Final code.

Author: clamesc

Exercise 2/.ipynb_checkpoints/Exercise 2 heartDataSet-checkpoint.ipynb

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+# -*- coding: utf-8 -*-
+"""
+Created on Tue Apr 19 16:39:22 2016
+
+@author: qwertzuiopu
+"""
+
+import numpy as np
+import scipy.io as sio
+
+def usingSVD(dataMatrix, desiredVariancePercentage=1.0):
+    # This function should implement the PCA using the Singular Value
+    # Decomposition (SVD) of the given dataMatrix
+    
+    # De-Meaning the feature space
+    meanDataMatrix = dataMatrix.mean(1)
+    demeanedDataMatrix = (dataMatrix.T - meanDataMatrix)
+    
+    # SVD Decomposition
+    # You need to transpose the data matrix
+    U, s, V = np.linalg.svd(demeanedDataMatrix / np.sqrt(dataMatrix.shape[1]-1)) # Divide by sqrt(N-1) to get consistent results
+    V = V.T     # Numpy gives V transposed
+    
+    # Enforce a sign convention on the coefficients -- the largest element (absolute) in each
+    # column will have a positive sign.
+    for i in range(V.shape[0]):
+        if V[:,i][np.argmax(np.fabs(V[:,i]))] < 0:
+            V[:,i] = -V[:,i]
+            
+    # Compute the accumelative Eigenvalues to finde the desired
+    # Variance
+    s = s**2
+    acc_eigenvals = np.sum(s)
+    
+    # Keep the eigenvectors and eigenvalues of the desired
+    # variance, i.e. keep the first two eigenvectors and
+    # eigenvalues if they have 90% of variance.
+    for i in range(s.shape[0]):
+        if np.sum(s[:i+1])/acc_eigenvals >= desiredVariancePercentage:
+            eigenvals = s[:i+1]
+            eigenvecs = V[:,:i+1]
+            break
+    
+    # Project the data
+    projectedData = np.dot(demeanedDataMatrix, eigenvecs)
+    
+    # Return Data
+    return eigenvecs, eigenvals, meanDataMatrix, demeanedDataMatrix.T, projectedData.T
+ 
+def usingCOV(dataMatrix, desiredVariancePercentage=1.0):
+    # This function should implement the PCA using the
+    # EigenValue Decomposition of a given Covariance Matrix 
+    
+    # De-Meaning the feature space 
+    meanDataMatrix = dataMatrix.mean(1)
+    demeanedDataMatrix = (dataMatrix.T - meanDataMatrix)
+            
+    # Computing the Covariance 
+    covMatrix = np.dot(demeanedDataMatrix.T, demeanedDataMatrix)
+            
+    # Eigen Value Decomposition
+    # In COV, you need to order the eigevectors according to largest eigenvalues
+    eigenValues, eigenVectors = np.linalg.eig(covMatrix / (dataMatrix.shape[1] - 1))
+    idx = eigenValues.argsort()[::-1]
+    eigenValues = eigenValues[idx]
+    eigenVectors = eigenVectors[:,idx]
+    
+    # Enforce a sign convention on the coefficients -- the largest element (absolute) in each
+    # column will have a positive sign.
+    for i in range(eigenVectors.shape[0]):
+        if eigenVectors[:,i][np.argmax(np.fabs(eigenVectors[:,i]))] < 0:
+            eigenVectors[:,i] = -eigenVectors[:,i]
+
+
+    # Compute the accumelative Eigenvalues to finde the desired
+    # Variance 
+    acc_eigenvals = np.sum(eigenValues)
+            
+    # Keep the eigenvectors and eigenvalues of the desired
+    # variance, i.e. keep the first two eigenvectors and
+    # eigenvalues if they have 90% of variance. 
+    for i in range(eigenValues.shape[0]):
+        if np.sum(eigenValues[:i+1])/acc_eigenvals >= desiredVariancePercentage:
+            eigenvals = eigenValues[:i+1]
+            eigenvecs = eigenVectors[:,:i+1]
+            break
+            
+    # Project the data 
+    projectedData = np.dot(demeanedDataMatrix, eigenvecs)
+    
+    # Return data
+    return eigenvecs, eigenvals, meanDataMatrix, demeanedDataMatrix.T, projectedData.T