Loading...
Please wait, while we are loading the content...
Similar Documents
Sparse eigen methods by d.c. programming (2007)
| Content Provider | CiteSeerX |
|---|---|
| Author | Sriperumbudur, Bharath K. Torres, David A. Lanckriet, Gert R. G. |
| Description | Eigenvalue problems are rampant in machine learning and statistics and appear in the context of classification, dimensionality reduction, etc. In this paper, we consider a cardinality constrained variational formulation of generalized eigenvalue problem with sparse principal component analysis (PCA) as a special case. Using ℓ1-norm approximation to the cardinality constraint, previous methods have proposed both convex and non-convex solutions to the sparse PCA problem. In contrast, 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 locally convex programs. We show that the proposed method not only explains more variance with sparse loadings on the principal directions but also has better scalability compared to other methods. We demonstrate these results on a collection of datasets of varying dimensionality, two of which are high-dimensional gene datasets where the goal is to find few relevant genes that explain as much variance as possible. 1. |
| File Format | |
| Language | English |
| Publisher Date | 2007-01-01 |
| Publisher Institution | In Z. Ghahramani (Ed.), Proc. of the 24th Annual International Conference on Machine Learning (pp. 831–838). N.p.: Omnipress |
| Access Restriction | Open |
| Subject Keyword | Negative Log-likelihood Previous Method Machine Learning Sparse Principal Component Analysis Dimensionality Reduction Convex Function Generalized Eigenvalue Problem Student T-distribution Variational Formulation High-dimensional Gene Datasets Relevant Gene 1-norm Approximation Convex Program Much Variance Special Case Non-convex Solution Eigenvalue Problem Sparse Loading Principal Direction Cardinality Constraint Sparse Eigen Method Sparse Pca Problem |
| Content Type | Text |
| Resource Type | Article |
