# Low Rank Convex Clustering For Matrix-Valued Observations

arXiv: https://arxiv.org/abs/2412.17328 · HTML: https://mlsanity.com/paper/2412.17328/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2024.

## Built on by (most cited first, 2 of 2)

- [Biconvex Biclustering](https://mlsanity.com/paper/2604.03936/) (2026)
- [Affinity Graph Connectivity in Convex Clustering](https://mlsanity.com/paper/2605.24673/) (2026)

## Abstract (arXiv)

Common clustering methods, such as k-means and convex clustering, group similar vector-valued observations into clusters. However, with the increasing prevalence of matrix-valued observations, which often exhibit low rank characteristics, there is a growing need for specialized clustering techniques for these data types. In this paper, we propose a low rank convex clustering model tailored for matrix-valued observations. Our approach extends the convex clustering model originally designed for vector-valued data to classify matrix-valued observations. Additionally, it serves as a convex relaxation of the low rank k-means method proposed by Z. Lyu, and D. Xia (arXiv:2207.04600). Theoretically, we establish exact cluster recovery for finite samples and asymptotic cluster recovery as the sample size approaches infinity. We also give a finite sample bound on prediction error in terms of centroid estimation, and further establish the prediction consistency. To make the model practically useful, we develop an efficient double-loop algorithm for solving it. Extensive numerical experiments are conducted to show the effectiveness of our proposed model.