Common and distinct components in data fusion

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.

Performance of methods that separate common and distinct variation in multiple data blocks

“…The calculation of scores and loadings differ for the different methods, as well as orthogonality constraints between scores. This will be explained in more detail in the following sections, but for a thorough description of the mathematical framework, we refer to Smilde et al Note also that often, only a subset of all the possible common subspaces are included in the final model, especially if the number of blocks is large.…”

“…This method is a combination of PCA and generalized canonical correlation analysis (GCA). Some applications of this approach have been published, and a similar method for asymmetric data fusion has also been developed . The GCA is a generalized version of the two‐block method canonical correlation analysis (CCA) and can be applied to any number of blocks .…”

“…Common variation (also called joint or overlapping) refers to underlying phenomena that are captured in several of the data blocks, while distinct variation (also called individual or unique) correspond to phenomena that are only found in one block. The concept is described in detail in Smilde et al This type of data may occur in many fields of science, for example: In chemistry, for instance, when mixtures of chemical compounds are analyzed by several spectroscopic techniques. The spectroscopic measurements may differ in their ability to detect chemical compounds, which results in data blocks with partially overlapping information. In biology, for instance, to infer pathways involved in diseases using gene expression levels, protein levels, and metabolite concentrations where each type of platform can be regarded as a data block. In sensory science, where the blocks might correspond to different but partly overlapping modalities such as smell, taste, and texture. The separation of common and distinct variation in cases with two, three, and four data blocks is illustrated schematically in Figure .…”

“…A unifying framework for the aforementioned methods has been published lately, also describing the existing methods in linear algebraic terms . The methods JIVE, DISCO, and OnPLS have been compared previously in a two‐block scenario .…”

Revealing Subgroups That Differ in Common and Distinctive Variation in Multi-Block Data: Clusterwise Sparse Simultaneous Component Analysis

“…The first approach detects the number of total components with the variance accounted for (VAF) method while determines the status (i.e., common or distinctive) of each component with the DISCO-SCA method. The second approach, the principal component analysis -general component analysis (PCA-GCA) method (Smilde et al, 2017), first applies PCA to determine the number of components in each data block and then applies GCA to determine the number of common components.…”