Title: Sparse principal component analysis based on least trimmed squares
Authors: Yixin Wang - University of Leuven (Belgium) [presenting]
Stefan Van Aelst - University of Leuven (Belgium)
Abstract: Sparse principal component analysis can be used to obtain stable and interpretable principal components from high-dimensional data. Robust sparse PCA is considered to handle outliers in the data. The new method LTS-SPCA starts from the MLTS-PCA method which provides a robust but non-sparse PCA solution. MLTS-PCA yields the PC subspace corresponding to the proportion of the data which gives the smallest sum of squared residuals. To get sparse solutions, LTS-SPCA then incorporates an $l_1$-norm penalty on the loading vectors to obtain sparsity. LTS-SPCA searches for the PC directions sequentially. This approach avoids that score outliers in the PC subspace destroy the sparse structure of the loadings. Simulation studies and real data examples show that LTS-SPCA can give accurate estimates, even when the data is highly contaminated. Moreover, compared to existing robust sparse PCA methods, LTS-SPCA can reduce the computation time to a great extent.