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Sparse logistic principal components analysis for binary data. (English) Zbl 1202.62084

Summary: We develop a new principal components analysis (PCA) type dimension reduction method for binary data. Different from the standard PCA which is defined on the observed data, the proposed PCA is defined on the logit transform of the success probabilities of the binary observations. Sparsity is introduced to the principal component (PC) loading vectors for enhanced interpretability and more stable extraction of the principal components. Our sparse PCA is formulated as solving an optimization problem with a criterion function motivated from a penalized Bernoulli likelihood. A majorization-minimization algorithm is developed to efficiently solve the optimization problem. The effectiveness of the proposed sparse logistic PCA method is illustrated by application to a single nucleotide polymorphism data set and a simulation study.

MSC:

62H25 Factor analysis and principal components; correspondence analysis
65C60 Computational problems in statistics (MSC2010)
90C90 Applications of mathematical programming
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