Principal Component Analysis - Engineering Applications

Dimensionality reduction is one of the preprocessing steps in many machine learning applications and it is used to transform the features into a lower dimension space. Principal Component Analysis (PCA) technique is one of the most famous unsupervised dimensionality reduction techniques. The goal of the PCA is to find the space, which represents the direction of the maximum variance of the given data. This paper highlights the basic background needed to understand and implement the PCA technique. This paper starts with basic definitions of the PCA technique and the algorithms of two methods of calculating PCA, namely, the covariance matrix and Singular Value Decomposition (SVD) methods. Moreover, a number of numerical examples are illustrated to show how the PCA space is calculated in easy steps. Three experiments are conducted to show how to apply PCA in the real applications including biometrics, image compression, and visualization of high-dimensional datasets.

Journal of Signal and Information Processing, 2013

The principal component analysis (PCA) is a kind of algorithms in biometrics. It is a statistics technical and used orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables. PCA also is a tool to reduce multidimensional data to lower dimensions while retaining most of the information. It covers standard deviation, covariance, and eigenvectors. This background knowledge is meant to make the PCA section very straightforward, but can be skipped if the concepts are already familiar.

PRINCIPAL …, 2012

— Principal Component Analysis (PCA) is a powerful statistical technique for variable reduction, It used when variables are highly correlated. PCA becomes an essential tool for multivariate data analysis and unsupervised dimension reduction. PCA incorporated with AI techniques to improve performance of many applications like image processing, pattern recognition, classification and anomaly detection. The goal of this survey is to provide a comprehensive review of the literature related to Principal Component Analysis (PCA).

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 table, to represent it as a set of new orthogonal variables called principal components, and to display the pattern of similarity of the observations and of the variables as points in maps. The quality of the PCA model can be evaluated using cross-validation techniques such as the bootstrap and the jackknife. PCA can be generalized as correspondence analysis (CA) in order to handle qualitative variables and as multiple factor analysis (MFA) in order to handle heterogeneous sets of variables. Mathematically, PCA depends upon the eigen-decomposition of positive semidefinite matrices and upon the singular value decomposition (SVD) of rectangular matrices.