Personalized Tucker Decomposition: Modeling Commonality and Peculiarity on Tensor Data

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.

References in corpus (10)

• Tensor Regression with Applications in Neuroimaging Data Analysis
• Changepoint detection for high-dimensional time series with missing data
• Structured Point Cloud Data Analysis via Regularized Tensor Regression for Process Modeling and Optimization
• The Internet of Federated Things (IoFT): A Vision for the Future and In-depth Survey of Data-driven Approaches for Federated Learning
• Tensor-based algorithms for image classification
• General Tensor Spectral Co-clustering for Higher-Order Data
• Smooth Robust Tensor Completion for Background/Foreground Separation with Missing Pixels: Novel Algorithm with Convergence Guarantee
• Personalized PCA: Decoupling Shared and Unique Features
• Multi-View Clustering via Semi-non-negative Tensor Factorization
• Covid-19 Analysis Using Tensor Methods