Model selection techniques for sparse weight‐based principal component analysis

Schipper, Niek C. de; Deun, Katrijn Van

doi:10.1002/cem.3289

Cited by 5 publications

(1 citation statement)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Estimating a smaller number of non-zero weights did not decrease the amount of explained variance, compared to the model found above with 107 non-zero weights per component. This is in line with previous findings in the literature that showed that high levels of sparsity in weights can still explain large amount of variance (de Schipper & Van Deun, 2021 ). In contrast, USLPCA-svd and USLPCA-multi resulted in 6.5% and 7.4%.…”

Section: Appendix A: Sparse Weights Indeterminacy Problemsupporting

confidence: 93%

A critical assessment of sparse PCA (research): why (one should acknowledge that) weights are not loadings

2023

View full text Add to dashboard Cite

Principal component analysis (PCA) is an important tool for analyzing large collections of variables. It functions both as a pre-processing tool to summarize many variables into components and as a method to reveal structure in data. Different coefficients play a central role in these two uses. One focuses on the weights when the goal is summarization, while one inspects the loadings if the goal is to reveal structure. It is well known that the solutions to the two approaches can be found by singular value decomposition; weights, loadings, and right singular vectors are mathematically equivalent. What is often overlooked, is that they are no longer equivalent in the setting of sparse PCA methods which induce zeros either in the weights or the loadings. The lack of awareness for this difference has led to questionable research practices in sparse PCA. First, in simulation studies data is generated mostly based only on structures with sparse singular vectors or sparse loadings, neglecting the structure with sparse weights. Second, reported results represent local optima as the iterative routines are often initiated with the right singular vectors. In this paper we critically re-assess sparse PCA methods by also including data generating schemes characterized by sparse weights and different initialization strategies. The results show that relying on commonly used data generating models can lead to over-optimistic conclusions. They also highlight the impact of choice between sparse weights versus sparse loadings methods and the initialization strategies. The practical consequences of this choice are illustrated with empirical datasets.

show abstract

Section: Appendix A: Sparse Weights Indeterminacy Problemsupporting

confidence: 93%

A critical assessment of sparse PCA (research): why (one should acknowledge that) weights are not loadings

2023

View full text Add to dashboard Cite

show abstract

Variable selection for both outcomes and predictors: sparse multivariate principal covariates regression

Park,

Ceulemans,

Van Deun

2024

Mach Learn

View full text Add to dashboard Cite

Datasets comprised of large sets of both predictor and outcome variables are becoming more widely used in research. In addition to the well-known problems of model complexity and predictor variable selection, predictive modelling with such large data also presents a relatively novel and under-studied challenge of outcome variable selection. Certain outcome variables in the data may not be adequately predicted by the given sets of predictors. In this paper, we propose the method of Sparse Multivariate Principal Covariates Regression that addresses these issues altogether by expanding the Principal Covariates Regression model to incorporate sparsity penalties on both of predictor and outcome variables. Our method is one of the first methods that perform variable selection for both predictors and outcomes simultaneously. Moreover, by relying on summary variables that explain the variance in both predictor and outcome variables, the method offers a sparse and succinct model representation of the data. In a simulation study, the method performed better than methods with similar aims such as sparse Partial Least Squares at prediction of the outcome variables and recovery of the population parameters. Lastly, we administered the method on an empirical dataset to illustrate its application in practice.

show abstract

Rating System for Quality Control of Functional Instant Drinks

Мустафина

Резніченко

Bakin

et al. 2022

Food Processing: Techniques and Technology

View full text Add to dashboard Cite

Excessive information about a functional product and its qualitative characteristics increases the competitiveness of the product and requires constant monitoring. The present research objective was to develop a rating system of qualitative characteristics for functional instant drinks. The system relied on the method of multidimensional statistical analysis and involved the main descriptors of consumer criteria and sensory properties of the product. The study featured functional instant fruit and berry drinks, e.g. raspberry, cranberry, cranberry, black currant, blueberry, sea buckthorn, blackberry, apricot, peach, apple, etc. The methods included a focus group approach, a sensory analysis, a new ordinal scale, and a modified method of multivariate statistical evaluation (PCA). The authors introduced a unified score scale for sensory evaluation of functional instant drinks, which reflected both standard quality indicators and consumer selection criteria. A modified method of multivariate statistical evaluation (PCA) was used to identify the characteristics that consumers see as the most important. The resulting rating system of the main descriptors reflects the information about consumer preferences and reveals significant sensory characteristics and indicators of quality of functional instant drinks. Clustering revealed two groups of consumers, young people aged 18–29 and those aged 30–59, with their own defining quality indicators. The article contains some useful labeling recommendations for producers of functional instant beverages. The recommendations can increase the competitiveness of the product and meet consumer demand for information. The new scale can be used for various types of functional fruit and berry drinks.

show abstract

Model selection techniques for sparse weight‐based principal component analysis

Cited by 5 publications

References 38 publications

A critical assessment of sparse PCA (research): why (one should acknowledge that) weights are not loadings

A critical assessment of sparse PCA (research): why (one should acknowledge that) weights are not loadings

Variable selection for both outcomes and predictors: sparse multivariate principal covariates regression

Rating System for Quality Control of Functional Instant Drinks

Contact Info

Product

Resources

About