Taux de dispersion des valeurs propres en ACP, AC et ACM
We define the quadratic concentration rate of a positive mesure, or quadratic dispersion rate of the values of its elementary density. When applied on the eigenvalues of a cloud of points in an Euclidean space, this rate is geometrically interpreted as an index of non-sphericity of the cloud, which...
Kaydedildi:
| Yayımlandı: | URI:https://journals.openedition.org/msh, |
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| Yazar: | |
| Materyal Türü: | Article ou chapitre numérique |
| Dil: | Français |
| Baskı/Yayın Bilgisi: |
Mathématiques et sciences humaines
2006
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| Online Erişim: | Accès Université d'Orléans et IFPM Accès Université d'Orléans et IFPM |
| Özet: | We define the quadratic concentration rate of a positive mesure, or quadratic dispersion rate of the values of its elementary density. When applied on the eigenvalues of a cloud of points in an Euclidean space, this rate is geometrically interpreted as an index of non-sphericity of the cloud, which accounts for its capacity to be well summarized by the first axis or axes. We provide and comment upon the expressions of corrected variance and dispersion rate of eigenvalues for the most usual methods of geometric data analysis : principal component analysis (weighted PCA, simple and standard) correspondence analysis (CA) and multiple correspondence analysis (MCA). These relationships particularly show that in standard PCA and in MCA, the average intensity of binary relations between variables is geometrically expressed by the non-sphericity of clouds of points. |
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