Penalized Partial Least Square applied to structured data

Camilo Broc, Borja Calvo, Benoit Liquet

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Abstract

Nowadays, data analysis applied to high dimension has arisen. The edification of high-dimensional data can be achieved by the gathering of different independent data. However, each independent set can introduce its own bias. We can cope with this bias introducing the observation set structure into our model. The goal of this article is to build theoretical background for the dimension reduction method sparse Partial Least Square (sPLS) in the context of data presenting such an observation set structure. The innovation consists in building different sPLS models and linking them through a common-Lasso penalization. This theory could be applied to any field, where observation present this kind of structure and, therefore, improve the sPLS in domains, where it is competitive. Furthermore, it can be extended to the particular case, where variables can be gathered in given a priori groups, where sPLS is defined as a sparse group Partial Least Square.

Original languageEnglish
Pages (from-to)329-344
Number of pages16
JournalArabian Journal of Mathematics
Volume9
Issue number2
Early online date4 Mar 2019
DOIs
Publication statusPublished - Aug 2020
Externally publishedYes

Bibliographical note

Copyright the Author(s) 2019. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

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