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- handle: 10670/1.pboc0n
- hal: hal-04296111
- doi: 10.1016/j.jmva.2021.104844
- WOS: 000759646700006
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info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmva.2021.104844
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Mots-clés
Blind source separation Dimension reduction Independent component analysis Invariant component selection Scatter matrices Supervised dimension reductionSujets proches
Instruction and study--Methods Instruction and study--MethodsCiter ce document
Klaus Nordhausen et al., « On the usage of joint diagonalization in multivariate statistics », HAL-SHS : économie et finance, ID : 10.1016/j.jmva.2021.104844
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Résumé
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.