Supervised Discriminative Sparse PCA with Adaptive Neighbors for Dimensionality Reduction

TL;DR

This paper introduces SDSPCAAN, a new linear dimensionality reduction method that combines global and local data structure preservation with supervised learning, improving robustness and effectiveness on high-dimensional data.

Contribution

The paper proposes a novel supervised discriminative sparse PCA method with adaptive neighbors that integrates global and local data structures for enhanced dimensionality reduction.

Findings

Outperforms existing methods on nine high-dimensional datasets

Effectively preserves both global and local data structures

Demonstrates robustness to noisy high-dimensional data

Abstract

Dimensionality reduction is an important operation in information visualization, feature extraction, clustering, regression, and classification, especially for processing noisy high dimensional data. However, most existing approaches preserve either the global or the local structure of the data, but not both. Approaches that preserve only the global data structure, such as principal component analysis (PCA), are usually sensitive to outliers. Approaches that preserve only the local data structure, such as locality preserving projections, are usually unsupervised (and hence cannot use label information) and uses a fixed similarity graph. We propose a novel linear dimensionality reduction approach, supervised discriminative sparse PCA with adaptive neighbors (SDSPCAAN), to integrate neighborhood-free supervised discriminative sparse PCA and projected clustering with adaptive neighbors. As a result, both global and local data structures, as well as the label information, are used for better dimensionality reduction. Classification experiments on nine high-dimensional datasets validated the effectiveness and robustness of our proposed SDSPCAAN.