Asymptotic Generalization Bound of Fisher's Linear Discriminant Analysis
Fisher's linear discriminant analysis (FLDA) is an important dimension reduction method in statistical pattern recognition. It has been shown that FLDA is asymptotically Bayes optimal under the homoscedastic Gaussian assumption. However, this classical result has the following two major limitat...
| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 36(2014), 12 vom: 14. Dez., Seite 2325-37 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
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2014
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on pattern analysis and machine intelligence |
| Schlagworte: | Journal Article Research Support, Non-U.S. Gov't |
| Zusammenfassung: | Fisher's linear discriminant analysis (FLDA) is an important dimension reduction method in statistical pattern recognition. It has been shown that FLDA is asymptotically Bayes optimal under the homoscedastic Gaussian assumption. However, this classical result has the following two major limitations: 1) it holds only for a fixed dimensionality D, and thus does not apply when D and the training sample size N are proportionally large; 2) it does not provide a quantitative description on how the generalization ability of FLDA is affected by D and N. In this paper, we present an asymptotic generalization analysis of FLDA based on random matrix theory, in a setting where both D and N increase and D/N → γ ∈ [0,1). The obtained lower bound of the generalization discrimination power overcomes both limitations of the classical result, i.e., it is applicable when D and N are proportionally large and provides a quantitative description of the generalization ability of FLDA in terms of the ratio γ = D/N and the population discrimination power. Besides, the discrimination power bound also leads to an upper bound on the generalization error of binary-classification with FLDA |
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| Beschreibung: | Date Completed 25.11.2015 Date Revised 10.09.2015 published: Print Citation Status PubMed-not-MEDLINE |
| ISSN: | 1939-3539 |
| DOI: | 10.1109/TPAMI.2014.2327983 |