Nonlinear Dimensionality Reduction for Discriminative Analytics of Multiple Datasets

TL;DR

This paper introduces discriminative PCA, a novel method for extracting features that distinguish a target dataset from background datasets, extending PCA with kernel methods for nonlinear data, and proves its optimality under certain conditions.

Contribution

The paper presents discriminative PCA (dPCA), a new approach for joint analysis of multiple datasets that identifies target-specific components and extends PCA with kernel methods for nonlinear data.

Findings

dPCA effectively isolates target-specific features.

Kernel dPCA captures nonlinear correlations.

Analytical solutions are obtained via eigenvalue decomposition.

Abstract

Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is challenged when it comes to analyzing multiple datasets jointly. In certain data science settings however, one is often interested in extracting the most discriminative information from one dataset of particular interest (a.k.a. target data) relative to the other(s) (a.k.a. background data). To this end, this paper puts forth a novel approach, termed discriminative (d) PCA, for such discriminative analytics of multiple datasets. Under certain conditions, dPCA is proved to be least-squares optimal in recovering the component vector unique to the target data relative to background data. To account for nonlinear data correlations, (linear) dPCA models for one or multiple background datasets are generalized through kernel-based learning. Interestingly, all dPCA variants admit an analytical solution obtainable with a single (generalized) eigenvalue decomposition. Finally, corroborating dimensionality reduction tests using both synthetic and real datasets are provided to validate the effectiveness of the proposed methods.