Sparse logistic functional principal component analysis for binary data

TL;DR

This paper introduces a sparse logistic functional principal component analysis method tailored for binary functional data, emphasizing interpretability through local sparsity and demonstrating theoretical and practical advantages.

Contribution

The paper proposes a novel SLFPCA method with sparsity and roughness penalties, along with an efficient MM algorithm and theoretical guarantees for consistency and sparsistency.

Findings

Demonstrates the effectiveness of SLFPCA through numerical experiments

Shows advantages of the method in real physical activity data analysis

Provides theoretical proof of consistency and sparsistency

Abstract

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 the 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 efficient algorithm is developed for the optimization of the penalized likelihood using majorization-minimization (MM) algorithm. 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.