Sparse logistic functional principal component analysis for binary data

被引:0
|
作者
Rou Zhong
Shishi Liu
Haocheng Li
Jingxiao Zhang
机构
[1] Renmin University of China,Center for Applied Statistics, School of Statistics
[2] Hangzhou Dianzi University,School of Economics
[3] University of Calgary,Department of Mathematics and Statistics
来源
Statistics and Computing | 2023年 / 33卷
关键词
Functional principal component analysis; Penalized Bernoulli likelihood; Binary data; Local sparsity; MM algorithm;
D O I
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中图分类号
学科分类号
摘要
Functional binary datasets occur frequently in real practice, whereas discrete characteristics of the data can bring challenges to model estimation. In this paper, we propose a sparse logistic functional principal component analysis (SLFPCA) method to handle functional binary data. The SLFPCA looks for local sparsity of the eigenfunctions to obtain convenience in interpretation. We formulate the problem through a penalized Bernoulli likelihood with both roughness penalty and sparseness penalty terms. An innovative algorithm is developed for the optimization of the penalized likelihood using majorization-minimization algorithm. The proposed method is accompanied by R package SLFPCA for implementation. The theoretical results indicate both consistency and sparsistency of the proposed method. We conduct a thorough numerical experiment to demonstrate the advantages of the SLFPCA approach. Our method is further applied to a physical activity dataset.
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