1. CenetBiplot: a new proposal of sparse and orthogonal biplots methods by means of elastic net CSVD
- Author
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Nerea González-García, Ana B. Nieto-Librero, and Purificación Galindo-Villardón
- Subjects
Statistics and Probability ,Elastic net regularization ,Biplot ,Computer science ,Constrained singular value decomposition ,Applied Mathematics ,1206.10 Matrices ,Elastic net ,1203.02 Lenguajes Algorítmicos ,Computer Science Applications ,1204 Geometría ,Matrix (mathematics) ,Orthogonality ,HJ-Biplot ,Singular value decomposition ,Principal component analysis ,Representation (mathematics) ,Sparsity ,Algorithm ,Sparse biplot ,Subspace topology - Abstract
[EN[ 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., Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work was not supported by any grant., Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCLE
- Published
- 2021
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