Least-Squares Log-Density Gradient Clustering for Riemannian Manifolds

Mina Ashizawa, Hiroaki Sasaki, Tomoya Sakai, Masashi Sugiyama
Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:537-546, 2017.

Abstract

Mean shift is a mode-seeking clustering algorithm that has been successfully used in a wide range of applications such as image segmentation and object tracking. To further improve the clustering performance, mean shift has been extended to various directions, including generalization to handle data on Riemannian manifolds and extension to directly estimating the density gradient without density estimation. In this paper, we combine these ideas and propose a novel mode-seeking algorithm for Riemannian manifolds with direct density-gradient estimation. Although the idea of combining the two extensions is rather straightforward, directly estimating the density gradient on Riemannian manifolds is mathematically challenging. We will provide a mathematically sound algorithm and demonstrate its usefulness through experiments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v54-ashizawa17a, title = {{Least-Squares Log-Density Gradient Clustering for Riemannian Manifolds}}, author = {Ashizawa, Mina and Sasaki, Hiroaki and Sakai, Tomoya and Sugiyama, Masashi}, booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics}, pages = {537--546}, year = {2017}, editor = {Singh, Aarti and Zhu, Jerry}, volume = {54}, series = {Proceedings of Machine Learning Research}, month = {20--22 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v54/ashizawa17a/ashizawa17a.pdf}, url = {https://proceedings.mlr.press/v54/ashizawa17a.html}, abstract = {Mean shift is a mode-seeking clustering algorithm that has been successfully used in a wide range of applications such as image segmentation and object tracking. To further improve the clustering performance, mean shift has been extended to various directions, including generalization to handle data on Riemannian manifolds and extension to directly estimating the density gradient without density estimation. In this paper, we combine these ideas and propose a novel mode-seeking algorithm for Riemannian manifolds with direct density-gradient estimation. Although the idea of combining the two extensions is rather straightforward, directly estimating the density gradient on Riemannian manifolds is mathematically challenging. We will provide a mathematically sound algorithm and demonstrate its usefulness through experiments.} }
Endnote
%0 Conference Paper %T Least-Squares Log-Density Gradient Clustering for Riemannian Manifolds %A Mina Ashizawa %A Hiroaki Sasaki %A Tomoya Sakai %A Masashi Sugiyama %B Proceedings of the 20th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2017 %E Aarti Singh %E Jerry Zhu %F pmlr-v54-ashizawa17a %I PMLR %P 537--546 %U https://proceedings.mlr.press/v54/ashizawa17a.html %V 54 %X Mean shift is a mode-seeking clustering algorithm that has been successfully used in a wide range of applications such as image segmentation and object tracking. To further improve the clustering performance, mean shift has been extended to various directions, including generalization to handle data on Riemannian manifolds and extension to directly estimating the density gradient without density estimation. In this paper, we combine these ideas and propose a novel mode-seeking algorithm for Riemannian manifolds with direct density-gradient estimation. Although the idea of combining the two extensions is rather straightforward, directly estimating the density gradient on Riemannian manifolds is mathematically challenging. We will provide a mathematically sound algorithm and demonstrate its usefulness through experiments.
APA
Ashizawa, M., Sasaki, H., Sakai, T. & Sugiyama, M.. (2017). Least-Squares Log-Density Gradient Clustering for Riemannian Manifolds. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 54:537-546 Available from https://proceedings.mlr.press/v54/ashizawa17a.html.

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