Depth-Based Classification for Distributions with Nonconvex Support
Halfspace depth became a popular nonparametric tool for statistical analysis of multivariate data during the last two decades. One of applications of data depth considered recently in literature is the classification problem. The data depth approach is used instead of the linear discriminant analys...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2013/629184 |
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| Summary: | Halfspace depth became a popular nonparametric tool for statistical
analysis of multivariate data during the last two decades. One of applications
of data depth considered recently in literature is the classification problem.
The data depth approach is used instead of the linear discriminant analysis
mostly to avoid the parametric assumptions and to get better classifier for
data whose distribution is not elliptically symmetric, for example, skewed data. In
our paper, we suggest to use weighted version of halfspace depth rather than
the halfspace depth itself in order to obtain lower misclassification rate in
the case of “nonconvex” distributions. Simulations show that the results of
depth-based classifiers are comparable with linear discriminant analysis for
two normal populations, while for nonelliptic distributions the classifier based
on weighted halfspace depth outperforms both linear discriminant analysis and
classifier based on the usual (nonweighted) halfspace depth. |
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| ISSN: | 1687-952X 1687-9538 |