Lecture 7 Multivariate Signal Analysis (Processing)and Biomedical Applications Prof.N.Rao
Prof. N. Rao Lecture 7 Multivariate Signal Analysis (Processing) and Biomedical Applications
Part 1:Singular Value Decomposition (SVD)and Applications
Part 1: Singular Value Decomposition (SVD) and Applications
Outline 。Introduction Significance and Motivation Mathematical definition of the SVD .Illustrative applications .SVD analysis of gene expression data ●Discussion
Introduction Significance and Motivation Mathematical definition of the SVD Illustrative applications SVD analysis of gene expression data Discussion Outline
Introduction .The goal of this chapter is to provide precise explanations of the use of SVD and PCA for gene expression analysis; Illustrating methods using simple examples
Introduction The goal of this chapter is to provide precise explanations of the use of SVD and PCA for gene expression analysis; Illustrating methods using simple examples
Mathematical definition of the SVD Let X denote an mx n matrix of real-valued data and rank r,where without loss of generality mn, and therefore r≤n. is the element value of the ith row in the jth column. The equation for singular value decomposition of X is the following: X=USVT (5.1)
Mathematical definition of the SVD Let X denote an m × n matrix of real-valued data and rank r, where without loss of generality m ≥ n, and therefore r ≤ n. xij is the element value of the ith row in the jth column. The equation for singular value decomposition of X is the following: (5.1)