Multiway clustering via tensor block models

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 estimati...

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Bibliographic Details
Published in:arXiv.org 2021-01
Main Authors: Wang, Miaoyan, Zeng, Yuchen
Format: Article
Language:English
Subjects:
Clustering
Computer simulation
Mathematical analysis
Recommender systems
Regularization
Tensors
Online Access:Get full text
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Summary: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.
ISSN:2331-8422