Multi-View Time-Series Clustering with Temporal Structure and Tensor Regularization

We propose a tensor-based method for multi-view time-series clustering that jointly models temporal information and structure shared across views. Within each view, we combine normalized dissimilarities derived from trajectory states and first-order differences to construct a clustering objective incorporating pairwise relations and triplet geometry. View weights are learned adaptively to balance the view-specific fitting losses. Across views, we learn a common clustering embedding through symmetrized products of subspace projectors and impose tensor nuclear norm regularization on orthogonally aligned view-specific embeddings. Orthogonal alignment accommodates differences in embedding bases while preserving the subspace of each view. The final cluster assignments are obtained from the common embedding. To solve the resulting nonconvex, nonsmooth problem, we develop a two-level algorithm combining proximal majorization–minimization with an inexact augmented Lagrangian method. Under the stated conditions, we prove that the splitting constraint residual converges to zero and every accumulation point of the outer primal iterates is a first-order stationary point of the original problem. Comparative experiments on multiple datasets demonstrate the method’s effectiveness in clustering multi-view time series. Parameter sensitivity analyses and ablation studies further assess the effects of key parameters and individual components on clustering performance.