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Multivariate Statistical Data Analysis- Principal Component Analysis (PCA)

Sidharth Prasad Mishra Uttam Sarkar Subhash Taraphder Sanjay Datta Devi Prasanna Swain Reshma Saikhom Sasmita Panda Menalsh Laishram
Vol 7(5), 60-78
DOI- http://dx.doi.org/10.5455/ijlr.20170415115235

Principal component analysis (PCA) is a multivariate technique that analyzes a data table in which observations are described by several inter-correlated quantitative dependent variables. Its goal is to extract the important information from the statistical data to represent it as a set of new orthogonal variables called principal components, and to display the pattern of similarity between the observations and of the variables as points in spot maps. Mathematically, PCA depends upon the eigen-decomposition of positive semi-definite matrices and upon the singular value decomposition (SVD) of rectangular matrices. It is determined by eigenvectors and eigenvalues. Eigenvectors and eigenvalues are numbers and vectors associated to square matrices. Together they provide the eigen-decomposition of a matrix, which analyzes the structure of this matrix such as correlation, covariance, or cross-product matrices. Performing PCA is quite simple in practice. Organize a data set as an m × n matrix, where m is the number of measurement types and n is the number of trials. Subtract of the mean for each measurement type or row xi. Calculate the SVD or the eigenvectors of the co-variance. It was found that there were many interesting applications of PCA, out of which in day today life knowingly or unknowingly multivariate data analysis and image compression are being used alternatively.

Keywords : Eigenvalue Eigenvector Linear Algebra Matrix Multivariate PCA

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