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

• ID: 2779, RIV: 10405157
• ISSN: 1862-5347, ISBN: not specified
• source: Advances in Data Analysis and Classification
• keywords: Analytic eigenvalue decomposition; Analytic singular value decomposition; Canonical correlation analysis; Economics; Multi-group case; Multiplicity; Partial least squares; Path-following
• authors: Lukáš Malec, Vladimír Janovský
• authors from KNM: Janovský Vladimír

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.