6533b853fe1ef96bd12ad61a
RESEARCH PRODUCT
On the usage of joint diagonalization in multivariate statistics
Anne Ruiz-gazenKlaus Nordhausensubject
Statistics and ProbabilityScatter matricesMultivariate statisticsContext (language use)010103 numerical & computational mathematics01 natural sciencesBlind signal separation010104 statistics & probabilitySliced inverse regression0101 mathematicsB- ECONOMIE ET FINANCESupervised dimension reductionMathematicsNumerical Analysisbusiness.industryCovariance matrixPattern recognitionriippumattomien komponenttien analyysimatemaattinen tilastotiedeLinear discriminant analysisInvariant component selectionIndependent component analysismonimuuttujamenetelmätPrincipal component analysisDimension reductionBlind source separationArtificial intelligenceStatistics Probability and Uncertaintybusinessdescription
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. peerReviewed
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2022-03-01 |