We consider the problem of jointly modeling and clustering populations of tensors by introducing a high-dimensional tensor mixture model with heterogeneous covariances. To effectively tackle the high dimensionality of tensor objects, we employ plausible dimension reduction assumptions that exploit the intrinsic structures of tensors such as low-rankness in the mean and separability in the covariance. In estimation, we develop an efficient high-dimensional expectation-conditional-maximization (HECM) algorithm that breaks the intractable optimization in the M-step into a sequence of much simpler conditional optimization problems, each of which is convex, admits regularization and has closed-form updating formulas. Our theoretical analysis is challenged by both the non-convexity in the EM-type estimation and having access to only the solutions of conditional maximizations in the M-step, leading to the notion of dual non-convexity. We demonstrate that the proposed HECM algorithm, with an appropriate initialization, converges geometrically to a neighborhood that is within statistical precision of the true parameter. The efficacy of our proposed method is demonstrated through comparative numerical experiments and an application to a medical study, where our proposal achieves an improved clustering accuracy over existing benchmarking methods.
Tensor Dirichlet Process Multinomial Mixture Model for Passenger Trajectory Clustering
University of Cologne（科隆大学）；Arizona State University（亚利桑那州立大学）；Tsinghua University（清华大学）；McGill University（麦吉尔大学）；The Hong Kong University of Science and Technology（香港科技大学）；HKUST (Guangzhou Campus)（香港科技大学（广州校区））
Choose A Table: Tensor Dirichlet Process Multinomial Mixture Model with Graphs for Passenger Trajectory Clustering
University of Cologne（科隆大学）；Arizona State University（亚利桑那州立大学）；Tsinghua University（清华大学）；McGill University（麦吉尔大学）；The Hong Kong University of Science and Technology（香港科技大学）；HKUST-GZ（香港科技大学（广州））
Multivariate Functional Data Modeling with Time-varying Clustering
We consider the situation where multivariate functional data has been collected over time at each of a set of sites. Our illustrative setting is bivariate, monitoring ozone and PM $_{10}$ levels as a function of time over the course of a year at a set of monitoring sites. The data we work with is from 24 monitoring sites in Mexico City which record hourly ozone and PM $_{10}$ levels. We use the data for the year 2017. Hence, we have 48 functions to work with. Our objective is to implement model-based clustering of the functions across the sites. Using our example, such clustering can be consid…
Low-Rank Robust Subspace Tensor Clustering for Metro Passenger Flow Modeling
School of Computing and Augmented Intelligence, Arizona State University（亚利桑那州立大学计算与增强智能学院）；Cologne Institute for Information Systems, University of Cologne（科隆大学科隆信息系统研究所）；EWI gGmbH, University of Cologne（科隆大学能源经济研究所）；Department of Industrial Engineering, Tsinghua University（清华大学工业工程系）；Department of Industrial Engineering and Decision Analytics, Hong Kong University of Science and Technology（香港科技大学工业工程与决策分析学系）；Information Hub, Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州）信息枢纽）
Division of Biostatistics Department of Population Health Grossman School of Medicine New York University（生物统计学系 人口健康部 Grossman 医学院 新 York 大学）；Department of Biostatistics Columbia University（生物统计学系 Columbia 大学）；Division of Biostatistics Department of Population Health Weill Cornell Medicine Cornell University（生物统计学系 人口健康部 Weill Cornell 医学院 Cornell 大学）
