  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.
