MissRASS-CPD: Robust Selection of Joint and Individual Features for Tensor Data Analysis

Abstract

Nowadays, multi-modal data collected from complex systems is ubiquitous. In such systems, each modality provides myopic information about the system. Therefore, fusing the data from all the modalities is critical to understanding the system as a whole. For example, to diagnose Inflammatory Bowel Diseases, ulcerative colitis (UC) and Crohn's disease (CD), different omics data are needed. Transcriptomic provides information about gene expressions, proteomic about protein levels, while metabolite about molecule concentrations produced by microorganisms. Using only one type of omics data results in limited diagnosis accuracy and inefficient treatment plans. Furthermore, to improve diagnosis and treatment, differences and similarities across groups (UC, CD, and healthy individuals) need to be incorporated into the analysis. In this work, we propose a framework that fuses multi-modal data while exploiting the similarities and differences across groups for accurate diagnosis. The framework finds the joint latent variables for each group and the individual latent variables for each modality, and identifies the key features in each modality. Furthermore, the framework is capable of imputing missing data and removing outliers.  Our method decomposes the data into a low-rank component, that captures the true signal, and a sparse component, that captures the outliers. Then, using CP decomposition on the low-rank component with a sparse group Lasso penalty, we simultaneously learn the joint and individual latent variables. The performance of the proposed framework is illustrated through simulated and real data examples. In particular, we use the proposed framework to identify key biomarkers for UC and CD patients.