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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832561209709166592 |
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| author | Daniel Hlubinka Ondrej Vencalek |
| author_facet | Daniel Hlubinka Ondrej Vencalek |
| author_sort | Daniel Hlubinka |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-30e799f42e7149348fbb748255cdb217 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-30e799f42e7149348fbb748255cdb2172025-02-03T01:25:34ZengWileyJournal of Probability and Statistics1687-952X1687-95382013-01-01201310.1155/2013/629184629184Depth-Based Classification for Distributions with Nonconvex SupportDaniel Hlubinka0Ondrej Vencalek1Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University in Prague, Sokolovska 83, 186 75 Praha 8, Czech RepublicDepartment of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacky University in Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech RepublicHalfspace 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.http://dx.doi.org/10.1155/2013/629184 |
| spellingShingle | Daniel Hlubinka Ondrej Vencalek Depth-Based Classification for Distributions with Nonconvex Support Journal of Probability and Statistics |
| title | Depth-Based Classification for Distributions with Nonconvex Support |
| title_full | Depth-Based Classification for Distributions with Nonconvex Support |
| title_fullStr | Depth-Based Classification for Distributions with Nonconvex Support |
| title_full_unstemmed | Depth-Based Classification for Distributions with Nonconvex Support |
| title_short | Depth-Based Classification for Distributions with Nonconvex Support |
| title_sort | depth based classification for distributions with nonconvex support |
| url | http://dx.doi.org/10.1155/2013/629184 |
| work_keys_str_mv | AT danielhlubinka depthbasedclassificationfordistributionswithnonconvexsupport AT ondrejvencalek depthbasedclassificationfordistributionswithnonconvexsupport |