SO‐CovSel: A novel method for variable selection in a multiblock framework

Abstract

With the development of technology and the relatively higher availability of new instrumentations, having multiblock data sets (eg, a set of samples analyzed by different analytical techniques) is becoming more and more common and, as a consequence, how to handle this kind of outcomes is a widely discussed topic. In such a context, where the number of involved variables is relatively high, selecting the most significant features is obviously relevant.For this reason, the possibility of joining a multiblock regression method, the sequential and orthogonalized partial least-squares (SO-PLS), with a variable selection approach called covariance selection (CovSel), has been investigated. The resulting method, sequential and orthogonalized covariance selection (SO-CovSel) is similar to SO-PLS, but the feature reduction provided by PLS is performed by CovSel. Finally, predictions are made by applying multiple linear regression on the subset of selected variables. The novel approach has been tested on different multiblock data sets both in regression and in classification (by combination with LDA), and it has been compared with another state-ofthe-art multiblock method. SO-CovSel has demonstrated to be suitable for its purpose: It has provided good predictions (both in regression and in classification) and, from the interpretation point of view, it has led to a meaningful selection of the original variables. variables in this framework has not widely been discussed yet. In the present paper, the possibility of plugging together a multiblock latent variable-based method, sequential and orthogonalized partial least-squares (SO-PLS), 4 and a variable selection method, covariance selection (CovSel), 5 has been examined, and a novel multiblock variable selection method, named SO-CovSel, has been developed.Among the many possible methodologies which have been proposed in literature, CovSel and SO-PLS have been chosen because they have demonstrated to lead to good predictions and, at the same time, both of them present some peculiarities which make them particularly suitable for the interpretation of complex systems.Analogously to SO-PLSR and SO-PLS-LDA, 6 SO-CovSel finds its application in different contexts; it can be combined with regression or with linear discriminant analysis (LDA). 7 In both contexts, it has led to selections of variables exceptionally suitable for the interpretation of the systems under study, and it has provided predictions which are comparable with those obtained applying another state-of-the-art method. | MATERIAL AND METHODS | Covariance selectionCovSel 5 is a variable selection method conceived to detect the most relevant features in a regression context. As the name suggests, the relevancy of each variable is evaluated estimating the covariance between each predictor and responses. Once the variable presenting the highest covariance is individuated and selected, all the other predictors and the responses are orthogonalized with respect to it, and the procedure is repeated until the fixed amount of...

Gut Microbial, Inflammatory and Metabolic Signatures in Older People with Physical Frailty and Sarcopenia: Results from the BIOSPHERE Study

“…After import into MatLab, serum concentrations of inflammatory and metabolic markers and the abundance of gut microbial OTUs were organized into three matrices (Table 2), to be further processed through a multi-block approach. Given its ability to provide accurate predictions and, at the same time, to identify a parsimonious number of relevant variables (putative markers), the analysis was carried out through the recently developed SO-CovSel algorithm [32]. 1-methylhistidine, 3-methylhistidine, 4-hydroxyproline, α-aminobutyric acid, β-alanine, β-aminobutyric acid, γ-aminobutyric acid, alanine, aminoadipic acid, anserine, arginine, asparagine, aspartic acid, carnosine, citrulline, cystathionine, cystine, ethanolamine, glutamic acid, glycine, histidine, isoleucine, leucine, lysine, methionine, ornithine, phenylalanine, phosphoethanolamine, phosphoserine, proline, sarcosine, serine, taurine, threonine, tryptophan, tyrosine, valine…”

Circulating Mitochondrial-Derived Vesicles, Inflammatory Biomarkers and Amino Acids in Older Adults With Physical Frailty and Sarcopenia: A Preliminary BIOSPHERE Multi-Marker Study Using Sequential and Orthogonalized Covariance Selection – Linear Discriminant Analysis

“…In order to identify relationships among different sets of data and to identify putative markers of PF&S, a recently proposed multi-block classification approach, called SO-CovSel–LDA (Biancolillo et al, 2020 ), was adopted. SO-CovSel–LDA is a highly efficient multi-block classification strategy, which combines a very parsimonious variable selection algorithm to be applied on each individual block (CovSel) (Roger et al, 2011 ) with the sequential inclusion of data matrices, after orthogonalization with respect to the previously selected variables.…”

“…In the present preliminary study, we took advantage of the well-characterized cohort of older adults recruited in the “BIOmarkers associated with Sarcopenia and Physical frailty in EldeRly pErsons” (BIOSPHERE) study (Calvani et al, 2018b , c ; Marzetti et al, 2019 ; Picca et al, 2019a , 2020a ) to simultaneously analyze biomediators pertaining to three different domains: inflammation, amino acid metabolism, and mitochondrial quality control (MQC). The availability of systemic inflammatory and metabolic data from this cohort (Calvani et al, 2018b ; Marzetti et al, 2019 ) and their complementation with the analysis of circulating MDVs (Picca et al, 2020a ) provided a composite dataset to explore the relationship among systemic inflammation, metabolic characteristics, and MDV trafficking in PF&S. Data analysis was performed through sequential and orthogonalized covariance selection coupled with linear discriminant analysis (SO-CovSel–LDA), an innovative analytical strategy that is particularly suited for dealing with multi-block datasets (i.e., experimental settings in which variables are assayed using different platforms and/or at different time points) (Biancolillo et al, 2020 ). SO-CovSel–LDA enabled selecting the variables of interest for PF&S from a large number of highly correlated candidate biomarkers.…”

The “develOpment of metabolic and functional markers of Dementia IN Older people” (ODINO) Study: Rationale, Design and Methods

“…PLS-DA offers the advantage of processing datasets containing a high number of variables even if they are highly correlated with one another. The analysis of the whole dataset, which encompasses multi-block data, will be performed through the recently developed sequential and orthogonalized covariance selection (SO-CovSel) [48]. The method, which allows a highly parsimonious variable selection, was used by our group for the identification of a gut microbial, inflammatory and metabolic fingerprint in older adults with physical frailty & sarcopenia [41].…”