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.

翻译：功能二元数据集在实际实践中经常出现,而数据的不同特性可能会给模型估计带来挑战。在本文中,我们提议了一种稀少的后勤功能主要组成部分分析(SLFPCA)方法来处理功能二元数据。 SLFPCA 寻找局部的隐形功能,以获得解释上的便利。我们通过惩罚性的伯努利可能性和粗糙处罚和稀疏处罚条款来制定问题。我们开发了一种高效的算法,以便利用主控-最小化算法优化受处罚的可能性。理论结果表明拟议方法的一致性和宽度。我们进行了彻底的数字实验,以展示 SLFPCA 方法的优点。我们的方法被进一步应用于物理活动数据集。