A Nonparametric Bayesian Approach to Modeling Overlapping Clusters

Katherine A. Heller, Zoubin Ghahramani
Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 2:187-194, 2007.

Abstract

Although clustering data into mutually exclusive partitions has been an extremely successful approach to unsupervised learning, there are many situations in which a richer model is needed to fully represent the data. This is the case in problems where data points actually simultaneously belong to multiple, overlapping clusters. For example a particular gene may have several functions, therefore belonging to several distinct clusters of genes, and a biologist may want to discover these through unsupervised modeling of gene expression data. We present a new nonparametric Bayesian method, the Infinite Overlapping Mixture Model (IOMM), for modeling overlapping clusters. The IOMM uses exponential family distributions to model each cluster and forms an overlapping mixture by taking products of such distributions, much like products of experts (Hinton, 2002). The IOMM allows an unbounded number of clusters, and assignments of points to (multiple) clusters is modeled using an Indian Buffet Process (IBP), (Griffiths and Ghahramani, 2006). The IOMM has the desirable properties of being able to focus in on overlapping regions while maintaining the ability to model a potentially infinite number of clusters which may overlap. We derive MCMC inference algorithms for the IOMM and show that these can be used to cluster movies into multiple genres.

Cite this Paper

BibTeX
@InProceedings{pmlr-v2-heller07a, title = {A Nonparametric Bayesian Approach to Modeling Overlapping Clusters}, author = {Heller, Katherine A. and Ghahramani, Zoubin}, booktitle = {Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics}, pages = {187--194}, year = {2007}, editor = {Meila, Marina and Shen, Xiaotong}, volume = {2}, series = {Proceedings of Machine Learning Research}, address = {San Juan, Puerto Rico}, month = {21--24 Mar}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v2/heller07a/heller07a.pdf}, url = {https://proceedings.mlr.press/v2/heller07a.html}, abstract = {Although clustering data into mutually exclusive partitions has been an extremely successful approach to unsupervised learning, there are many situations in which a richer model is needed to fully represent the data. This is the case in problems where data points actually simultaneously belong to multiple, overlapping clusters. For example a particular gene may have several functions, therefore belonging to several distinct clusters of genes, and a biologist may want to discover these through unsupervised modeling of gene expression data. We present a new nonparametric Bayesian method, the Infinite Overlapping Mixture Model (IOMM), for modeling overlapping clusters. The IOMM uses exponential family distributions to model each cluster and forms an overlapping mixture by taking products of such distributions, much like products of experts (Hinton, 2002). The IOMM allows an unbounded number of clusters, and assignments of points to (multiple) clusters is modeled using an Indian Buffet Process (IBP), (Griffiths and Ghahramani, 2006). The IOMM has the desirable properties of being able to focus in on overlapping regions while maintaining the ability to model a potentially infinite number of clusters which may overlap. We derive MCMC inference algorithms for the IOMM and show that these can be used to cluster movies into multiple genres.} }
Endnote
%0 Conference Paper %T A Nonparametric Bayesian Approach to Modeling Overlapping Clusters %A Katherine A. Heller %A Zoubin Ghahramani %B Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2007 %E Marina Meila %E Xiaotong Shen %F pmlr-v2-heller07a %I PMLR %P 187--194 %U https://proceedings.mlr.press/v2/heller07a.html %V 2 %X Although clustering data into mutually exclusive partitions has been an extremely successful approach to unsupervised learning, there are many situations in which a richer model is needed to fully represent the data. This is the case in problems where data points actually simultaneously belong to multiple, overlapping clusters. For example a particular gene may have several functions, therefore belonging to several distinct clusters of genes, and a biologist may want to discover these through unsupervised modeling of gene expression data. We present a new nonparametric Bayesian method, the Infinite Overlapping Mixture Model (IOMM), for modeling overlapping clusters. The IOMM uses exponential family distributions to model each cluster and forms an overlapping mixture by taking products of such distributions, much like products of experts (Hinton, 2002). The IOMM allows an unbounded number of clusters, and assignments of points to (multiple) clusters is modeled using an Indian Buffet Process (IBP), (Griffiths and Ghahramani, 2006). The IOMM has the desirable properties of being able to focus in on overlapping regions while maintaining the ability to model a potentially infinite number of clusters which may overlap. We derive MCMC inference algorithms for the IOMM and show that these can be used to cluster movies into multiple genres.
RIS
TY - CPAPER TI - A Nonparametric Bayesian Approach to Modeling Overlapping Clusters AU - Katherine A. Heller AU - Zoubin Ghahramani BT - Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics DA - 2007/03/11 ED - Marina Meila ED - Xiaotong Shen ID - pmlr-v2-heller07a PB - PMLR DP - Proceedings of Machine Learning Research VL - 2 SP - 187 EP - 194 L1 - http://proceedings.mlr.press/v2/heller07a/heller07a.pdf UR - https://proceedings.mlr.press/v2/heller07a.html AB - Although clustering data into mutually exclusive partitions has been an extremely successful approach to unsupervised learning, there are many situations in which a richer model is needed to fully represent the data. This is the case in problems where data points actually simultaneously belong to multiple, overlapping clusters. For example a particular gene may have several functions, therefore belonging to several distinct clusters of genes, and a biologist may want to discover these through unsupervised modeling of gene expression data. We present a new nonparametric Bayesian method, the Infinite Overlapping Mixture Model (IOMM), for modeling overlapping clusters. The IOMM uses exponential family distributions to model each cluster and forms an overlapping mixture by taking products of such distributions, much like products of experts (Hinton, 2002). The IOMM allows an unbounded number of clusters, and assignments of points to (multiple) clusters is modeled using an Indian Buffet Process (IBP), (Griffiths and Ghahramani, 2006). The IOMM has the desirable properties of being able to focus in on overlapping regions while maintaining the ability to model a potentially infinite number of clusters which may overlap. We derive MCMC inference algorithms for the IOMM and show that these can be used to cluster movies into multiple genres. ER -
APA
Heller, K.A. & Ghahramani, Z.. (2007). A Nonparametric Bayesian Approach to Modeling Overlapping Clusters. Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 2:187-194 Available from https://proceedings.mlr.press/v2/heller07a.html.

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