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Intrinsic dimensionality and small sample properties of classifiers
Kybernetika, Tome 34 (1998) no. 4, pp. 461-466 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Small learning-set properties of the Euclidean distance, the Parzen window, the minimum empirical error and the nonlinear single layer perceptron classifiers depend on an “intrinsic dimensionality” of the data, however the Fisher linear discriminant function is sensitive to all dimensions. There is no unique definition of the “intrinsic dimensionality”. The dimensionality of the subspace where the data points are situated is not a sufficient definition of the “intrinsic dimensionality”. An exact definition depends both, on a true distribution of the pattern classes, and on the type of the classifier used.
Small learning-set properties of the Euclidean distance, the Parzen window, the minimum empirical error and the nonlinear single layer perceptron classifiers depend on an “intrinsic dimensionality” of the data, however the Fisher linear discriminant function is sensitive to all dimensions. There is no unique definition of the “intrinsic dimensionality”. The dimensionality of the subspace where the data points are situated is not a sufficient definition of the “intrinsic dimensionality”. An exact definition depends both, on a true distribution of the pattern classes, and on the type of the classifier used.
Classification : 62H30, 68T05
Keywords: intrinsic dimensionality; nonlinear classifiers 
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Raudys, Šarūnas. Intrinsic dimensionality and small sample properties of classifiers. Kybernetika, Tome 34 (1998) no. 4, pp. 461-466. http://geodesic.mathdoc.fr/item/KYB_1998_34_4_a17/

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