1. Projection sparse principal component analysis: An efficient least squares method
- Author
-
Gemai Chen and Giovanni Maria Merola
- Subjects
Statistics and Probability ,Numerical Analysis ,Dimensionality reduction ,020206 networking & telecommunications ,Feature selection ,02 engineering and technology ,Variance (accounting) ,01 natural sciences ,Least squares ,010104 statistics & probability ,Cardinality ,Power iteration ,Principal component analysis ,0202 electrical engineering, electronic engineering, information engineering ,0101 mathematics ,Statistics, Probability and Uncertainty ,Projection (set theory) ,Algorithm ,Mathematics - Abstract
We propose a new sparse principal component analysis (SPCA) method in which the solutions are obtained by projecting the full cardinality principal components onto subsets of variables. The resulting components are guaranteed to explain a given proportion of variance. The computation of these solutions is very efficient. The proposed method compares well with the optimal least squares sparse components. We show that other SPCA methods fail to identify the best sparse approximations of the principal components and explain less variance than our solutions. We illustrate and compare our method with others with extensive simulations and with the analysis of the computational results for nine datasets of increasing dimensions up to 16,000 variables.
- Published
- 2019