Convergence of a block coordinate descent method for nondifferentiable minimization
Journal of Optimization Theory and Applications
Sparse principal component analysis via regularized low rank matrix approximation
Journal of Multivariate Analysis
Principal component analysis of binary data by iterated singular value decomposition
Computational Statistics & Data Analysis
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Sparse logistic principal component analysis was proposed in Lee et al. (2010) for exploratory analysis of binary data. Relying on the joint estimation of multiple principal components, the algorithm therein is computationally too demanding to be useful when the data dimension is high. We develop a computationally fast algorithm using a combination of coordinate descent and majorization-minimization (MM) auxiliary optimization. Our new algorithm decouples the joint estimation of multiple components into separate estimations and consists of closed-form elementwise updating formulas for each sparse principal component. The performance of the proposed algorithm is tested using simulation and high-dimensional real-world datasets.