Common and Distinct Components in Data Fusion

TL;DR

This paper introduces a unified linear algebra framework for identifying common and distinct components in multi-set data fusion, aiding understanding of relationships across diverse scientific fields.

Contribution

It provides a comprehensive, rigorous framework that unifies existing methods for distinguishing shared and unique data components, facilitating comparison and advancement.

Findings

Framework unifies existing methods for data component analysis.

Illustrates methods with practical biological and food science examples.

Enhances understanding of relationships between multiple data sets.

Abstract

In many areas of science multiple sets of data are collected pertaining to the same system. Examples are food products which are characterized by different sets of variables, bio-processes which are on-line sampled with different instruments, or biological systems of which different genomics measurements are obtained. Data fusion is concerned with analyzing such sets of data simultaneously to arrive at a global view of the system under study. One of the upcoming areas of data fusion is exploring whether the data sets have something in common or not. This gives insight into common and distinct variation in each data set, thereby facilitating understanding the relationships between the data sets. Unfortunately, research on methods to distinguish common and distinct components is fragmented, both in terminology as well as in methods: there is no common ground which hampers comparing methods and understanding their relative merits. This paper provides a unifying framework for this subfield of data fusion by using rigorous arguments from linear algebra. The most frequently used methods for distinguishing common and distinct components are explained in this framework and some practical examples are given of these methods in the areas of (medical) biology and food science.