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

Nerea González-García (), Ana Belén Nieto-Librero () and Purificación Galindo-Villardón ()
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Nerea González-García: University of Salamanca
Ana Belén Nieto-Librero: University of Salamanca
Purificación Galindo-Villardón: University of Salamanca

Advances in Data Analysis and Classification, 2023, vol. 17, issue 1, No 2, 5-19

Abstract: 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 .

Keywords: Sparse biplot; Constrained singular value decomposition; Orthogonality; Sparsity; Elastic net; HJ-Biplot; 15A23; 62J07; 62Hxx; 62H25; 62P10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11634-021-00468-1

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