%0 Journal Article
%T Compression of Breast Cancer Images By Principal Component Analysis
%J International Journal of Advanced Biological and Biomedical Research
%I Sami Publishing Company
%Z 2383-2762
%A Saraswat, Monika
%A Wadhwani, A. K.
%A Dubey, Manish
%D 2013
%\ 07/01/2013
%V 1
%N 7
%P 767-776
%! Compression of Breast Cancer Images By Principal Component Analysis
%K SNR
%K MSE
%K PSNR
%K Mammograms
%K PCA
%R
%X The principle of dimensionality reduction with PCA is the representation of the dataset ‘X’in terms of eigenvectors ei ∈ RN of its covariance matrix. The eigenvectors oriented in the direction with the maximum variance of X in RN carry the most relevant information of X. These eigenvectors are called principal components [8]. Assume that n images in a set are originally represented in matrix form as Ui∈ Rr ×c, i = 1,......,n, where r and c are, repetitively, the number of rows and columns of the matrix. In vectorized representation (matrix-to-vector alignment) each Ui is a N = r × c- dimensional vector ai computed by sequentially concatenating all of the lines of the matrix Ui. To compute the Principal Components the covariance matrix of U is formed and Eigen values, with the corresponding eigenvectors, are evaluated. The Eigen vectors forms a set of linearly independent vectors, i.e., the base {φ} n i=1 which consist of a new axis system [10]
%U http://www.ijabbr.com/article_7803_c1bfed921b1cb6eddb3d3d9a00f75143.pdf