DRCT: A Novel Method for Dimensional Reduction on High-Dimensional Data

Dimensionality reduction techniques are widely used in face recognition, facial expression recognition, document recognition, and text processing.Common methods for dimensionality reduction include Linear Discriminant Analysis (LDA) and Principal Component Analysis (PCA).The goal of LDA is to maximize the ratio of between-class variance to within-class variance in a lower-dimensional space, while PCA aims to maximize the variance in the lower-dimensional space.For classification problems, PCA tends to lose valuable information, particularly in datasets where class separability information lies in low-variance components.Conversely, LDA more effectively preserves separability information.However, LDA has several limitations, including: failure in small sample size (SSS) problems, the requirement for Gaussian-distributed data, and its disregard for within-class data structure.This study proposes the Dimensionality Reduction based on Coordinate Transformation (DRCT) method, an extension of the LDA-based coordinate transformation (LDA-CT) method.DRCT iteratively applies LDA-CT to reduce every two features into a single new feature, subsequently adding one feature at a time to create the next new feature until all features are included.Beyond addressing the SSS issue, DRCT mitigates the effects of non-Gaussian data and considers within-class data structure.Experimental results on 10 low-dimensional public datasets and four high-dimensional public datasets demonstrate that DRCT outperforms LDA, with the most significant accuracy improvements observed on the YaleB and GT-face datasets, achieving accuracies of 0.942 and 0.964, compared to LDA's 0.732 and 0.807.