Data dimensional reduction and principal components analysis

Abstract

Research in the fields of machine learning and intelligent systems addresses essential problem of developing computer algorithms that can deal with huge amounts of data and then utilize this data in an intellectual way to solve a variety of real-world problems. In many applications, to interpret data with a large number of variables in a meaningful way, it is essential to reduce the number of variables and interpret linear combinations of the data. Principal Component Analysis (PCA) is an unsupervised learning technique that uses sophisticated mathematical principles to reduce the dimensionality of large datasets. The goal of this paper is to provide a complete understanding of the sophisticated PCA in the fields of machine learning and data dimensional reduction. It explains its mathematical aspect and describes its relationship with Singular Value Decomposition (SVD) when PCA is calculated using the covariance matrix. In addition, with the use of MATLAB, the paper shows the usefulness of PCA in representing and visualizing Iris dataset using a smaller number of variables.