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Invariant co-ordinate selection
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DOI：10.1111/j.1467-9868.2009.00706.x.png)
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Abstract
En 中文
A general method for exploring multivariate data by comparing different estimates of multivariate scatter is presented. The method is based on the eigenvalue-eigenvector decomposition of one scatter matrix relative to another. In particular, it is shown that the eigenvectors can be used to generate an affine invariant co-ordinate system for the multivariate data. Consequently, we view this method as a method for invariant co-ordinate selection. By plotting the data with respect to this new invariant co-ordinate system, various data structures can be revealed. For example, under certain independent components models, it is shown that the invariant co- ordinates correspond to the independent components. Another example pertains to mixtures of elliptical distributions. In this case, it is shown that a subset of the invariant co-ordinates corresponds to Fisher's linear discriminant subspace, even though the class identifications of the data points are unknown. Some illustrative examples are given.
Keywords:
Affine invariance
Cluster analysis
Independent components analysis
Mixture models
Multivariate diagnostics
Multivariate scatter
Principal components
Projection pursuit
Robust statistics
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