Document de travail

On the usage of joint diagonalization in multivariate statistics

Klaus Nordhausen et Anne Ruiz-Gazen

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.

Mots-clés

Blind Source Separation; Dimension Reduction; Independent Component Analysis; Invariant Component Selection; Scatter Matrices; Supervised Dimension Reduction;

Remplacé par

Klaus Nordhausen et Anne Ruiz-Gazen, « On the usage of joint diagonalization in multivariate statistics », Journal of Multivariate Analysis, n° 104844, 2021, à paraître.

Référence

Klaus Nordhausen et Anne Ruiz-Gazen, « On the usage of joint diagonalization in multivariate statistics », TSE Working Paper, n° 21-1268, novembre 2021.

Voir aussi

Publié dans

TSE Working Paper, n° 21-1268, novembre 2021