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CenetBiplot: a new proposal of sparse and orthogonal biplots methods by means of elastic net CSVD

Author

Listed:
  • Nerea González-García

    (University of Salamanca
    Instituto de Investigación Biomédica de Salamanca (IBSAL))

  • Ana Belén Nieto-Librero

    (University of Salamanca
    Instituto de Investigación Biomédica de Salamanca (IBSAL))

  • Purificación Galindo-Villardón

    (University of Salamanca
    Instituto de Investigación Biomédica de Salamanca (IBSAL)
    Bernardo O’Higgins University)

Abstract

In this work, a new mathematical algorithm for sparse and orthogonal constrained biplots, called CenetBiplots, is proposed. Biplots provide a joint representation of observations and variables of a multidimensional matrix in the same reference system. In this subspace the relationships between them can be interpreted in terms of geometric elements. CenetBiplots projects a matrix onto a low-dimensional space generated simultaneously by sparse and orthogonal principal components. Sparsity is desired to select variables automatically, and orthogonality is necessary to keep the geometrical properties that ensure the biplots graphical interpretation. To this purpose, the present study focuses on two different objectives: 1) the extension of constrained singular value decomposition to incorporate an elastic net sparse constraint (CenetSVD), and 2) the implementation of CenetBiplots using CenetSVD. The usefulness of the proposed methodologies for analysing high-dimensional and low-dimensional matrices is shown. Our method is implemented in R software and available for download from https://github.com/ananieto/SparseCenetMA .

Suggested Citation

  • 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.
    • Handle: RePEc:spr:advdac:v:17:y:2023:i:1:d:10.1007_s11634-021-00468-1
    DOI: 10.1007/s11634-021-00468-1
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    References listed on IDEAS

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