Multiway clustering via tensor block models
This provides a method for multiway clustering in tensor data, applicable across domains like genomics and recommendation systems, but appears incremental as an extension of existing tensor models with regularization.
The authors tackled the problem of identifying multiway block structure from noisy tensors, which arises in genomics, recommendation systems, and other applications, by proposing a tensor block model with unified least-square estimation and sparse regularization, demonstrating outperformance over previous methods in simulations and real datasets.
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.