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.

翻译：我们提出个性化Tucker分解（perTucker）以解决传统张量分解方法在捕捉不同数据集异质性方面的局限性。perTucker将张量数据分解为共享全局分量与个性化局部分量。我们引入模态正交性假设，并开发了一种近端梯度正则化块坐标下降算法，该算法可保证收敛至稳定点。通过学习跨数据集的独特表示与通用表示，我们通过模拟实验以及太阳耀斑检测、吨位信号分类两项案例研究，论证了perTucker在异常检测、客户分类与聚类中的有效性。