Data Integration Via Analysis of Subspaces (DIVAS)

TL;DR

DIVAS is a novel method for integrating multi-omics data by analyzing subspace structures, effectively identifying shared and distinct features across data types, especially in high-dimensional, low-sample-size scenarios.

Contribution

The paper introduces DIVAS, a new algorithm combining subspace perturbation theory and convex optimization for multi-block data integration with built-in inference.

Findings

Effective in high-dimensional, low-sample-size settings

Identifies partially-shared structures across data types

Provides statistical inference on subspace relationships

Abstract

Modern data collection in many data paradigms, including bioinformatics, often incorporates multiple traits derived from different data types (i.e. platforms). We call this data multi-block, multi-view, or multi-omics data. The emergent field of data integration develops and applies new methods for studying multi-block data and identifying how different data types relate and differ. One major frontier in contemporary data integration research is methodology that can identify partially-shared structure between sub-collections of data types. This work presents a new approach: Data Integration Via Analysis of Subspaces (DIVAS). DIVAS combines new insights in angular subspace perturbation theory with recent developments in matrix signal processing and convex-concave optimization into one algorithm for exploring partially-shared structure. Based on principal angles between subspaces, DIVAS provides built-in inference on the results of the analysis, and is effective even in high-dimension-low-sample-size (HDLSS) situations.