DPCA: Dimensionality Reduction for Discriminative Analytics of Multiple Large-Scale Datasets

TL;DR

This paper introduces DPCA, a new method for discriminative dimensionality reduction across multiple large-scale datasets, focusing on extracting features unique to a target dataset relative to others.

Contribution

It develops a novel discriminative analysis approach that maximizes the variance ratio, solved efficiently via a single SVD, with proven optimality under certain data models.

Findings

Outperforms existing methods in synthetic and real data tests

Efficiently solves a generalized eigenvalue problem with one SVD

Effectively identifies dataset-specific features

Abstract

Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain setups, one wishes to extract the most significant information of one dataset relative to other datasets. Specifically, the interest may be on identifying, namely extracting features that are specific to a single target dataset but not the others. This paper develops a novel approach for such so-termed discriminative data analysis, and establishes its optimality in the least-squares (LS) sense under suitable data modeling assumptions. The criterion reveals linear combinations of variables by maximizing the ratio of the variance of the target data to that of the remainders. The novel approach solves a generalized eigenvalue problem by performing SVD just once. Numerical tests using synthetic and real datasets showcase the merits of the proposed approach relative to its competing alternatives.