Mahalanobis Distance Minimization Mapping: M3

Abstract

This paper presents a versatile linear regression method between high-dimensional spaces based on Mahalanobis distance minimization criterion. Standard regression methods suffer from ¿multi-collinearity¿ problem, which makes regressions unstable and unreliable. For solving this problem, dimensionality reduction methods, such as PCR, PLS, and CCA, are widely used. These dimensionality reduction methods can robustly capture the major correlations between input and output variables by suppressing the minor correlations. However, the minor correlations are sometimes necessary for estimating natural outputs. In this paper, we propose Mahalanobis-distance Minimization Mapping (M3), which avoids multi-collinearity problem without reducing the dimensionality. M3 estimates the most likely output according to the training sample distribution. We conducted experiments for comparing the accuracy among M3, CCA, and other methods, and we confirmed that M3 always estimates the most accurate outputs among them.