CDPA: Common and Distinctive Pattern Analysis between High-dimensional Datasets

TL;DR

This paper introduces CDPA, a novel unsupervised method for analyzing high-dimensional datasets by decomposing data into common and distinctive patterns, considering both latent factors and coefficient matrices, with proven consistency and practical benefits.

Contribution

The paper proposes a new decomposition method, CDPA, that uniquely captures both common and distinctive patterns in high-dimensional data, improving over existing approaches.

Findings

CDPA effectively characterizes common and distinctive data patterns.

Simulation studies show good finite-sample performance.

Real data analysis demonstrates practical benefits of CDPA.

Abstract

A representative model in integrative analysis of two high-dimensional correlated datasets is to decompose each data matrix into a low-rank common matrix generated by latent factors shared across datasets, a low-rank distinctive matrix corresponding to each dataset, and an additive noise matrix. Existing decomposition methods claim that their common matrices capture the common pattern of the two datasets. However, their so-called common pattern only denotes the common latent factors but ignores the common pattern between the two coefficient matrices of these common latent factors. We propose a new unsupervised learning method, called the common and distinctive pattern analysis (CDPA), which appropriately defines the two types of data patterns by further incorporating the common and distinctive patterns of the coefficient matrices. A consistent estimation approach is developed for high-dimensional settings, and shows reasonably good finite-sample performance in simulations. Our simulation studies and real data analysis corroborate that the proposed CDPA can provide better characterization of common and distinctive patterns and thereby benefit data mining.