EIGEN SPACE APPROACH Sample Clauses

EIGEN SPACE APPROACH. The simplest way of performing PCA is to create a covariance matrix and find the Eigen vectors and corresponding Eigen values: Z =[ z1−c , z2−c . . . zm−c ] (40) Q=ZZT (41) Where “m” is the number of training images, z1 , z2 . . . zm are the training image’s intensity values of size N ×N , which form a matrix Z, shown above, of size N 2 X N 2 , c represents the average intensity values over all the training images, and Q is the covariance matrix. The Eigen values and Eigen vectors are then extracted from the covariance matrix Q. In practice, these eigenvector / value pairs are found through Singular Value Decomposition (SVD) as other techniques are too slow for very large covariance matrices such as these. This system requires only minor alteration to serve our purposes, as the eigenvectors can be retrieved from the SVD process by reading either the U or V matrices created (Eigenvectors), then taking the singular values, which represent the eigenvalues. The next stage is to find the important eigenvector / value pairs, which should capture a high percentage of the variation in the images, by ranking them. Once done, future images can be projected into the same space by simply: gi=ET  zi−c  Where, E =[ e1 , e2 . . . ek ] (6.24)