Personalized Tucker Decomposition: Modeling Commonality and Peculiarity on Tensor Data

TL;DR

This paper introduces perTucker, a personalized tensor decomposition method that captures both shared and individual features across datasets, improving tasks like anomaly detection and classification.

Contribution

It develops a novel personalized Tucker decomposition with a convergence-guaranteed algorithm for modeling heterogeneity in tensor data.

Findings

Effective in anomaly detection, client classification, and clustering.

Demonstrated superior performance on solar flare detection and tonnage signal classification.

Provides a new approach to modeling dataset heterogeneity in tensor analysis.

Abstract

We propose personalized Tucker decomposition (perTucker) to address the limitations of traditional tensor decomposition methods in capturing heterogeneity across different datasets. perTucker decomposes tensor data into shared global components and personalized local components. We introduce a mode orthogonality assumption and develop a proximal gradient regularized block coordinate descent algorithm that is guaranteed to converge to a stationary point. By learning unique and common representations across datasets, we demonstrate perTucker's effectiveness in anomaly detection, client classification, and clustering through a simulation study and two case studies on solar flare detection and tonnage signal classification.