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

In this work, a new mathematical algorithm for sparse and orthogonal constrained biplots, called C(enet)Biplots, 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. C(enet)Biplots 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 C(enet)Biplots 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 .

Automated summary

In this study, a new mathematical algorithm called C(enet)Biplots is proposed for sparse and orthogonal constrained biplots. Biplots provide a joint representation of observations and variables in a multidimensional matrix, allowing for interpretation of their relationships in geometric terms. The proposed algorithm, C(enet)Biplots, projects the matrix onto a low-dimensional space generated by sparse and orthogonal principal components. The method is implemented in R software and is shown to be useful for analyzing high-dimensional and low-dimensional matrices.