Sparsity in principal component analysis: A survey

作者：Xiang, Kui^*; Li, Bing Nan

来源：Acta Electronica Sinica, 2012, 40(12): 2525-2532.

DOI：10.3969/j.issn.0372-2112.2012.12.027

• Least absolute shrinkage and selection operators
• Least angle regressions
• Low-rank matrix approximations
• Matrix decomposition
• Multivariate statistics
• Principal Components
• Semidefinite relaxation
• Sparsity

Principal component analysis (PCA) is a popular multivariate statistic technique. However, the principal component estimation is often inconsistent while the samples are high-dimensional, and the principal component meaning is unintelligible too. The above two difficulties can be partially overcome by variable selection with sparse constraints. The basic concept of sparsity and the design standard of penalties were described in this survey. A typical sparse constraint, lasso, was introduced as well as its related morphs: fused lasso, group lasso, adaptive lasso and elastic net. Any of these constraints can be added into PCA to build a framework of spars PCA, and the emphasis was on how to transform sparse PCA into a convex optimizing problem and quickly solve it. Many transforming styles on sparse PCA were compared: singular value decomposition, sparse regression, low rank matrix approximation, penalized matrix decomposition and semi-definite relaxations. The approaches to solving the common and generalized lasso problems were analyzed based on least angle regression (LAR). The element of sparse PCA in functional data was discussed as a prospect.

• 出版日期2012
• 单位合肥工业大学