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import numpy as np
from scipy.stats import zscore
def similarity(X, Y, method):
'''
SIMILARITY Computes similarity matrices
Usage:
sim = similarity(X, Y, method)
Input:
X N1 x M matrix
Y N2 x M matrix
method string defining one of the following similarity measure
'SMC', 'smc' : Simple Matching Coefficient
'Jaccard', 'jac' : Jaccard coefficient
'ExtendedJaccard', 'ext' : The Extended Jaccard coefficient
'Cosine', 'cos' : Cosine Similarity
'Correlation', 'cor' : Correlation coefficient
Output:
sim Estimated similarity matrix between X and Y
If input is not binary, SMC and Jaccard will make each
attribute binary according to x>median(x)
Copyright, Morten Morup and Mikkel N. Schmidt
Technical University of Denmark '''
X = np.mat(X)
Y = np.mat(Y)
N1, M = np.shape(X)
N2, M = np.shape(Y)
method = method[:3].lower()
if method=='smc': # SMC
X,Y = binarize(X,Y);
sim = ((X*Y.T)+((1-X)*(1-Y).T))/M
elif method=='jac': # Jaccard
X,Y = binarize(X,Y);
sim = (X*Y.T)/(M-(1-X)*(1-Y).T)
elif method=='ext': # Extended Jaccard
XYt = X*Y.T
sim = XYt / (np.log( np.exp(sum(np.power(X.T,2))).T * np.exp(sum(np.power(Y.T,2))) ) - XYt)
elif method=='cos': # Cosine
sim = (X*Y.T)/(np.sqrt(sum(np.power(X.T,2))).T * np.sqrt(sum(np.power(Y.T,2))))
elif method=='cor': # Correlation
X_ = zscore(X,axis=1,ddof=1)
Y_ = zscore(Y,axis=1,ddof=1)
sim = (X_*Y_.T)/(M-1)
return sim
def binarize(X,Y=None):
''' Force binary representation of the matrix, according to X>median(X) '''
if Y==None:
X = np.matrix(X)
Xmedians = np.ones((np.shape(X)[0],1)) * np.median(X,0)
Xflags = X>Xmedians
X[Xflags] = 1; X[~Xflags] = 0
return X
else:
X = np.matrix(X); Y = np.matrix(Y);
XYmedian= np.median(np.bmat('X; Y'),0)
Xmedians = np.ones((np.shape(X)[0],1)) * XYmedian
Xflags = X>Xmedians
X[Xflags] = 1; X[~Xflags] = 0
Ymedians = np.ones((np.shape(Y)[0],1)) * XYmedian
Yflags = Y>Ymedians
Y[Yflags] = 1; Y[~Yflags] = 0
return [X,Y]
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