Sparse Uncorrelated Linear Discriminant Analysis

Xiaowei Zhang, Delin Chu
Proceedings of the 30th International Conference on Machine Learning, PMLR 28(1):45-52, 2013.

Abstract

In this paper, we develop a novel approach for sparse uncorrelated linear discriminant analysis (ULDA). Our proposal is based on characterization of all solutions of the generalized ULDA. We incorporate sparsity into the ULDA transformation by seeking the solution with minimum \ell_1-norm from all minimum dimension solutions of the generalized ULDA. The problem is then formulated as a \ell_1-minimization problem and is solved by accelerated linearized Bregman method. Experiments on high-dimensional gene expression data demonstrate that our approach not only computes extremely sparse solutions but also performs well in classification. Experimental results also show that our approach can help for data visualization in low-dimensional space.

Cite this Paper

BibTeX
@InProceedings{pmlr-v28-zhang13, title = {Sparse Uncorrelated Linear Discriminant Analysis}, author = {Zhang, Xiaowei and Chu, Delin}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {45--52}, year = {2013}, editor = {Dasgupta, Sanjoy and McAllester, David}, volume = {28}, number = {1}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/zhang13.pdf}, url = {https://proceedings.mlr.press/v28/zhang13.html}, abstract = {In this paper, we develop a novel approach for sparse uncorrelated linear discriminant analysis (ULDA). Our proposal is based on characterization of all solutions of the generalized ULDA. We incorporate sparsity into the ULDA transformation by seeking the solution with minimum \ell_1-norm from all minimum dimension solutions of the generalized ULDA. The problem is then formulated as a \ell_1-minimization problem and is solved by accelerated linearized Bregman method. Experiments on high-dimensional gene expression data demonstrate that our approach not only computes extremely sparse solutions but also performs well in classification. Experimental results also show that our approach can help for data visualization in low-dimensional space.} }
Endnote
%0 Conference Paper %T Sparse Uncorrelated Linear Discriminant Analysis %A Xiaowei Zhang %A Delin Chu %B Proceedings of the 30th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Sanjoy Dasgupta %E David McAllester %F pmlr-v28-zhang13 %I PMLR %P 45--52 %U https://proceedings.mlr.press/v28/zhang13.html %V 28 %N 1 %X In this paper, we develop a novel approach for sparse uncorrelated linear discriminant analysis (ULDA). Our proposal is based on characterization of all solutions of the generalized ULDA. We incorporate sparsity into the ULDA transformation by seeking the solution with minimum \ell_1-norm from all minimum dimension solutions of the generalized ULDA. The problem is then formulated as a \ell_1-minimization problem and is solved by accelerated linearized Bregman method. Experiments on high-dimensional gene expression data demonstrate that our approach not only computes extremely sparse solutions but also performs well in classification. Experimental results also show that our approach can help for data visualization in low-dimensional space.
RIS
TY - CPAPER TI - Sparse Uncorrelated Linear Discriminant Analysis AU - Xiaowei Zhang AU - Delin Chu BT - Proceedings of the 30th International Conference on Machine Learning DA - 2013/02/13 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-zhang13 PB - PMLR DP - Proceedings of Machine Learning Research VL - 28 IS - 1 SP - 45 EP - 52 L1 - http://proceedings.mlr.press/v28/zhang13.pdf UR - https://proceedings.mlr.press/v28/zhang13.html AB - In this paper, we develop a novel approach for sparse uncorrelated linear discriminant analysis (ULDA). Our proposal is based on characterization of all solutions of the generalized ULDA. We incorporate sparsity into the ULDA transformation by seeking the solution with minimum \ell_1-norm from all minimum dimension solutions of the generalized ULDA. The problem is then formulated as a \ell_1-minimization problem and is solved by accelerated linearized Bregman method. Experiments on high-dimensional gene expression data demonstrate that our approach not only computes extremely sparse solutions but also performs well in classification. Experimental results also show that our approach can help for data visualization in low-dimensional space. ER -
APA
Zhang, X. & Chu, D.. (2013). Sparse Uncorrelated Linear Discriminant Analysis. Proceedings of the 30th International Conference on Machine Learning, in Proceedings of Machine Learning Research 28(1):45-52 Available from https://proceedings.mlr.press/v28/zhang13.html.

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