OnPLS—a novel multiblock method for the modelling of predictive and orthogonal variation

Abstract

This paper presents a new multiblock analysis method called OnPLS, a general extension of O2PLS to the multiblock case. The proposed method is equivalent to O2PLS in cases involving only two matrices, but generalises to cases involving more than two matrices without giving preference to any particular matrix: the method is fully symmetric. OnPLS extracts a minimal number of globally predictive components that exhibit maximal covariance and correlation. Furthermore, the method can be used to study orthogonal variation, i.e. local phenomena captured in the data that are specific to individual combinations of matrices or to individual matrices. The method's utility was demonstrated by its application to three synthetic data sets. It was shown that OnPLS affords a reduced number of globally predictive components and increased intercorrelations of scores, and that it greatly facilitates interpretation of the predictive model.

OnPLS integration of transcriptomic, proteomic and metabolomic data shows multi-level oxidative stress responses in the cambium of transgenic hipI- superoxide dismutase Populus plants

“…OnPLS [9,10] is a recently published extension of O2PLS [27,28] that generalizes to multiblock cases where several blocks of data are subjected to analysis. The problem that O2PLS aims to solve is described as follows: Given two data blocks X 1 ( M  ×  N ) and X 2 ( M  ×  K ) we can split the variation in each X block into two parts, X  =  X J  +  X U   + E, where X J and X U correspond to the joint and unique variation respectively.…”

Sample-poor estimation of order and common signal subspace with application to fusion of medical imaging data

“…, [6, 15, 19, 23]. Other methods for estimating the number of common and distinctive sources include: orthogonal n -way partial least squares (OnPLS) [24], generalized singular value decomposition [4], and distinctive and common components with simultaneous-component analysis (DISCO-SCA) [37]. These methods all assume sufficient sample support and thus perform poorly when the number of samples is not significantly greater than the number of observations.…”

Reflections on Partial Least Squares Path Modeling

“…In this manner, the underlying model would be the same for both methods, which would allow meaningful comparisons of their relative performance. Naturally, when comparing the approaches within a composite-based modeling scheme, unreliability and measurement error should not be evaluated and compared using procedures rooted in the common factor model (Rigdon, 2012 but not all of the blocks; and (c) a unique component that reflects variance specific to a single block (Löfstedt, Eriksson, Wormbs, & Trygg, 2012;Löfstedt, Hoffman, & Trygg, 2013;Löfstedt, Hanafi, & Trygg, 2013;Löfstedt & Trygg, 2011). Although this approach does not completely purge measurement error from each construct, as accomplished with the common factor model, it disattenuates the estimates of the core hypothesized relationships by removing all variation that is irrelevant to prediction, which is a major advance in the component-based modeling domain.…”