Structured Sparse Principal Component Analysis

Rodolphe Jenatton, Guillaume Obozinski, Francis Bach
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:366-373, 2010.

Abstract

We present an extension of sparse PCA, or sparse dictionary learning, where the sparsity patterns of all dictionary elements are structured and constrained to belong to a prespecified set of shapes. This structured sparse PCA is based on a structured regularization recently introduced by Jenatton et al.(2009). While classical sparse priors only deal with cardinality, the regularization we use encodes higher-order information about the data. We propose an efficient and simple optimization procedure to solve this problem. Experiments with two practical tasks, the denoising of sparse structured signals and face recognition, demonstrate the benefits of the proposed structured approach over unstructured approaches.

Cite this Paper


BibTeX
@InProceedings{pmlr-v9-jenatton10a, title = {Structured Sparse Principal Component Analysis}, author = {Jenatton, Rodolphe and Obozinski, Guillaume and Bach, Francis}, booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics}, pages = {366--373}, year = {2010}, editor = {Teh, Yee Whye and Titterington, Mike}, volume = {9}, series = {Proceedings of Machine Learning Research}, address = {Chia Laguna Resort, Sardinia, Italy}, month = {13--15 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/jenatton10a/jenatton10a.pdf}, url = { http://proceedings.mlr.press/v9/jenatton10a.html }, abstract = {We present an extension of sparse PCA, or sparse dictionary learning, where the sparsity patterns of all dictionary elements are structured and constrained to belong to a prespecified set of shapes. This structured sparse PCA is based on a structured regularization recently introduced by Jenatton et al.(2009). While classical sparse priors only deal with cardinality, the regularization we use encodes higher-order information about the data. We propose an efficient and simple optimization procedure to solve this problem. Experiments with two practical tasks, the denoising of sparse structured signals and face recognition, demonstrate the benefits of the proposed structured approach over unstructured approaches.} }
Endnote
%0 Conference Paper %T Structured Sparse Principal Component Analysis %A Rodolphe Jenatton %A Guillaume Obozinski %A Francis Bach %B Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2010 %E Yee Whye Teh %E Mike Titterington %F pmlr-v9-jenatton10a %I PMLR %P 366--373 %U http://proceedings.mlr.press/v9/jenatton10a.html %V 9 %X We present an extension of sparse PCA, or sparse dictionary learning, where the sparsity patterns of all dictionary elements are structured and constrained to belong to a prespecified set of shapes. This structured sparse PCA is based on a structured regularization recently introduced by Jenatton et al.(2009). While classical sparse priors only deal with cardinality, the regularization we use encodes higher-order information about the data. We propose an efficient and simple optimization procedure to solve this problem. Experiments with two practical tasks, the denoising of sparse structured signals and face recognition, demonstrate the benefits of the proposed structured approach over unstructured approaches.
RIS
TY - CPAPER TI - Structured Sparse Principal Component Analysis AU - Rodolphe Jenatton AU - Guillaume Obozinski AU - Francis Bach BT - Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - Mike Titterington ID - pmlr-v9-jenatton10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 366 EP - 373 L1 - http://proceedings.mlr.press/v9/jenatton10a/jenatton10a.pdf UR - http://proceedings.mlr.press/v9/jenatton10a.html AB - We present an extension of sparse PCA, or sparse dictionary learning, where the sparsity patterns of all dictionary elements are structured and constrained to belong to a prespecified set of shapes. This structured sparse PCA is based on a structured regularization recently introduced by Jenatton et al.(2009). While classical sparse priors only deal with cardinality, the regularization we use encodes higher-order information about the data. We propose an efficient and simple optimization procedure to solve this problem. Experiments with two practical tasks, the denoising of sparse structured signals and face recognition, demonstrate the benefits of the proposed structured approach over unstructured approaches. ER -
APA
Jenatton, R., Obozinski, G. & Bach, F.. (2010). Structured Sparse Principal Component Analysis. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:366-373 Available from http://proceedings.mlr.press/v9/jenatton10a.html .

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