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.
翻译:在许多应用领域,人们越来越多地可以获得电离层数据。我们为二进制数据开发了数种高分解方法。与传统的高分分解法不同的是,对连续价值数据进行高分解,加上平差损失,我们用伯南利的可能性,为二进制数据制定后勤分解方法。为了提高估计因素的可解释性,进一步提高其稳定性,我们建议通过考虑$@%1}-norm和$\ell%0}-norm 常规化的可能性,对后勤高分解法进行稀疏的配方。为了处理由此产生的优化问题,我们开发了计算算法,将高压功率法和主要化-最小化(MM)算法的优点结合起来。我们通过模拟研究,展示了我们分析二进制数据的方法的效用。为了说明拟议方法的有效性,我们分析了关于国家及其政治关系的数据集,并对估计因素进行联合组合,以找出国家和政治关系之间的联系。