Personalized Tucker Decomposition: Modeling Commonality and Peculiarity on Tensor Data
This work addresses heterogeneity in tensor data for applications like solar flare detection and tonnage signal classification, but it is incremental as it builds on existing tensor decomposition methods.
The authors tackled the problem of capturing heterogeneity across tensor datasets by proposing personalized Tucker decomposition (perTucker), which decomposes data into shared global and personalized local components, and demonstrated its effectiveness in anomaly detection, client classification, and clustering with simulation and case studies.
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.