Sparse Logistic Tensor Decomposition for Binary Data

06/27/2021
by   Jianhao Zhang, et al.
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Tensor data are increasingly available in many application domains. We develop several tensor decomposition methods for binary tensor data. Different from classical tensor decompositions for continuous-valued data with squared error loss, we formulate logistic tensor decompositions for binary data with a Bernoulli likelihood. To enhance the interpretability of estimated factors and improve their stability further, we propose sparse formulations of logistic tensor decomposition by considering ℓ_1-norm and ℓ_0-norm regularized likelihood. To handle the resulting optimization problems, we develop computational algorithms which combine the strengths of tensor power method and majorization-minimization (MM) algorithm. Through simulation studies, we demonstrate the utility of our methods in analysis of binary tensor data. To illustrate the effectiveness of the proposed methods, we analyze a dataset concerning nations and their political relations and perform co-clustering of estimated factors to find associations between the nations and political relations.

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