From dc77e1c88e7973ef2b7ec3afa2d22ec830a82dbe Mon Sep 17 00:00:00 2001
From: Camil Staps
Date: Mon, 21 Sep 2015 15:17:40 +0200
Subject: Assignment 1 continuing, only 1.2.2c-e to be done

---
 Assignment 1/similarity.py | 72 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 72 insertions(+)
 create mode 100644 Assignment 1/similarity.py

(limited to 'Assignment 1/similarity.py')

diff --git a/Assignment 1/similarity.py b/Assignment 1/similarity.py
new file mode 100644
index 0000000..4a49317
--- /dev/null
+++ b/Assignment 1/similarity.py	
@@ -0,0 +1,72 @@
+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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