D-CDLF: Decomposition of Common and Distinctive Latent Factors for Multi-view High-dimensional Data

TL;DR

This paper introduces D-CDLF, a novel method for decomposing multi-view high-dimensional data into common and distinctive latent factors, ensuring uncorrelatedness among all factors, and addresses high-dimensional estimation challenges.

Contribution

D-CDLF is the first method to simultaneously enforce uncorrelatedness between common and distinctive factors and among distinctive factors from different views in multi-view data.

Findings

Effectively separates common and view-specific factors.

Ensures uncorrelatedness among all latent factors.

Addresses high-dimensional estimation challenges.

Abstract

A typical approach to the joint analysis of multiple high-dimensional data views is to decompose each view's data matrix into three parts: a low-rank common-source matrix generated by common latent factors of all data views, a low-rank distinctive-source matrix generated by distinctive latent factors of the corresponding data view, and an additive noise matrix. Existing decomposition methods often focus on the uncorrelatedness between the common latent factors and distinctive latent factors, but inadequately address the equally necessary uncorrelatedness between distinctive latent factors from different data views. We propose a novel decomposition method, called Decomposition of Common and Distinctive Latent Factors (D-CDLF), to effectively achieve both types of uncorrelatedness for two-view data. We also discuss the estimation of the D-CDLF under high-dimensional settings.