Overview and Recent Advances in Partial Least Squares

Partial Least Squares (PLS) is a wide class of methods for modeling relations between sets of observed variables by means of latent variables. It comprises of regression and classification tasks as well as dimension reduction techniques and modeling tools. The underlying assumption of all PLS methods is that the observed data is generated by a system or process which is driven by a small number of latent (not directly observed or measured) variables. Projections of the observed data to its latent structure by means of PLS was developed by Herman Wold and coworkers [48, 49, 52]. PLS has received a great amount of attention in the field of chemometrics. The algorithm has become a standard tool for processing a wide spectrum of chemical data problems. The success of PLS in chemometrics resulted in a lot of applications in other scientific areas including bioinformatics, food research, medicine, pharmacology, social sciences, physiology–to name but a few [28, 25, 53, 29, 18, 22]. This chapter introduces the main concepts of PLS and provides an overview of its application to different data analysis problems. Our aim is to present a concise introduction, that is, a valuable guide for anyone who is concerned with data analysis. In its general form PLS creates orthogonal score vectors (also called latent vectors or components) by maximising the covariance between different sets of variables. PLS dealing with two blocks of variables is considered in this chapter, although the PLS extensions to model relations among a higher number of sets exist [44, 46, 47, 48, 39]. PLS is similar to Canonical Correlation Analysis (CCA) where latent vectors with maximal correlation are extracted [24]. There are different PLS techniques to extract latent vectors, and each of them gives rise to a variant of PLS. PLS can be naturally extended to regression problems. The predictor and predicted (response) variables are each considered as a block of variables. PLS then extracts the score vectors which serve as a new predictor representation