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Abstract Details
Activity Number:
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600
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Type:
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Invited
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Date/Time:
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Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
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Sponsor:
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Biometrics Section
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Abstract - #300190 |
Title:
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Discriminant Analysis for High-Dimensional Problems
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Author(s):
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Daniela Witten*+ and Robert Tibshirani
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Companies:
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University of Washington and Stanford University
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Address:
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F-649, Health Sciences Building, Seattle, WA, 98195, USA
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Keywords:
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classification ;
lda ;
regularization ;
lasso ;
sparsity
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Abstract:
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We consider the classification setting, in which the data consist of p features measured on n observations, each of which belongs to one of K classes. Linear discriminant analysis (LDA) is a classical method for this problem, and it follows from three distinct viewpoints: maximum likelihood, optimal scoring, and Fisher's discriminant problem. In the high-dimensional setting where p>>n, LDA is not appropriate for two reasons. First, the standard estimate for the within-class covariance matrix is singular, and so the usual discriminant rule cannot be applied. Second, when p is large, it is difficult to interpret the classification rule obtained from LDA, since it involves all p features. A number of proposals have been made in the literature for solving this problem, and have centered around adapting the maximum likelihood and optimal scoring problems to the high-dimensional setting using regularization approaches. Fisher's discriminant problem has been largely overlooked because when penalties are applied, the problem is highly non-convex. We use a minorization algorithm to overcome this obstacle, and show that the resulting classifier is interpretable and accurate.
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