D-CDLF: Decomposition of Common and Distinctive Latent Factors for Multi-view High-dimensional Data
This addresses a methodological gap in multi-view data analysis for researchers, but it is incremental as it builds on existing decomposition methods by adding a specific uncorrelatedness constraint.
The paper tackled the problem of decomposing multi-view high-dimensional data into common and distinctive latent factors, proposing D-CDLF to effectively achieve uncorrelatedness between common and distinctive factors as well as between distinctive factors from different views, with results including estimation under high-dimensional settings.
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.