Generalized L1 penalized matrix factorization

Morten Arendt Rasmussen

doi:10.1002/cem.2855

Generalized L₁ penalized matrix factorization

Morten Arendt Rasmussen^*

^*Corresponding author for this work

Food Analytics and Biotechnology

4 Citations (Scopus)

Abstract

Traditionally, chemometric models consists of parameters found by solving a least squares criterion. However, these models can suffer from overfitting, as well as being hard to interpret because of the large number of active parameters. This work proposes the use of a generalized L₁ norm penalty for constraining models to obey certain structural properties, including parameter sparsity and sparsity on pairwise differences between parameter estimates. The utility of this framework is used to modify principal component analysis, partial least squares, canonical correlation analysis, and multivariate analysis of variance type of models applied to synthetic and chemical data. This work argues that L₁ norm penalized models offers parsimony, robustness and predictive performance, and reveals a path for modifying unconstrained chemometric models through convex penalties.

Original language	English
Article number	e2855
Journal	Journal of Chemometrics
Volume	31
Issue number	4
Number of pages	9
ISSN	0886-9383
DOIs	https://doi.org/10.1002/cem.2855
Publication status	Published - 2017

Keywords

L1 norm
MANOVA
PCA
penalized methods
PLS

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10.1002/cem.2855

Cite this

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