A Dirichlet Process Mixture Model for Spherical Data

Julian Straub, Jason Chang, Oren Freifeld, John Fisher III
Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38:930-938, 2015.

Abstract

Directional data, naturally represented as points on the unit sphere, appear in many applications. However, unlike the case of Euclidean data, flexible mixture models on the sphere that can capture correlations, handle an unknown number of components and extend readily to high-dimensional data have yet to be suggested. For this purpose we propose a Dirichlet process mixture model of Gaussian distributions in distinct tangent spaces (DP-TGMM) to the sphere. Importantly, the formulation of the proposed model allows the extension of recent advances in efficient inference for Bayesian nonparametric models to the spherical domain. Experiments on synthetic data as well as real-world 3D surface normal and 20-dimensional semantic word vector data confirm the expressiveness and applicability of the DP-TGMM.

Cite this Paper

BibTeX
@InProceedings{pmlr-v38-straub15, title = {{A Dirichlet Process Mixture Model for Spherical Data}}, author = {Straub, Julian and Chang, Jason and Freifeld, Oren and Fisher III, John}, booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics}, pages = {930--938}, year = {2015}, editor = {Lebanon, Guy and Vishwanathan, S. V. N.}, volume = {38}, series = {Proceedings of Machine Learning Research}, address = {San Diego, California, USA}, month = {09--12 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v38/straub15.pdf}, url = {https://proceedings.mlr.press/v38/straub15.html}, abstract = {Directional data, naturally represented as points on the unit sphere, appear in many applications. However, unlike the case of Euclidean data, flexible mixture models on the sphere that can capture correlations, handle an unknown number of components and extend readily to high-dimensional data have yet to be suggested. For this purpose we propose a Dirichlet process mixture model of Gaussian distributions in distinct tangent spaces (DP-TGMM) to the sphere. Importantly, the formulation of the proposed model allows the extension of recent advances in efficient inference for Bayesian nonparametric models to the spherical domain. Experiments on synthetic data as well as real-world 3D surface normal and 20-dimensional semantic word vector data confirm the expressiveness and applicability of the DP-TGMM.} }
Endnote
%0 Conference Paper %T A Dirichlet Process Mixture Model for Spherical Data %A Julian Straub %A Jason Chang %A Oren Freifeld %A John Fisher III %B Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2015 %E Guy Lebanon %E S. V. N. Vishwanathan %F pmlr-v38-straub15 %I PMLR %P 930--938 %U https://proceedings.mlr.press/v38/straub15.html %V 38 %X Directional data, naturally represented as points on the unit sphere, appear in many applications. However, unlike the case of Euclidean data, flexible mixture models on the sphere that can capture correlations, handle an unknown number of components and extend readily to high-dimensional data have yet to be suggested. For this purpose we propose a Dirichlet process mixture model of Gaussian distributions in distinct tangent spaces (DP-TGMM) to the sphere. Importantly, the formulation of the proposed model allows the extension of recent advances in efficient inference for Bayesian nonparametric models to the spherical domain. Experiments on synthetic data as well as real-world 3D surface normal and 20-dimensional semantic word vector data confirm the expressiveness and applicability of the DP-TGMM.
RIS
TY - CPAPER TI - A Dirichlet Process Mixture Model for Spherical Data AU - Julian Straub AU - Jason Chang AU - Oren Freifeld AU - John Fisher III BT - Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics DA - 2015/02/21 ED - Guy Lebanon ED - S. V. N. Vishwanathan ID - pmlr-v38-straub15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 38 SP - 930 EP - 938 L1 - http://proceedings.mlr.press/v38/straub15.pdf UR - https://proceedings.mlr.press/v38/straub15.html AB - Directional data, naturally represented as points on the unit sphere, appear in many applications. However, unlike the case of Euclidean data, flexible mixture models on the sphere that can capture correlations, handle an unknown number of components and extend readily to high-dimensional data have yet to be suggested. For this purpose we propose a Dirichlet process mixture model of Gaussian distributions in distinct tangent spaces (DP-TGMM) to the sphere. Importantly, the formulation of the proposed model allows the extension of recent advances in efficient inference for Bayesian nonparametric models to the spherical domain. Experiments on synthetic data as well as real-world 3D surface normal and 20-dimensional semantic word vector data confirm the expressiveness and applicability of the DP-TGMM. ER -
APA
Straub, J., Chang, J., Freifeld, O. & Fisher III, J.. (2015). A Dirichlet Process Mixture Model for Spherical Data. Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 38:930-938 Available from https://proceedings.mlr.press/v38/straub15.html.

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