Linked Component Analysis from Matrices to High Order Tensors: Applications to Biomedical Data

TL;DR

This paper reviews matrix-based and tensor-based component analysis methods for multi-block biomedical data, emphasizing their ability to extract shared and individual features, with demonstrations on real data.

Contribution

It introduces extensions of component analysis methods to multiway tensor data, enabling flexible extraction of common and individual features in biomedical applications.

Findings

Tensor methods effectively extract shared features across data blocks.

Multi-block tensor decomposition reveals both common and unique components.

Applications demonstrate improved biomedical data analysis.

Abstract

With the increasing availability of various sensor technologies, we now have access to large amounts of multi-block (also called multi-set, multi-relational, or multi-view) data that need to be jointly analyzed to explore their latent connections. Various component analysis methods have played an increasingly important role for the analysis of such coupled data. In this paper, we first provide a brief review of existing matrix-based (two-way) component analysis methods for the joint analysis of such data with a focus on biomedical applications. Then, we discuss their important extensions and generalization to multi-block multiway (tensor) data. We show how constrained multi-block tensor decomposition methods are able to extract similar or statistically dependent common features that are shared by all blocks, by incorporating the multiway nature of data. Special emphasis is given to the flexible common and individual feature analysis of multi-block data with the aim to simultaneously extract common and individual latent components with desired properties and types of diversity. Illustrative examples are given to demonstrate their effectiveness for biomedical data analysis.