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Sparse HJ Biplot: A New Methodology via Elastic Net

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  • Mitzi Cubilla-Montilla

    (Departamento de Estadística, Facultad de Ciencias Naturales, Exactas y Tecnología, Universidad de Panamá, Panama City 0824, Panama
    Sistema Nacional de Investigación, Secretaría Nacional de Ciencia, Tecnología e Innovación (SENACYT), Panama City 0824, Panama)

  • Ana Belén Nieto-Librero

    (Department of Statistics, University of Salamanca, 37008 Salamanca, Spain
    Institute of Biomedical Research of Salamanca, 37008 Salamanca, Spain)

  • M. Purificación Galindo-Villardón

    (Department of Statistics, University of Salamanca, 37008 Salamanca, Spain
    Institute of Biomedical Research of Salamanca, 37008 Salamanca, Spain)

  • Carlos A. Torres-Cubilla

    (Department of Data Analytics, Banco General, Panama City 07096, Panama)

Abstract

The HJ biplot is a multivariate analysis technique that allows us to represent both individuals and variables in a space of reduced dimensions. To adapt this approach to massive datasets, it is necessary to implement new techniques that are capable of reducing the dimensionality of the data and improving interpretation. Because of this, we propose a modern approach to obtaining the HJ biplot called the elastic net HJ biplot, which applies the elastic net penalty to improve the interpretation of the results. It is a novel algorithm in the sense that it is the first attempt within the biplot family in which regularisation methods are used to obtain modified loadings to optimise the results. As a complement to the proposed method, and to give practical support to it, a package has been developed in the R language called SparseBiplots. This package fills a gap that exists in the context of the HJ biplot through penalized techniques since in addition to the elastic net, it also includes the ridge and lasso to obtain the HJ biplot. To complete the study, a practical comparison is made with the standard HJ biplot and the disjoint biplot, and some results common to these methods are analysed.

Suggested Citation

  • Mitzi Cubilla-Montilla & Ana Belén Nieto-Librero & M. Purificación Galindo-Villardón & Carlos A. Torres-Cubilla, 2021. "Sparse HJ Biplot: A New Methodology via Elastic Net," Mathematics, MDPI, vol. 9(11), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1298-:d:569636
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    References listed on IDEAS

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    1. Nerea González-García & Ana Belén Nieto-Librero & Purificación Galindo-Villardón, 2023. "CenetBiplot: a new proposal of sparse and orthogonal biplots methods by means of elastic net CSVD," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 5-19, March.
    2. Juan Carlos Laria & Line H. Clemmensen & Bjarne K. Ersbøll & David Delgado-Gómez, 2022. "A Generalized Linear Joint Trained Framework for Semi-Supervised Learning of Sparse Features," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    3. Wilson Rojas-Preciado & Mauricio Rojas-Campuzano & Purificación Galindo-Villardón & Omar Ruiz-Barzola, 2023. "Control Chart T2Qv for Statistical Control of Multivariate Processes with Qualitative Variables," Mathematics, MDPI, vol. 11(12), pages 1-32, June.

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