On the usage of joint diagonalization in multivariate statistics

Klaus Nordhausen () and Anne Ruiz-Gazen
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Klaus Nordhausen: JYU - University of Jyväskylä

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Abstract: 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.

Keywords: Blind source separation; Dimension reduction; Independent component analysis; Invariant component selection; Scatter matrices; Supervised dimension reduction (search for similar items in EconPapers)
Date: 2022-03
New Economics Papers: this item is included in nep-ecm
Note: View the original document on HAL open archive server: https://hal.science/hal-04296111v1
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Published in Journal of Multivariate Analysis, 2022, 188, pp.104844. ⟨10.1016/j.jmva.2021.104844⟩

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Journal Article: On the usage of joint diagonalization in multivariate statistics (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04296111

DOI: 10.1016/j.jmva.2021.104844

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