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Advances in Data Analysis and Classification

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16-08-2019 | Regular Article

Connecting the multivariate partial least squares with canonical analysis: a path-following approach

Authors: Lukáš Malec, Vladimír Janovský

Published in: Advances in Data Analysis and Classification | Issue 3/2020

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Abstract

Despite the fact that the regularisation of multivariate methods is a well-known and widely used statistical procedure, very few studies have considered it from the perspective of analytic matrix decomposition. Here, we introduce a link between one variant of partial least squares (PLS) and canonical correlation analysis (CCA) for multiple groups, as well as two groups covered as a special case. A continuation algorithm based on the implicit function theorem is selected, with particular attention paid to potential non-generic points based on real economic data inputs. Both degenerated crossings and multiple eigenvalues are identified on the paths. The theory of Chebyshev polynomials is applied in order to generate novel insights into the phenomenon simply generalisable to a variety of other techniques.

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In terms of their significance in practice, the singular value and eigenvalue decompositions of a real symmetric matrix are identical.

Note that because matrix B is specifically block diagonal in this study, joint processing of its square root and inverse are realised separately for each individual block.

As mentioned above, theory of Lagrange multipliers is standardly used to solve the problem.

Note, for the inductive statistical conclusions, there the transformation should be realised because of relatively high positively skewed data.

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Title: Connecting the multivariate partial least squares with canonical analysis: a path-following approach
Authors: Lukáš Malec
Vladimír Janovský
Publication date: 16-08-2019
Publisher: Springer Berlin Heidelberg
Published in: Advances in Data Analysis and Classification / Issue 3/2020
Print ISSN: 1862-5347
Electronic ISSN: 1862-5355
DOI: https://doi.org/10.1007/s11634-019-00370-x

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