  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.
