Sparse Logistic Tensor Decomposition for Binary Data

TL;DR

This paper introduces sparse logistic tensor decomposition methods tailored for binary data, utilizing regularized likelihood and advanced algorithms to improve interpretability and stability, with applications in political relation analysis.

Contribution

The paper develops novel sparse logistic tensor decomposition techniques with regularization and algorithms, specifically designed for binary tensor data analysis.

Findings

Effective in binary tensor data analysis

Enhances interpretability of factors

Demonstrates utility through political relation data

Abstract

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 $\ell_{1}$-norm and $\ell_{0}$-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.