Authors: Federico Marini
Source: Journal of Chemometrics (article, 2020-01-01)
Field: Chemistry — Analytical Chemistry

Orthogonal PLS (O‐PLS) and related algorithms The concept of orthogonalized partial least squares regression or, better, as it was originally named, orthogonalized projection to latent structures (O-PLS) was first introduced in 2001 1, 2 by Johann Trygg and Svante Wold, as a way to deal with the large amount of variation in predictor matrices for multivariate calibration (and classification), not correlated to the responses. In this context, O-PLS operates by partitioning the systematic variance in the X block into a Y relevant and an orthogonal data sets, both having a bilinear structure. As soon as the algorithm has been published, it has immediately gained a lot of interest and rapid popularity, as shown in Figure 1, where it is evident that the trend of published papers using algorithms from the O-PLS family or referring to them is growing exponentially. In particular, as shown in Figure 2, where the main field of application of O-PLS and O-PLS-related algorithm is displayed in the form of a pie chart, it is unequivocal that, apart from the “natural” application to purely chemistry-related problems, as expected for an algorithm born within the chemometric community, a large share of the researches fall under the wide umbrella of -omic sciences. It is undubious that a part of the O-PLS popularity in the -omic field can be related to its availability as the main tool in one of the most widely adopted software in the area, but it is also true that the -omic sciences are one of the disciplines where the impact of irrelevant variation on the data is high and where the quest for straightforward identification of interpretable marker is the stake. On the other hand, probably also because of its popularity, during the years, there has been a large debate on the O-PLS algorithm itself, to highlight its real peculiarities, whether it really had unique features or, on the other hand, to understand whether it should just be seen as one out of the many possibilities of identifying sources of common and distinctive variation among two or more blocks 3-7. Starting from these considerations, in this special section of the issue, four papers representing the different aspects of how the research and the debate around O-PLS and related issues have evolved so far, are collected. Sjögren et al confirm the multidisciplinary interest around O-PLS, by showing how multivariate data analysis can be applied in the context of text analysis in a combination with common machine learning preprocessing methodologies. In particular, their attention is focused on demonstrating how PCA, O-PLS, and its multiblock analog On-PLS on bag-of-words representations of abstracts, claims, and detailed descriptions could provide an accurate classification of patents from big pharma companies 8. On the other hand, starting from the above-mentioned multiblock analog of O-PLS, On-PLS, but extending the applicability also to other multiblock models, Skotare et al. present different tools for data visualization. In particular, they propose a correlation matrix plot, to highlight the relationships between blocks found by multiblock models. Moreover, they also introduce additional plots, a multiblock scatter plot, a metadata correlation plot, and a variation distribution plot, which are meant to simplify the interpretation 9. Indahl's paper 10 is an example of the theoretical debate which has developed around O-PLS and similar algorithms sharing the characteristics of being all derived from the orthogonal signal correction (OSC) principle 11. Here, the mathematics behind O-PLS and related algorithm is thoroughly examined to verify whether all the claims associated with these methods are really met or not. Lastly, Stocchero 12 introduces a new posttransformation method, called posttransformation of the latent variable space (ptLV), to separate the nonpredictive data from the predictive one. Its peculiarities are that it works on the score space and can be applied also to kernel-PLS2 (KPLS2) and that, differently from other posttransformation approaches, does not require the explicit calculation of the weight matrix. Partial least squares regression ; Algorithm ; Context (archaeology) ; Chemometrics ; Field (mathematics) ; Multivariate statistics ; Computer science ; Projection (relational algebra) ; Mathematics ; Statistics ; Data mining ; Artificial intelligence ; Machine learning Spectroscopy and Chemometric Analyses ; Metabolomics and Mass Spectrometry Studies ; Advanced Chemical Sensor Technologies