On the usage of joint diagonalization in multivariate statistics
Nordhausen, K., & Ruiz-Gazen, A. (2022). On the usage of joint diagonalization in multivariate statistics. Journal of Multivariate Analysis, 188, Article 104844. https://doi.org/10.1016/j.jmva.2021.104844
Published inJournal of Multivariate Analysis
© 2021 the Authors
Scatter matrices generalize the covariance matrix and are useful in many multivariate data analysis methods, including well-known principal component analysis (PCA), which is based on the diagonalization of the covariance matrix. The simultaneous diagonalization of two or more scatter matrices goes beyond PCA and is used more and more often. In this paper, we offer an overview of many methods that are based on a joint diagonalization. These methods range from the unsupervised context with invariant coordinate selection and blind source separation, which includes independent component analysis, to the supervised context with discriminant analysis and sliced inverse regression. They also encompass methods that handle dependent data such as time series or spatial data.
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Additional information about fundingThe work of KN was supported by the Austrian Science Fund (FWF) under grant P31881-N32. ARG acknowledges funding from ANRunder grant ANR-17-EURE-0010 (Investissements d’Avenir program).
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