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reorg and work in progress
author Nicolas Saunier <nicolas.saunier@polymtl.ca>
date Tue, 04 Jul 2017 18:00:01 -0400
parents 7345f0d51faa
children d6c1c05d11f5
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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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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))
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29
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30 def save(self, filename):
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31 self.model.save(filename)
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33 class SVM(StatModel):
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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)
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48
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49 def train(self, samples, responses):
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50 self.model.train(samples, responses, params = self.params)
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51
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52 def predict(self, hog):
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53 return self.model.predict(hog)
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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
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84 def kMedoids(similarityMatrix, initialCentroids = None, k = None):
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85 '''Algorithm that clusters any dataset based on a similarity matrix
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86 Either the initialCentroids or k are passed'''
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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
563
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134
908
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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
907
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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
908
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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
908
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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
908
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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
908
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193 # sort instances based on length
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194 indices = range(len(instances))
908
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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 = []
907
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208 if initialPrototypeIndices is None:
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209 prototypeIndices = [indices[0]]
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210 else:
908
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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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diff changeset
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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diff changeset
226 if len(clusters[label]) >= 2: # no point if only one element in cluster
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diff changeset
227 for j in clusters[label][:-1]:
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diff changeset
228 if similarities[i][j] < 0:
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diff changeset
229 similarities[i][j] = similarityFunc(instances[i], instances[j])
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diff changeset
230 similarities[j][i] = similarities[i][j]
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diff changeset
231 clusterIndices = clusters[label]
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diff changeset
232 clusterSimilarities = similarities[clusterIndices][:,clusterIndices]
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diff changeset
233 newCentroidIdx = clusterIndices[clusterSimilarities.sum(0).argmax()]
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diff changeset
234 if prototypeIndices[label] != newCentroidIdx:
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diff changeset
235 prototypeIndices[label] = newCentroidIdx
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diff changeset
236 elif randomInitialization: # replace prototype by current instance i if longer
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diff changeset
237 if len(instances[prototypeIndices[label]]) < len(instances[i]):
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diff changeset
238 prototypeIndices[label] = i
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diff changeset
239
907
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240 if assign:
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diff changeset
241 return assignToPrototypeClusters(instances, prototypeIndices, similarities, minSimilarity, similarityFunc, minClusterSize)
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242 else:
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diff changeset
243 return prototypeIndices, None
738
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244
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diff changeset
245 def computeClusterSizes(labels, prototypeIndices, outlierIndex = -1):
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diff changeset
246 clusterSizes = {i: sum(np.array(labels) == i) for i in prototypeIndices}
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diff changeset
247 clusterSizes['outlier'] = sum(np.array(labels) == outlierIndex)
738
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diff changeset
248 return clusterSizes
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diff changeset
249
908
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diff changeset
250 def computeClusterStatistics(labels, prototypeIndices, instances, similarities, similarityFunc, clusters = None, outlierIndex = -1):
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diff changeset
251 if clusters is None:
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diff changeset
252 clusters = {protoId:[] for protoId in prototypeIndices+[-1]}
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diff changeset
253 for i,l in enumerate(labels):
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diff changeset
254 clusters[l].append(i)
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diff changeset
255 clusters = [clusters[protoId] for protoId in prototypeIndices]
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Nicolas Saunier <nicolas.saunier@polymtl.ca>
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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 plotGMM(mean, covariance, gmmId, fig, color, alpha = 0.3):
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270 v, w = np.linalg.eigh(covariance)
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271 angle = 180*np.arctan2(w[0][1], w[0][0])/np.pi
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272 v *= 4
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273 ell = mpl.patches.Ellipse(mean, v[0], v[1], 180+angle, color=color)
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274 ell.set_clip_box(fig.bbox)
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275 ell.set_alpha(alpha)
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276 fig.axes[0].add_artist(ell)
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277 plt.plot([mean[0]], [mean[1]], 'x'+color)
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278 plt.annotate(str(gmmId), xy=(mean[0]+1, mean[1]+1))
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279
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280 def plotGMMClusters(model, labels = None, dataset = None, fig = None, colors = utils.colors, nUnitsPerPixel = 1., alpha = 0.3):
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281 '''plot the ellipse corresponding to the Gaussians
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282 and the predicted classes of the instances in the dataset'''
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283 if fig is None:
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284 fig = plt.figure()
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285 if len(fig.get_axes()) == 0:
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286 fig.add_subplot(111)
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287 for i in xrange(model.n_components):
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288 mean = model.means_[i]/nUnitsPerPixel
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289 covariance = model.covariances_[i]/nUnitsPerPixel
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290 # plot points
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291 if dataset is not None:
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292 tmpDataset = dataset/nUnitsPerPixel
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293 plt.scatter(tmpDataset[labels == i, 0], tmpDataset[labels == i, 1], .8, color=colors[i])
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294 # plot an ellipse to show the Gaussian component
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295 plotGMM(mean, covariance, i, fig, colors[i], alpha)
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296 if dataset is None: # to address issues without points, the axes limits are not redrawn
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297 minima = model.means_.min(0)
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298 maxima = model.means_.max(0)
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299 xwidth = 0.5*(maxima[0]-minima[0])
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300 ywidth = 0.5*(maxima[1]-minima[1])
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301 plt.xlim(minima[0]-xwidth,maxima[0]+xwidth)
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302 plt.ylim(minima[1]-ywidth,maxima[1]+ywidth)