Optimal clustering under uncertainty.
Classical clustering algorithms typically either lack an underlying probability framework to make them predictive or focus on parameter estimation rather than defining and minimizing a notion of error. Recent work addresses these issues by developing a probabilistic framework based on the theory of...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2018-01-01
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| Series: | PLoS ONE |
| Online Access: | http://europepmc.org/articles/PMC6168142?pdf=render |
| _version_ | 1819067932103147520 |
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| author | Lori A Dalton Marco E Benalcázar Edward R Dougherty |
| author_facet | Lori A Dalton Marco E Benalcázar Edward R Dougherty |
| author_sort | Lori A Dalton |
| collection | DOAJ |
| description | Classical clustering algorithms typically either lack an underlying probability framework to make them predictive or focus on parameter estimation rather than defining and minimizing a notion of error. Recent work addresses these issues by developing a probabilistic framework based on the theory of random labeled point processes and characterizing a Bayes clusterer that minimizes the number of misclustered points. The Bayes clusterer is analogous to the Bayes classifier. Whereas determining a Bayes classifier requires full knowledge of the feature-label distribution, deriving a Bayes clusterer requires full knowledge of the point process. When uncertain of the point process, one would like to find a robust clusterer that is optimal over the uncertainty, just as one may find optimal robust classifiers with uncertain feature-label distributions. Herein, we derive an optimal robust clusterer by first finding an effective random point process that incorporates all randomness within its own probabilistic structure and from which a Bayes clusterer can be derived that provides an optimal robust clusterer relative to the uncertainty. This is analogous to the use of effective class-conditional distributions in robust classification. After evaluating the performance of robust clusterers in synthetic mixtures of Gaussians models, we apply the framework to granular imaging, where we make use of the asymptotic granulometric moment theory for granular images to relate robust clustering theory to the application. |
| first_indexed | 2024-12-21T16:26:06Z |
| format | Article |
| id | doaj.art-732e553d17dd4b3386a01ab6fe7cc915 |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-21T16:26:06Z |
| publishDate | 2018-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-732e553d17dd4b3386a01ab6fe7cc9152022-12-21T18:57:26ZengPublic Library of Science (PLoS)PLoS ONE1932-62032018-01-011310e020462710.1371/journal.pone.0204627Optimal clustering under uncertainty.Lori A DaltonMarco E BenalcázarEdward R DoughertyClassical clustering algorithms typically either lack an underlying probability framework to make them predictive or focus on parameter estimation rather than defining and minimizing a notion of error. Recent work addresses these issues by developing a probabilistic framework based on the theory of random labeled point processes and characterizing a Bayes clusterer that minimizes the number of misclustered points. The Bayes clusterer is analogous to the Bayes classifier. Whereas determining a Bayes classifier requires full knowledge of the feature-label distribution, deriving a Bayes clusterer requires full knowledge of the point process. When uncertain of the point process, one would like to find a robust clusterer that is optimal over the uncertainty, just as one may find optimal robust classifiers with uncertain feature-label distributions. Herein, we derive an optimal robust clusterer by first finding an effective random point process that incorporates all randomness within its own probabilistic structure and from which a Bayes clusterer can be derived that provides an optimal robust clusterer relative to the uncertainty. This is analogous to the use of effective class-conditional distributions in robust classification. After evaluating the performance of robust clusterers in synthetic mixtures of Gaussians models, we apply the framework to granular imaging, where we make use of the asymptotic granulometric moment theory for granular images to relate robust clustering theory to the application.http://europepmc.org/articles/PMC6168142?pdf=render |
| spellingShingle | Lori A Dalton Marco E Benalcázar Edward R Dougherty Optimal clustering under uncertainty. PLoS ONE |
| title | Optimal clustering under uncertainty. |
| title_full | Optimal clustering under uncertainty. |
| title_fullStr | Optimal clustering under uncertainty. |
| title_full_unstemmed | Optimal clustering under uncertainty. |
| title_short | Optimal clustering under uncertainty. |
| title_sort | optimal clustering under uncertainty |
| url | http://europepmc.org/articles/PMC6168142?pdf=render |
| work_keys_str_mv | AT loriadalton optimalclusteringunderuncertainty AT marcoebenalcazar optimalclusteringunderuncertainty AT edwardrdougherty optimalclusteringunderuncertainty |