https://www.cs.cmu.edu/~pmuthuku/mlsp_page/lectures/Parafac.pdf

PARAFAC. Tutorial and applications

This paper briefly presents the aims, requirements and results of partial least squares regression analysis (PLSR), and its potential utility in ecological studies. This statistical technique is particularly well suited to analyzing a large array of related predictor variables (i.e. not truly independent), with a sample size not large enough compared to the number of independent variables, and in cases in which an attempt is made to approach complex phenomena or syndromes that must be defined as a combination of several variables obtained independently. A simulation experiment is carried out to compare this technique with multiple regression (MR) and with a combination of principal component analysis and multiple regression (PCA+MR), varying the number of predictor variables and sample sizes. PLSR models explained a similar amount of variance to those results obtained by MR and PCA+MR. However, PLSR was more reliable than other techniques when identifying relevant variables and their magnitudes of influence, especially in cases of small sample size and low tolerance. Finally, we present one example of PLSR to illustrate its application and interpretation in ecology.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1600-0706.2008.16881.x

Partial least squares regression as an alternative to current regression methods used in ecology

Anthocyanins occur widely in plants, being responsible for their blue, purple, violet, magenta, red and orange coloration; while betalains, consisting of red-violet betacyanins and yellow-orange betaxanthins, occur exclusively in families of the order Caryophyllales. The occurrence of these two classes of pigments is mutually exclusive. Their stability is markedly influenced by environmental and processing factors such as pH, temperature, O2, enzymes and condensation reactions. Due to their inherent instability these pigments, and betalains in particular, have not been widely used as food colorants. However, structural variants of the anthocyanins, i.e. polyacylated and copigmented species, have demonstrated remarkable stability and have great potential for use as stable natural colorants. Anthocyanin and betalain preparations can be used to colour a variety of foods and pharmaceuticals with compatible physicochemical properties, yielding highly coloured and high quality products. Their application could be enhanced, however, with new sources and stable structural variants, modification of current processes and foods, and technological advances (e.g. industry-scale extractions/purifications, microbial purifications, biotechnology) that would make purer and more stable preparations available. In this chapter the chemistry and biochemistry of anthocyanins and betalains—their structure and distribution, functions, biosynthesis, factors influencing their stability, methods of extraction and analysis, and current and potential sources and uses—are reviewed.

Anthocyanins and betalains

One challenge in the analysis of event-related potentials (ERPs) is to identify task-related differences in scalp topography. The multivariate Partial Least Squares (PLS) analysis was used to identify the spatiotemporal distribution of ERP differences related to experimental manipulations. Two simulations included latency shifts and amplitude changes at peaks with temporal overlap. PLS identified effects only at modeled timepoints and electrodes. In contrast, principal components analysis identified differences at most timepoints. We also demonstrated that PLS identified combinations of waveform differences, not isolated sources. ERP components in an auditory oddball task were also assessed with PLS. The primary distinction was between ERPs on hit and correct rejection trials, expressed at multiple timepoints and electrodes. PLS provides a mechanism to describe experimental differences in ERP waveforms, simultaneously across the head.

Spatiotemporal analysis of experimental differences in event-related potential data with partial least squares.

alpha-oxidation of fatty acids in higher plants. Identification of a pathogen-inducible oxygenase (piox) as an alpha-dioxygenase and biosynthesis of 2-hydroperoxylinolenic acid.

Magny S. Thomassen

Papers

Partial least-squares regression on design variables as an alternative to analysis of variance

Kinetic studies on strawberry anthocyanin hydrolysis by a thermostable anthocyanin-β-glycosidase from Aspergillus niger

Studies on fatty acid α-oxidation in cucumber