Dimensionality Reduction Using Factor Analysis

Abstract

In many pattern recognition applications, a large number of features are extracted in order to ensure an accurate classification of unknown classes. One way to solve the problems of high dimensions is to first reduce the dimensionality of the data to a manageable size, keeping as much of the original information as possible and then feed the reduced-dimensional data into a pattern recognition system. In this situation, dimensionality reduction process becomes the pre-processing stage of the pattern recognition system. In addition to this, probablility density estimation, with fewer variables is a simpler approach for dimensionality reduction. Dimensionality reduction is useful in speech recognition, data compression, visualization and exploratory data analysis. Some of the techniques which can be used for dimensionality reduction are; Factor Analysis (FA), Principal Component Analysis(PCA), and Linear Discriminant Analysis(LDA). Factor Analysis can be considered as an extension of Principal Component Analysis. The EM (expectation maximization) algorithm is ideally suited to problems of this sort, in that it produces maximum-likelihood (ML) estimates of parameters when there is a many-to-one mapping from an underlying distribution to the distribution governing the observation, conditioned upon the obervations. The maximization step then provides a new estimate of the parameters. This research work compares the techniques; Factor Analysis (Expectation-Maximization algorithm based), Principal Component Analysis and Linear Discriminant Analysis for dimensionality reduction and investigates Local Factor Analysis (EM algorithm based) and Local Principal Component Analysis using Vector Quantization.