A new method for dimensionality reduction of multi-dimensional data using Copulas

Abstract

A new technique for the Dimensionality Reduction of Multi-Dimensional Data is presented in this paper. This technique employs the theory of Copulas to estimate the multivariate joint probability distribution without constraints to specific types of marginal distributions of random variables that represent the dimensions of our Data. A Copulas-based model, provides a complete and scale-free description of dependence that is more suitable to be modeled using well-known multivariate parametric laws. The model can be readily used for comparing of dependence of random variables by estimating the parameters of the Copula and to better see the relationship between data. This dependence is thereafter used for detecting the Redundant Values and noise in order to clean the original data, reduce them (eliminate Redundant attributes) and obtain representative Samples of good quality. We compared the proposed approach with singular values decomposition (SVD) technique, one of the most efficient method of Data mining.