  We consider the problem of identifying multiway block structure from a large
noisy tensor. Such problems arise frequently in applications such as genomics,
recommendation system, topic modeling, and sensor network localization. We
propose a tensor block model, develop a unified least-square estimation, and
obtain the theoretical accuracy guarantees for multiway clustering. The
statistical convergence of the estimator is established, and we show that the
associated clustering procedure achieves partition consistency. A sparse
regularization is further developed for identifying important blocks with
elevated means. The proposal handles a broad range of data types, including
binary, continuous, and hybrid observations. Through simulation and application
to two real datasets, we demonstrate the outperformance of our approach over
previous methods.
