The Sparse Eigenvalue Problem TeX Export

@article{citeulike:4640138, abstract = {In this paper, we consider the sparse eigenvalue problem wherein the goal is to obtain a sparse solution to the generalized eigenvalue problem. We achieve this by constraining the cardinality of the solution to the generalized eigenvalue problem and obtain sparse principal component analysis (PCA), sparse canonical correlation analysis (CCA) and sparse Fisher discriminant analysis (FDA) as special cases. Unlike the \$\ell\_1\$-norm approximation to the cardinality constraint, which previous methods have used in the context of sparse PCA, we propose a tighter approximation that is related to the negative log-likelihood of a Student's t-distribution. The problem is then framed as a d.c. (difference of convex functions) program and is solved as a sequence of convex programs by invoking the majorization-minimization method. The resulting algorithm is proved to exhibit global convergence behavior. The performance of the algorithm is empirically demonstrated on both sparse PCA (finding few relevant genes that explain as much variance as possible in a high-dimensional gene dataset) and sparse CCA (cross-language document retrieval and vocabulary selection for music retrieval) applications.}, archivePrefix = {arXiv}, author = {Sriperumbudur, Bharath and Torres, David and Lanckriet, Gert}, citeulike-article-id = {4640138}, citeulike-linkout-0 = {http://arxiv.org/abs/0901.1504}, citeulike-linkout-1 = {http://arxiv.org/pdf/0901.1504}, eprint = {0901.1504}, keywords = {cca, cross\_language\_document\_retrieval, dc\_program, fda, generalized\_eigenvalue\_problem, global\_convergence\_analysis, majorization\_minimization, music\_annotation, pca}, month = {Jan}, posted-at = {2009-05-27 01:17:07}, priority = {2}, title = {The Sparse Eigenvalue Problem}, url = {http://arxiv.org/abs/0901.1504}, year = {2009} }

TY - JOUR ID - citeulike:4640138 L3 - citeulike-article-id:4640138 N2 - In this paper, we consider the sparse eigenvalue problem wherein the goal is to obtain a sparse solution to the generalized eigenvalue problem. We achieve this by constraining the cardinality of the solution to the generalized eigenvalue problem and obtain sparse principal component analysis (PCA), sparse canonical correlation analysis (CCA) and sparse Fisher discriminant analysis (FDA) as special cases. Unlike the $\ell_1$-norm approximation to the cardinality constraint, which previous methods have used in the context of sparse PCA, we propose a tighter approximation that is related to the negative log-likelihood of a Student's t-distribution. The problem is then framed as a d.c. (difference of convex functions) program and is solved as a sequence of convex programs by invoking the majorization-minimization method. The resulting algorithm is proved to exhibit global convergence behavior. The performance of the algorithm is empirically demonstrated on both sparse PCA (finding few relevant genes that explain as much variance as possible in a high-dimensional gene dataset) and sparse CCA (cross-language document retrieval and vocabulary selection for music retrieval) applications. TI - The Sparse Eigenvalue Problem KW - cca KW - cross_language_document_retrieval KW - dc_program KW - fda KW - generalized_eigenvalue_problem KW - global_convergence_analysis KW - majorization_minimization KW - music_annotation KW - pca AU - Sriperumbudur, Bharath AU - Torres, David AU - Lanckriet, Gert PY - 2009/Jan/12/ UR - http://arxiv.org/abs/0901.1504 ER -