Separating common from distinctive variation

Abstract

BackgroundJoint and individual variation explained (JIVE), distinct and common simultaneous component analysis (DISCO) and O2-PLS, a two-block (X-Y) latent variable regression method with an integral OSC filter can all be used for the integrated analysis of multiple data sets and decompose them in three terms: a low(er)-rank approximation capturing common variation across data sets, low(er)-rank approximations for structured variation distinctive for each data set, and residual noise. In this paper these three methods are compared with respect to their mathematical properties and their respective ways of defining common and distinctive variation.ResultsThe methods are all applied on simulated data and mRNA and miRNA data-sets from GlioBlastoma Multiform (GBM) brain tumors to examine their overlap and differences. When the common variation is abundant, all methods are able to find the correct solution. With real data however, complexities in the data are treated differently by the three methods.ConclusionsAll three methods have their own approach to estimate common and distinctive variation with their specific strength and weaknesses. Due to their orthogonality properties and their used algorithms their view on the data is slightly different. By assuming orthogonality between common and distinctive, true natural or biological phenomena that may not be orthogonal at all might be misinterpreted.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-1037-2) contains supplementary material, which is available to authorized users.

Common and distinct components in data fusion

“…This will result in the following models for X 1 and X 2 : where T 1D collects the orthogonal components F 1 z l (hence the name O[rthogonal]2PLS) and P 1D its loadings, and likewise for T 2D and P 2D . The orthogonality properties between the different matrices are shown in Table (see the work of Van der Kloet et al). This means that O2PLS takes the viewpoint of Figure 3A (apart from the fact that each block has its own common component).…”

“…To our best knowledge, there are only a limited number of papers discussing and comparing several methods for distinguishing common and distinct variation. 5,[14][15][16] Our paper differs in several aspects: (1) we present a general mathematical framework and (2) we present more properties of the methods.…”

“…where T 1D collects the orthogonal components F 1 z l (hence the name O[rthogonal]2PLS) and P 1D its loadings, and likewise for T 2D and P 2D . The orthogonality properties between the different matrices are shown in 15 ). This means that O2PLS takes the viewpoint of Figure 3A (apart from the fact that each block has its own common component).…”

“…This will be proven now for the 2-block situation for simplicity, but is easily generalized to the more than 2-block situation. Equation 15 can also be written as…”

“…The main aim of the examples is to illustrate typical applications and how the concepts of common and distinct components can shed light on relations between multiblock data sets. To our best knowledge, there are only a limited number of papers discussing and comparing several methods for distinguishing common and distinct variation . Our paper differs in several aspects: (1) we present a general mathematical framework and (2) we present more properties of the methods.…”