Principal Component Analysis using Singular Value Decomposition for Image Compression

ABSTRACT Principal components analysis (PCA) is one of a family of techniques for taking high-dimensional data, and using the dependencies between the variables to represent it in a more tractable, lower-dimensional form, without losing too much information. PCA is one of the simplest and most robust ways of doing such dimensionality reduction. It is also one of the best, and has been rediscovered many times in many fields, so it is also known as the Karhunen-Lo_eve transformation, the Hotelling transformation, the method of empirical orthogonal functions, and singular value decomposition. General Terms n v ariances, covariance, symmetric matrix, identity matrix, orthogonal matrix, diagonal matrix variables are identical. It is in fact correct to div Keywords Principal Component Analysis (PCA), Singular Value decomposition (SVD) 1. INTRODUCTION Assume the data set is represented in terms of m×n matrix. Let the data set is X where m is considered as columns of the samples i.e. observations and n is considered as the variables. To transform the matrix in linear form i.e. X to another matrix Y having same dimension i.e. m×n, so that for some m×m matrix P i.e.