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Activity Number:
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423
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Type:
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Contributed
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Date/Time:
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Wednesday, August 5, 2009 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Statistical Learning and Data Mining
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| Abstract - #304122 |
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Title:
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Properties of the Quadratic Subspace in Discriminant Analysis
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Author(s):
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Santiago Velilla*+
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Companies:
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Universidad Carlos III de Madrid
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Address:
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Departamento de Estadistica, Getafe Madrid, International, 28903, Spain
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Keywords:
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Location-dispersion orthogonality ; Reduced quadratic discrimination ; SAVE ; SIR and SIRII
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Abstract:
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The concept of quadratic subspace is analyzed as a helpful tool for dimension reduction in quadratic discriminant analysis (QDA). It is argued that an adequate representation of the quadratic subspace leads to better methods for both data representation and classification. Several results describe the structure of the quadratic subspace, that is shown to contain some of the subspaces previously proposed in the literature for finding differences between the class means and covariances. A suitable assumption of orthogonality between location and dispersion subspaces allows to derive a convenient reduced version of the full QDA rule. A real data example is analyzed.
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