# Dynamic Tensor Clustering

arXiv: https://arxiv.org/abs/1708.07259 · HTML: https://mlsanity.com/paper/1708.07259/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Aug 2017.

## Built on by (most cited first, 12 of 12)

- [Optimal Estimation and Computational Limit of Low-rank Gaussian Mixtures](https://mlsanity.com/paper/2201.09040/) (2022)
- [Optimal Clustering by Lloyd Algorithm for Low-Rank Mixture Model](https://mlsanity.com/paper/2207.04600/) (2022)
- [Low-Rank Robust Subspace Tensor Clustering for Metro Passenger Flow Modeling](https://mlsanity.com/paper/2404.04403/) (2024)
- [Covariate-assisted Sparse Tensor Completion](https://mlsanity.com/paper/2103.06428/) (2021)
- [Multi-Slice Clustering for 3-order Tensor Data](https://mlsanity.com/paper/2109.10803/) (2021)
- [Conditional Uncertainty Quantification for Tensorized Topological Neural Networks](https://mlsanity.com/paper/2410.15241/) (2024)
- [Tensor-Fused Multi-View Graph Contrastive Learning](https://mlsanity.com/paper/2410.15247/) (2024)
- [Personalized Tucker Decomposition: Modeling Commonality and Peculiarity on Tensor Data](https://mlsanity.com/paper/2309.03439/) (2023)
- [Jointly Modeling and Clustering Tensors in High Dimensions](https://mlsanity.com/paper/2104.07773/) (2021)
- [Optimal Variable Clustering for High-Dimensional Matrix Valued Data](https://mlsanity.com/paper/2112.12909/) (2021)
- [DBSCAN of Multi-Slice Clustering for Third-Order Tensors](https://mlsanity.com/paper/2303.07768/) (2023)
- [Tensor Methods in High Dimensional Data Analysis: Opportunities and Challenges](https://mlsanity.com/paper/2405.18412/) (2024)

## Abstract (arXiv)

Dynamic tensor data are becoming prevalent in numerous applications. Existing tensor clustering methods either fail to account for the dynamic nature of the data, or are inapplicable to a general-order tensor. Also there is often a gap between statistical guarantee and computational efficiency for existing tensor clustering solutions. In this article, we aim to bridge this gap by proposing a new dynamic tensor clustering method, which takes into account both sparsity and fusion structures, and enjoys strong statistical guarantees as well as high computational efficiency. Our proposal is based upon a new structured tensor factorization that encourages both sparsity and smoothness in parameters along the specified tensor modes. Computationally, we develop a highly efficient optimization algorithm that benefits from substantial dimension reduction. In theory, we first establish a non-asymptotic error bound for the estimator from the structured tensor factorization. Built upon this error bound, we then derive the rate of convergence of the estimated cluster centers, and show that the estimated clusters recover the true cluster structures with a high probability. Moreover, our proposed method can be naturally extended to co-clustering of multiple modes of the tensor data. The efficacy of our approach is illustrated via simulations and a brain dynamic functional connectivity analysis from an Autism spectrum disorder study.