Dimensionality Reduction for Spectral Clustering

Donglin Niu, Jennifer Dy, Michael I. Jordan
Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, PMLR 15:552-560, 2011.

Abstract

Spectral clustering is a flexible clustering methodology that is applicable to a variety of data types and has the particular virtue that it makes few assumptions on cluster shapes. It has become popular in a variety of application areas, particularly in computational vision and bioinformatics. The approach appears, however, to be particularly sensitive to irrelevant and noisy dimensions in the data. We thus introduce an approach that automatically learns the relevant dimensions and spectral clustering simultaneously. We pursue an augmented form of spectral clustering in which an explicit projection operator is incorporated in the relaxed optimization functional. We optimize this functional over both the projection and the spectral embedding. Experiments on simulated and real data show that this approach yields significant improvements in the performance of spectral clustering.

Cite this Paper

BibTeX
@InProceedings{pmlr-v15-niu11a, title = {Dimensionality Reduction for Spectral Clustering}, author = {Niu, Donglin and Dy, Jennifer and Jordan, Michael I.}, booktitle = {Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics}, pages = {552--560}, year = {2011}, editor = {Gordon, Geoffrey and Dunson, David and Dudík, Miroslav}, volume = {15}, series = {Proceedings of Machine Learning Research}, address = {Fort Lauderdale, FL, USA}, month = {11--13 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v15/niu11a/niu11a.pdf}, url = {https://proceedings.mlr.press/v15/niu11a.html}, abstract = {Spectral clustering is a flexible clustering methodology that is applicable to a variety of data types and has the particular virtue that it makes few assumptions on cluster shapes. It has become popular in a variety of application areas, particularly in computational vision and bioinformatics. The approach appears, however, to be particularly sensitive to irrelevant and noisy dimensions in the data. We thus introduce an approach that automatically learns the relevant dimensions and spectral clustering simultaneously. We pursue an augmented form of spectral clustering in which an explicit projection operator is incorporated in the relaxed optimization functional. We optimize this functional over both the projection and the spectral embedding. Experiments on simulated and real data show that this approach yields significant improvements in the performance of spectral clustering.} }
Endnote
%0 Conference Paper %T Dimensionality Reduction for Spectral Clustering %A Donglin Niu %A Jennifer Dy %A Michael I. Jordan %B Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2011 %E Geoffrey Gordon %E David Dunson %E Miroslav Dudík %F pmlr-v15-niu11a %I PMLR %P 552--560 %U https://proceedings.mlr.press/v15/niu11a.html %V 15 %X Spectral clustering is a flexible clustering methodology that is applicable to a variety of data types and has the particular virtue that it makes few assumptions on cluster shapes. It has become popular in a variety of application areas, particularly in computational vision and bioinformatics. The approach appears, however, to be particularly sensitive to irrelevant and noisy dimensions in the data. We thus introduce an approach that automatically learns the relevant dimensions and spectral clustering simultaneously. We pursue an augmented form of spectral clustering in which an explicit projection operator is incorporated in the relaxed optimization functional. We optimize this functional over both the projection and the spectral embedding. Experiments on simulated and real data show that this approach yields significant improvements in the performance of spectral clustering.
RIS
TY - CPAPER TI - Dimensionality Reduction for Spectral Clustering AU - Donglin Niu AU - Jennifer Dy AU - Michael I. Jordan BT - Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics DA - 2011/06/14 ED - Geoffrey Gordon ED - David Dunson ED - Miroslav Dudík ID - pmlr-v15-niu11a PB - PMLR DP - Proceedings of Machine Learning Research VL - 15 SP - 552 EP - 560 L1 - http://proceedings.mlr.press/v15/niu11a/niu11a.pdf UR - https://proceedings.mlr.press/v15/niu11a.html AB - Spectral clustering is a flexible clustering methodology that is applicable to a variety of data types and has the particular virtue that it makes few assumptions on cluster shapes. It has become popular in a variety of application areas, particularly in computational vision and bioinformatics. The approach appears, however, to be particularly sensitive to irrelevant and noisy dimensions in the data. We thus introduce an approach that automatically learns the relevant dimensions and spectral clustering simultaneously. We pursue an augmented form of spectral clustering in which an explicit projection operator is incorporated in the relaxed optimization functional. We optimize this functional over both the projection and the spectral embedding. Experiments on simulated and real data show that this approach yields significant improvements in the performance of spectral clustering. ER -
APA
Niu, D., Dy, J. & Jordan, M.I.. (2011). Dimensionality Reduction for Spectral Clustering. Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 15:552-560 Available from https://proceedings.mlr.press/v15/niu11a.html.

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