Adaptive Density Level Set Clustering

Ingo Steinwart
Proceedings of the 24th Annual Conference on Learning Theory, PMLR 19:703-738, 2011.

Abstract

Clusters are often defined to be the connected components of a density level set. Unfortunately, this definition depends on a level that needs to be user specified by some means. In this paper we present a simple algorithm that is able to asymptotically determine the optimal level, that is, the level at which there is the first split in the cluster tree of the data generating distribution. We further show that this algorithm asymptotically recovers the corresponding connected components. Unlike previous work, our analysis does not require strong assumptions on the density such as continuity or even smoothness.

Cite this Paper

BibTeX
@InProceedings{pmlr-v19-steinwart11a, title = {Adaptive Density Level Set Clustering}, author = {Steinwart, Ingo}, booktitle = {Proceedings of the 24th Annual Conference on Learning Theory}, pages = {703--738}, year = {2011}, editor = {Kakade, Sham M. and von Luxburg, Ulrike}, volume = {19}, series = {Proceedings of Machine Learning Research}, address = {Budapest, Hungary}, month = {09--11 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v19/steinwart11a/steinwart11a.pdf}, url = {https://proceedings.mlr.press/v19/steinwart11a.html}, abstract = {Clusters are often defined to be the connected components of a density level set. Unfortunately, this definition depends on a level that needs to be user specified by some means. In this paper we present a simple algorithm that is able to asymptotically determine the optimal level, that is, the level at which there is the first split in the cluster tree of the data generating distribution. We further show that this algorithm asymptotically recovers the corresponding connected components. Unlike previous work, our analysis does not require strong assumptions on the density such as continuity or even smoothness.} }
Endnote
%0 Conference Paper %T Adaptive Density Level Set Clustering %A Ingo Steinwart %B Proceedings of the 24th Annual Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2011 %E Sham M. Kakade %E Ulrike von Luxburg %F pmlr-v19-steinwart11a %I PMLR %P 703--738 %U https://proceedings.mlr.press/v19/steinwart11a.html %V 19 %X Clusters are often defined to be the connected components of a density level set. Unfortunately, this definition depends on a level that needs to be user specified by some means. In this paper we present a simple algorithm that is able to asymptotically determine the optimal level, that is, the level at which there is the first split in the cluster tree of the data generating distribution. We further show that this algorithm asymptotically recovers the corresponding connected components. Unlike previous work, our analysis does not require strong assumptions on the density such as continuity or even smoothness.
RIS
TY - CPAPER TI - Adaptive Density Level Set Clustering AU - Ingo Steinwart BT - Proceedings of the 24th Annual Conference on Learning Theory DA - 2011/12/21 ED - Sham M. Kakade ED - Ulrike von Luxburg ID - pmlr-v19-steinwart11a PB - PMLR DP - Proceedings of Machine Learning Research VL - 19 SP - 703 EP - 738 L1 - http://proceedings.mlr.press/v19/steinwart11a/steinwart11a.pdf UR - https://proceedings.mlr.press/v19/steinwart11a.html AB - Clusters are often defined to be the connected components of a density level set. Unfortunately, this definition depends on a level that needs to be user specified by some means. In this paper we present a simple algorithm that is able to asymptotically determine the optimal level, that is, the level at which there is the first split in the cluster tree of the data generating distribution. We further show that this algorithm asymptotically recovers the corresponding connected components. Unlike previous work, our analysis does not require strong assumptions on the density such as continuity or even smoothness. ER -
APA
Steinwart, I.. (2011). Adaptive Density Level Set Clustering. Proceedings of the 24th Annual Conference on Learning Theory, in Proceedings of Machine Learning Research 19:703-738 Available from https://proceedings.mlr.press/v19/steinwart11a.html.

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