146 'Represents a cluster, with a prototype id and the list of instances in cluster' |
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147 def __init__(prototypeId, memberIndices = []): |
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148 self.prototypeId = prototypeId |
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149 self.memberIndices = memberIndices |
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150 |
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151 def assignToPrototypeClusters(instances, prototypeIndices, similarities, minSimilarity, similarityFunc = None, minClusterSize = 0): |
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152 '''Assigns instances to prototypes |
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153 if minClusterSize is not None, the clusters will be refined by removing iteratively the smallest clusters |
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154 and reassigning all elements in the cluster until no cluster is smaller than minClusterSize''' |
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155 indices = [i for i in range(len(instances)) if i not in prototypeIndices] |
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156 labels = [-1]*len(instances) |
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157 assign = True |
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158 while assign: |
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159 for i in prototypeIndices: |
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160 labels[i] = i |
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161 for i in indices: |
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162 if similarityFunc is not None: |
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163 for j in prototypeIndices: |
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164 if similarities[i][j] < 0: |
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165 similarities[i][j] = similarityFunc(instances[i], instances[j]) |
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166 similarities[j][i] = similarities[i][j] |
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167 prototypeIdx = similarities[i][prototypeIndices].argmax() |
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168 if similarities[i][prototypeIndices[prototypeIdx]] >= minSimilarity: |
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169 labels[i] = prototypeIndices[prototypeIdx] |
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170 else: |
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171 labels[i] = -1 # outlier |
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172 clusterSizes = {i: sum(np.array(labels) == i) for i in prototypeIndices} |
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173 smallestClusterIndex = min(clusterSizes, key = clusterSizes.get) |
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174 assign = (clusterSizes[smallestClusterIndex] < minClusterSize) |
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175 if assign: |
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176 prototypeIndices.remove(smallestClusterIndex) |
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177 indices = [i for i in range(similarities.shape[0]) if labels[i] == smallestClusterIndex] |
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178 return prototypeIndices, labels |
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179 def prototypeCluster(instances, similarities, minSimilarity, similarityFunc = None, optimizeCentroid = True, randomInitialization = False, initialPrototypeIndices = None): |
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180 '''Finds exemplar (prototype) instance that represent each cluster |
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181 Returns the prototype indices (in the instances list) |
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182 |
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183 the elements in the instances list must have a length (method __len__), or one can use the random initialization |
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184 the positions in the instances list corresponds to the similarities |
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185 if similarityFunc is provided, the similarities are calculated as needed (this is faster) if not in similarities (negative if not computed) |
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186 similarities must still be allocated with the right size |
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187 |
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188 if an instance is different enough (<minSimilarity), |
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189 it will become a new prototype. |
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190 Non-prototype instances will be assigned to an existing prototype |
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191 |
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192 if optimizeCentroid is True, each time an element is added, we recompute the centroid trajectory as the most similar to all in the cluster |
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193 |
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194 initialPrototypeIndices are indices in instances |
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195 |
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196 TODO: check how similarity evolves in clusters''' |
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197 if len(instances) == 0: |
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198 print('no instances to cluster (empty list)') |
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199 return None |
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200 if similarityFunc is None: |
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201 print('similarityFunc is None') |
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202 return None |
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203 |
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204 # sort instances based on length |
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205 indices = range(len(instances)) |
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206 if randomInitialization or optimizeCentroid: |
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207 indices = np.random.permutation(indices) |
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208 else: |
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209 def compare(i, j): |
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210 if len(instances[i]) > len(instances[j]): |
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211 return -1 |
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212 elif len(instances[i]) == len(instances[j]): |
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213 return 0 |
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214 else: |
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215 return 1 |
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216 indices.sort(compare) |
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217 # go through all instances |
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218 clusters = [] |
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219 if initialPrototypeIndices is None: |
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220 prototypeIndices = [indices[0]] |
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221 else: |
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222 prototypeIndices = initialPrototypeIndices # think of the format: if indices, have to be in instances |
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223 for i in prototypeIndices: |
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224 clusters.append([i]) |
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225 indices.remove(i) |
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226 for i in indices: |
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227 for j in prototypeIndices: |
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228 if similarities[i][j] < 0: |
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229 similarities[i][j] = similarityFunc(instances[i], instances[j]) |
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230 similarities[j][i] = similarities[i][j] |
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231 label = similarities[i][prototypeIndices].argmax() |
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232 if similarities[i][prototypeIndices[label]] < minSimilarity: |
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233 prototypeIndices.append(i) |
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234 clusters.append([]) |
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235 else: |
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236 clusters[label].append(i) |
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237 if optimizeCentroid: |
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238 if len(clusters[label]) >= 2: # no point if only one element in cluster |
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239 for j in clusters[label][:-1]: |
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240 if similarities[i][j] < 0: |
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241 similarities[i][j] = similarityFunc(instances[i], instances[j]) |
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242 similarities[j][i] = similarities[i][j] |
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243 clusterIndices = clusters[label] |
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244 clusterSimilarities = similarities[clusterIndices][:,clusterIndices] |
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245 newCentroidIdx = clusterIndices[clusterSimilarities.sum(0).argmax()] |
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246 if prototypeIndices[label] != newCentroidIdx: |
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247 prototypeIndices[label] = newCentroidIdx |
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248 elif len(instances[prototypeIndices[label]]) < len(instances[i]): # replace prototype by current instance i if longer # otherwise, possible to test if randomInitialization or initialPrototypes is not None |
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249 prototypeIndices[label] = i |
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250 return prototypeIndices |
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251 |
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252 def computeClusterSizes(labels, prototypeIndices, outlierIndex = -1): |
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253 clusterSizes = {i: sum(np.array(labels) == i) for i in prototypeIndices} |
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254 clusterSizes['outlier'] = sum(np.array(labels) == outlierIndex) |
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255 return clusterSizes |
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256 |
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257 def computeClusterStatistics(labels, prototypeIndices, instances, similarities, similarityFunc, clusters = None, outlierIndex = -1): |
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258 if clusters is None: |
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259 clusters = {protoId:[] for protoId in prototypeIndices+[-1]} |
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260 for i,l in enumerate(labels): |
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261 clusters[l].append(i) |
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262 clusters = [clusters[protoId] for protoId in prototypeIndices] |
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263 for i, cluster in enumerate(clusters): |
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264 n = len(cluster) |
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265 print('cluster {}: {} elements'.format(prototypeIndices[i], n)) |
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266 if n >=2: |
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267 for j,k in enumerate(cluster): |
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268 for l in cluster[:j]: |
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269 if similarities[k][l] < 0: |
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270 similarities[k][l] = similarityFunc(instances[k], instances[l]) |
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271 similarities[l][k] = similarities[k][l] |
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272 print('Mean similarity to prototype: {}'.format((similarities[prototypeIndices[i]][cluster].sum()+1)/(n-1))) |
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273 print('Mean overall similarity: {}'.format((similarities[cluster][:,cluster].sum()+n)/(n*(n-1)))) |
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274 |
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275 # Gaussian Mixture Models |
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276 def plotGMM(mean, covariance, gmmId, fig, color, alpha = 0.3): |
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277 v, w = np.linalg.eigh(covariance) |
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278 angle = 180*np.arctan2(w[0][1], w[0][0])/np.pi |
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279 v *= 4 |
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280 ell = mpl.patches.Ellipse(mean, v[0], v[1], 180+angle, color=color) |
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281 ell.set_clip_box(fig.bbox) |
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282 ell.set_alpha(alpha) |
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283 fig.axes[0].add_artist(ell) |
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284 plt.plot([mean[0]], [mean[1]], 'x'+color) |
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285 plt.annotate(str(gmmId), xy=(mean[0]+1, mean[1]+1)) |
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286 |
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287 def plotGMMClusters(model, labels = None, dataset = None, fig = None, colors = utils.colors, nUnitsPerPixel = 1., alpha = 0.3): |
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288 '''plot the ellipse corresponding to the Gaussians |
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289 and the predicted classes of the instances in the dataset''' |
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290 if fig is None: |
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291 fig = plt.figure() |
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292 if len(fig.get_axes()) == 0: |
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293 fig.add_subplot(111) |
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294 for i in xrange(model.n_components): |
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295 mean = model.means_[i]/nUnitsPerPixel |
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296 covariance = model.covariances_[i]/nUnitsPerPixel |
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297 # plot points |
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298 if dataset is not None: |
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299 tmpDataset = dataset/nUnitsPerPixel |
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300 plt.scatter(tmpDataset[labels == i, 0], tmpDataset[labels == i, 1], .8, color=colors[i]) |
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301 # plot an ellipse to show the Gaussian component |
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302 plotGMM(mean, covariance, i, fig, colors[i], alpha) |
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303 if dataset is None: # to address issues without points, the axes limits are not redrawn |
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304 minima = model.means_.min(0) |
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305 maxima = model.means_.max(0) |
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306 xwidth = 0.5*(maxima[0]-minima[0]) |
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307 ywidth = 0.5*(maxima[1]-minima[1]) |
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308 plt.xlim(minima[0]-xwidth,maxima[0]+xwidth) |
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309 plt.ylim(minima[1]-ywidth,maxima[1]+ywidth) |