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

Lukáš Malec () and Vladimír Janovský
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Lukáš Malec: University College of Business
Vladimír Janovský: Charles University

Advances in Data Analysis and Classification, 2020, vol. 14, issue 3, No 5, 589-609

Abstract: 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.

Keywords: Canonical correlation analysis; Partial least squares; Multi-group case; Analytic singular value decomposition; Analytic eigenvalue decomposition; Multiplicity; Path-following; Economics; 62H20; 46N10; 62P20 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11634-019-00370-x

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