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annotate python/ml.py @ 908:b297525b2cbf
added options to the prototype cluster algorithm, work in progress
author | Nicolas Saunier <nicolas.saunier@polymtl.ca> |
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date | Mon, 26 Jun 2017 00:10:35 -0400 |
parents | 9fd7b18f75b4 |
children | 1cd878812529 |
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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 class StatModel(object): |
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23 '''Abstract class for loading/saving model''' |
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24 def load(self, filename): |
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25 if path.exists(filename): |
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26 self.model.load(filename) |
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27 else: |
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28 print('Provided filename {} does not exist: model not loaded!'.format(filename)) |
380 | 29 |
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30 def save(self, filename): |
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31 self.model.save(filename) |
380 | 32 |
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33 class SVM(StatModel): |
380 | 34 '''wrapper for OpenCV SimpleVectorMachine algorithm''' |
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35 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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36 self.model = cv2.SVM() |
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37 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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38 # OpenCV3 |
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39 # self.model = cv2.SVM() |
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40 # self.model.setType(svmType) |
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41 # self.model.setKernel(kernelType) |
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42 # self.model.setDegree(degree) |
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43 # self.model.setGamma(gamma) |
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44 # self.model.setCoef0(coef0) |
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45 # self.model.setC(Cvalue) |
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46 # self.model.setNu(nu) |
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47 # self.model.setP(p) |
380 | 48 |
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49 def train(self, samples, responses): |
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50 self.model.train(samples, responses, params = self.params) |
380 | 51 |
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52 def predict(self, hog): |
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53 return self.model.predict(hog) |
380 | 54 |
55 | |
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56 ##################### |
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57 # Clustering |
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58 ##################### |
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59 |
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60 class Centroid(object): |
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61 'Wrapper around instances to add a counter' |
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62 |
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63 def __init__(self, instance, nInstances = 1): |
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64 self.instance = instance |
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65 self.nInstances = nInstances |
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66 |
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67 # def similar(instance2): |
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68 # return self.instance.similar(instance2) |
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69 |
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70 def add(self, instance2): |
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71 self.instance = self.instance.multiply(self.nInstances)+instance2 |
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72 self.nInstances += 1 |
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73 self.instance = self.instance.multiply(1/float(self.nInstances)) |
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74 |
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75 def average(c): |
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76 inst = self.instance.multiply(self.nInstances)+c.instance.multiply(instance.nInstances) |
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77 inst.multiply(1/(self.nInstances+instance.nInstances)) |
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78 return Centroid(inst, self.nInstances+instance.nInstances) |
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79 |
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80 def plot(self, options = ''): |
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81 self.instance.plot(options) |
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82 text(self.instance.position.x+1, self.instance.position.y+1, str(self.nInstances)) |
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83 |
386 | 84 def kMedoids(similarityMatrix, initialCentroids = None, k = None): |
85 '''Algorithm that clusters any dataset based on a similarity matrix | |
86 Either the initialCentroids or k are passed''' | |
87 pass | |
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88 |
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89 def assignCluster(data, similarFunc, initialCentroids = None, shuffleData = True): |
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90 '''k-means algorithm with similarity function |
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91 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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92 The number of clusters will be determined accordingly |
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93 |
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94 data: list of instances |
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95 averageCentroid: ''' |
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96 localdata = copy(data) # shallow copy to avoid modifying data |
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97 if shuffleData: |
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98 shuffle(localdata) |
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99 if initialCentroids is None: |
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100 centroids = [Centroid(localdata[0])] |
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101 else: |
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102 centroids = deepcopy(initialCentroids) |
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103 for instance in localdata[1:]: |
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104 i = 0 |
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105 while i<len(centroids) and not similarFunc(centroids[i].instance, instance): |
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106 i += 1 |
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107 if i == len(centroids): |
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108 centroids.append(Centroid(instance)) |
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109 else: |
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110 centroids[i].add(instance) |
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111 |
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112 return centroids |
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113 |
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114 # TODO recompute centroids for each cluster: instance that minimizes some measure to all other elements |
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115 |
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116 def spectralClustering(similarityMatrix, k, iter=20): |
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117 '''Spectral Clustering algorithm''' |
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118 n = len(similarityMatrix) |
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119 # create Laplacian matrix |
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120 rowsum = np.sum(similarityMatrix,axis=0) |
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121 D = np.diag(1 / np.sqrt(rowsum)) |
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122 I = np.identity(n) |
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123 L = I - np.dot(D,np.dot(similarityMatrix,D)) |
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124 # compute eigenvectors of L |
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125 U,sigma,V = np.linalg.svd(L) |
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126 # create feature vector from k first eigenvectors |
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127 # by stacking eigenvectors as columns |
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128 features = np.array(V[:k]).T |
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129 # k-means |
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130 features = whiten(features) |
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131 centroids,distortion = kmeans(features,k, iter) |
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132 code,distance = vq(features,centroids) # code starting from 0 (represent first cluster) to k-1 (last cluster) |
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133 return code,sigma |
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134 |
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135 class Cluster: |
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136 'Represents a cluster, with a prototype id and the list of instances in cluster' |
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137 def __init__(prototypeId, memberIndices = []): |
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138 self.prototypeId = prototypeId |
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139 self.memberIndices = memberIndices |
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140 |
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141 def assignToPrototypeClusters(instances, prototypeIndices, similarities, minSimilarity, similarityFunc = None, minClusterSize = None): |
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142 '''Assigns instances to prototypes |
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143 if minClusterSize is not None, the clusters will be refined by removing iteratively the smallest clusters |
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144 and reassigning all elements in the cluster until no cluster is smaller than minClusterSize''' |
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145 indices = [i for i in range(len(instances)) if i not in prototypeIndices] |
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146 labels = [-1]*len(instances) |
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147 assign = True |
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148 while assign: |
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149 for i in prototypeIndices: |
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150 labels[i] = i |
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151 for i in indices: |
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152 if similarityFunc is not None: |
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153 for j in prototypeIndices: |
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154 if similarities[i][j] < 0: |
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155 similarities[i][j] = similarityFunc(instances[i], instances[j]) |
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156 similarities[j][i] = similarities[i][j] |
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157 prototypeIdx = similarities[i][prototypeIndices].argmax() |
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158 if similarities[i][prototypeIndices[prototypeIdx]] >= minSimilarity: |
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159 labels[i] = prototypeIndices[prototypeIdx] |
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160 else: |
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161 labels[i] = -1 # outlier |
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162 clusterSizes = {i: sum(np.array(labels) == i) for i in prototypeIndices} |
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163 smallestClusterIndex = min(clusterSizes, key = clusterSizes.get) |
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164 assign = (clusterSizes[smallestClusterIndex] < minClusterSize) |
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165 if assign: |
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166 prototypeIndices.remove(smallestClusterIndex) |
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167 indices = [i for i in range(similarities.shape[0]) if labels[i] == smallestClusterIndex] |
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168 return prototypeIndices, labels |
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169 |
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170 def prototypeCluster(instances, similarities, minSimilarity, similarityFunc = None, minClusterSize = 0, optimizeCentroid = True, randomInitialization = False, assign = True, initialPrototypeIndices = None): |
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171 '''Finds exemplar (prototype) instance that represent each cluster |
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172 Returns the prototype indices (in the instances list) and the cluster label of each instance |
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173 |
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174 the elements in the instances list must have a length (method __len__), or one can use the random initialization |
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175 the positions in the instances list corresponds to the similarities |
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176 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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177 similarities must still be allocated with the right size |
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178 |
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179 if an instance is different enough (<minSimilarity), |
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180 it will become a new prototype. |
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181 Non-prototype instances will be assigned to an existing prototype |
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182 |
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183 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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184 |
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185 TODO: check how similarity evolves in clusters''' |
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186 if len(instances) == 0: |
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187 print('no instances to cluster (empty list)') |
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188 return None |
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189 if similarityFunc is None: |
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190 print('similarityFunc is None') |
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191 return None |
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192 |
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193 # sort instances based on length |
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194 indices = range(len(instances)) |
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195 if randomInitialization or optimizeCentroid: |
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196 indices = np.random.permutation(indices) |
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197 else: |
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198 def compare(i, j): |
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199 if len(instances[i]) > len(instances[j]): |
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200 return -1 |
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201 elif len(instances[i]) == len(instances[j]): |
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202 return 0 |
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203 else: |
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204 return 1 |
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205 indices.sort(compare) |
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206 # go through all instances |
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207 clusters = [] |
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208 if initialPrototypeIndices is None: |
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209 prototypeIndices = [indices[0]] |
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210 else: |
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211 prototypeIndices = initialPrototypeIndices # think of the format: if indices, have to be in instances |
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212 for i in prototypeIndices: |
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213 clusters.append([i]) |
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214 for i in indices[1:]: |
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215 for j in prototypeIndices: |
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216 if similarities[i][j] < 0: |
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217 similarities[i][j] = similarityFunc(instances[i], instances[j]) |
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218 similarities[j][i] = similarities[i][j] |
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219 label = similarities[i][prototypeIndices].argmax() |
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220 if similarities[i][prototypeIndices[label]] < minSimilarity: |
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221 prototypeIndices.append(i) |
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222 clusters.append([]) |
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223 else: |
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224 clusters[label].append(i) |
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225 if optimizeCentroid: |
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226 if len(clusters[label]) >= 2: # no point if only one element in cluster |
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227 for j in clusters[label][:-1]: |
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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 clusterIndices = clusters[label] |
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232 clusterSimilarities = similarities[clusterIndices][:,clusterIndices] |
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233 newCentroidIdx = clusterIndices[clusterSimilarities.sum(0).argmax()] |
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234 if prototypeIndices[label] != newCentroidIdx: |
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235 prototypeIndices[label] = newCentroidIdx |
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236 elif randomInitialization: # replace prototype by current instance i if longer |
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237 if len(instances[prototypeIndices[label]]) < len(instances[i]): |
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238 prototypeIndices[label] = i |
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239 |
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240 if assign: |
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241 return assignToPrototypeClusters(instances, prototypeIndices, similarities, minSimilarity, similarityFunc, minClusterSize) |
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242 else: |
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243 return prototypeIndices, None |
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244 |
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245 def computeClusterSizes(labels, prototypeIndices, outlierIndex = -1): |
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246 clusterSizes = {i: sum(np.array(labels) == i) for i in prototypeIndices} |
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247 clusterSizes['outlier'] = sum(np.array(labels) == outlierIndex) |
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248 return clusterSizes |
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249 |
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250 def computeClusterStatistics(labels, prototypeIndices, instances, similarities, similarityFunc, clusters = None, outlierIndex = -1): |
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251 if clusters is None: |
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252 clusters = {protoId:[] for protoId in prototypeIndices+[-1]} |
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253 for i,l in enumerate(labels): |
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254 clusters[l].append(i) |
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255 clusters = [clusters[protoId] for protoId in prototypeIndices] |
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256 for i, cluster in enumerate(clusters): |
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257 n = len(cluster) |
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258 print('cluster {}: {} elements'.format(prototypeIndices[i], n)) |
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259 if n >=2: |
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260 for j,k in enumerate(cluster): |
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261 for l in cluster[:j]: |
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262 if similarities[k][l] < 0: |
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263 similarities[k][l] = similarityFunc(instances[k], instances[l]) |
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264 similarities[l][k] = similarities[k][l] |
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265 print('Mean similarity to prototype: {}'.format((similarities[prototypeIndices[i]][cluster].sum()+1)/(n-1))) |
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266 print('Mean overall similarity: {}'.format((similarities[cluster][:,cluster].sum()+n)/(n*(n-1)))) |
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267 |
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268 # Gaussian Mixture Models |
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269 def plotGMMClusters(model, dataset = None, fig = None, colors = utils.colors, nUnitsPerPixel = 1., alpha = 0.3): |
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270 '''plot the ellipse corresponding to the Gaussians |
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271 and the predicted classes of the instances in the dataset''' |
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272 if fig is None: |
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273 fig = plt.figure() |
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274 labels = model.predict(dataset) |
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275 tmpDataset = dataset/nUnitsPerPixel |
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276 for i in xrange(model.n_components): |
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277 mean = model.means_[i]/nUnitsPerPixel |
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278 covariance = model.covars_[i]/nUnitsPerPixel |
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279 if dataset is not None: |
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280 plt.scatter(tmpDataset[labels == i, 0], tmpDataset[labels == i, 1], .8, color=colors[i]) |
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281 plt.annotate(str(i), xy=(mean[0]+1, mean[1]+1)) |
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282 |
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283 # Plot an ellipse to show the Gaussian component |
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284 v, w = np.linalg.eigh(covariance) |
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285 angle = np.arctan2(w[0][1], w[0][0]) |
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286 angle = 180*angle/np.pi # convert to degrees |
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287 v *= 4 |
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288 ell = mpl.patches.Ellipse(mean, v[0], v[1], 180+angle, color=colors[i]) |
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289 ell.set_clip_box(fig.bbox) |
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290 ell.set_alpha(alpha) |
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291 fig.axes[0].add_artist(ell) |
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292 return labels |