Error - Calculating Euclidean distance for PCA in python

Question

I am trying to implement face recognition by Principal Component Analysis (PCA) using python. I am following the steps in this tutorial: http://onionesquereality.wordpress.com/2009/02/11/face-recognition-using-eigenfaces-and-distance-classifiers-a-tutorial/

Here is my code:

import os
from PIL import Image
import numpy as np
import glob
import numpy.linalg as linalg


#Step1: put database images into a 2D array
filenames = glob.glob('C:\\Users\\Karim\\Downloads\\att_faces\\New folder/*.pgm')
filenames.sort()
img = [Image.open(fn).convert('L').resize((90, 90)) for fn in filenames]
images = np.asarray([np.array(im).flatten() for im in img])


#Step 2: find the mean image and the mean-shifted input images
mean_image = images.mean(axis=0)
shifted_images = images - mean_image


#Step 3: Covariance
c = np.cov(shifted_images)


#Step 4: Sorted eigenvalues and eigenvectors
eigenvalues,eigenvectors = linalg.eig(c)
idx = np.argsort(-eigenvalues)
eigenvalues = eigenvalues[idx]
eigenvectors = eigenvectors[:, idx]


#Step 5: Only keep the top 'num_eigenfaces' eigenvectors
num_components = 20
eigenvalues = eigenvalues[0:num_components].copy()
eigenvectors = eigenvectors[:, 0:num_components].copy()


#Step 6: Finding weights
w = eigenvectors.T * np.asmatrix(shifted_images)


#Step 7: Input image
input_image = Image.open('C:\\Users\\Karim\\Downloads\\att_faces\\1.pgm').convert('L').resize((90, 90))
input_image = np.asarray(input_image).flatten()


#Step 8: get the normalized image, covariance, eigenvalues and eigenvectors for input image
shifted_in = input_image - mean_image
c = np.cov(input_image)
cmat = c.reshape(1,1)
eigenvalues_in, eigenvectors_in = linalg.eig(cmat)


#Step 9: Fing weights of input image
w_in = eigenvectors_in.T * np.asmatrix(shifted_in)
print w_in
print w_in.shape

#Step 10: Euclidean distance
d = np.sqrt(np.sum((w - w_in)**2))
idx = np.argmin(d)
match = images[idx]

I am havin a problem in Step 10 as I am getting this error: Traceback (most recent call last): File "C:/Users/Karim/Desktop/Bachelor 2/New folder/new3.py", line 59, in <module> d = np.sqrt(np.sum((w - w_in)**2)) File "C:\Python27\lib\site-packages\numpy\matrixlib\defmatrix.py", line 343, in __pow__ return matrix_power(self, other) File "C:\Python27\lib\site-packages\numpy\matrixlib\defmatrix.py", line 160, in matrix_power raise ValueError("input must be a square array") ValueError: input must be a square array

Anyone can help??

Answer 1

I think you want to change the line where you calculate d to something like this:

#Step 10: Euclidean distance
d = np.sqrt(np.sum(np.asarray(w - w_in)**2, axis=1)

This gives you a list of length M (number of training images) of the squared, summed, rooted distances between each images pixels. I believe that you don't want the matrix product, you want the elementwise square of each value, hence the np.asarray to make it not a matrix. This gives you the 'euclidean' difference between w_in and each of the w matrices.

Answer 2

When you go (w - w_in), the result is not a square matrix. To multiply a matrix by itself it must be square (that's just a property of matrix multiplication). So either you've constructed your w and w_in matrices wrong, or what you actually meant to do is square each element in the matrix (w - w_in) which is a different operation. Search for element-wise multiplication to find the numpy syntax.