Linear dimensionality reduction via a heteroscedastic extension of LDA : the Chernoff criterion
We propose an eigenvector-based heteroscedastic linear dimension reduction (LDR) technique for multiclass data. The technique is based on a heteroscedastic two-class technique which utilizes the so-called Chernoff criterion, and successfully extends the well-known linear discriminant analysis (LDA)....
| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 26(2004), 6 vom: 26. Juni, Seite 732-9 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2004
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on pattern analysis and machine intelligence |
| Schlagworte: | Journal Article |
| Zusammenfassung: | We propose an eigenvector-based heteroscedastic linear dimension reduction (LDR) technique for multiclass data. The technique is based on a heteroscedastic two-class technique which utilizes the so-called Chernoff criterion, and successfully extends the well-known linear discriminant analysis (LDA). The latter, which is based on the Fisher criterion, is incapable of dealing with heteroscedastic data in a proper way. For the two-class case, the between-class scatter is generalized so to capture differences in (co)variances. It is shown that the classical notion of between-class scatter can be associated with Euclidean distances between class means. From this viewpoint, the between-class scatter is generalized by employing the Chernoff distance measure, leading to our proposed heteroscedastic measure. Finally, using the results from the two-class case, a multiclass extension of the Chernoff criterion is proposed. This criterion combines separation information present in the class mean as well as the class covariance matrices. Extensive experiments and a comparison with similar dimension reduction techniques are presented |
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| Beschreibung: | Date Completed 31.07.2008 Date Revised 26.06.2008 published: Print Citation Status MEDLINE |
| ISSN: | 1939-3539 |
| DOI: | 10.1109/TPAMI.2004.13 |