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Automatic sparse principal component analysis
Author(s) -
Park Heewon,
Yamaguchi Rui,
Imoto Seiya,
Miyano Satoru
Publication year - 2021
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11579
Subject(s) - principal component analysis , dimensionality reduction , sparse pca , singular value decomposition , computer science , sparse approximation , pattern recognition (psychology) , artificial intelligence , robust principal component analysis , projection (relational algebra) , sparse matrix , dimension (graph theory) , feature selection , regularization (linguistics) , curse of dimensionality , algorithm , mathematics , physics , quantum mechanics , pure mathematics , gaussian
The wide availability of computers enables us to accumulate a huge amount of data, thus effective tools to extract information from the huge volume of data have become critical. Principal component analysis (PCA) is a useful and traditional tool for dimensionality reduction of massive high‐dimensional datasets. Recently, sparse principal component (PC) loading estimation based on L 1 ‐type regularization has drawn a large amount of attention. Although sparse PCA makes interpretation easily and performs dimension reduction without disturbance from noisy features, the existing studies on sparse PCA were based on an arbitrary number of PCs without any statistical justification. We propose a novel method, called as automatic sparse PCA, which can perform PC selection and sparse PC loading estimation, simultaneously. For PC selection, we first develop sparse singular value decomposition (sparse SVD), then incorporate sparsity into PC loading estimation. The proposed method enables us to perform dimension reduction and PC loading estimation, simultaneously. Furthermore, we can perform PCA without disturbance from noisy features. It can be seen through Monte Carlo experiments that the proposed automatic sparse PCA outperforms sparse structure identification and reconstructing data based on low‐dimensional projection. The proposed method is also applied to a number of real datasets and it can be also seen that our method achieves effectiveness for estimation accuracy and interpreting PCA results.