A coordinate descent MM algorithm for fast computation of sparse logistic PCA

• Published in: Computational statistics & data analysis Vol. 62; pp. 26 - 38
• Main Authors: Lee, Seokho, Huang, Jianhua Z.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.2013
• Subjects: algorithms; Binary data; Coordinate descent algorithm; data collection; MM algorithm; Penalized maximum likelihood; Principal component analysis; Penalized maximum likelihood; Binary data; MM algorithm; Coordinate descent algorithm; Principal component analysis
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2013.01.001

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.