# Statistical Properties of Convex Clustering

arXiv: https://arxiv.org/abs/1503.08340 · HTML: https://mlsanity.com/paper/1503.08340/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2015.

## Built on by (most cited first, 19 of 19)

- [GraphMAD: Graph Mixup for Data Augmentation using Data-Driven Convex Clustering](https://mlsanity.com/paper/2210.15721/) (2022)
- [Uniform Concentration Bounds toward a Unified Framework for Robust Clustering](https://mlsanity.com/paper/2110.14148/) (2021)
- [Local versions of sum-of-norms clustering](https://mlsanity.com/paper/2109.09589/) (2021)
- [Sum-of-norms clustering does not separate nearby balls](https://mlsanity.com/paper/2104.13753/) (2021)
- [On Convex Clustering Solutions](https://mlsanity.com/paper/2105.08348/) (2021)
- [Bregman Power k-Means for Clustering Exponential Family Data](https://mlsanity.com/paper/2206.10860/) (2022)
- [Multi-Task Learning Regression via Convex Clustering](https://mlsanity.com/paper/2304.13342/) (2023)
- [Network Clustering for Latent State and Changepoint Detection](https://mlsanity.com/paper/2111.01273/) (2021)
- [Randomly Projected Convex Clustering Model: Motivation, Realization, and Cluster Recovery Guarantees](https://mlsanity.com/paper/2303.16841/) (2023)
- [Fusion Subspace Clustering for Incomplete Data](https://mlsanity.com/paper/2205.10872/) (2022)
- [Simple and Scalable Algorithms for Cluster-Aware Precision Medicine](https://mlsanity.com/paper/2211.16553/) (2022)
- [Re-embedding data to strengthen recovery guarantees of clustering](https://mlsanity.com/paper/2301.10901/) (2023)
- [Adaptive Self-supervised Robust Clustering for Unstructured Data with Unknown Cluster Number](https://mlsanity.com/paper/2407.20119/) (2024)
- [Tree-Guided L1-Convex Clustering](https://mlsanity.com/paper/2503.24012/) (2025)
- [Bounds on Perfect Node Classification: A Convex Graph Clustering Perspective](https://mlsanity.com/paper/2508.20231/) (2025)
- [A New Framework for Convex Clustering in Kernel Spaces: Finite Sample Bounds, Consistency and Performance Insights](https://mlsanity.com/paper/2511.05159/) (2025)
- [Convex Clustering Redefined: Robust Learning with the Median of Means Estimator](https://mlsanity.com/paper/2511.14784/) (2025)
- [Biconvex Biclustering](https://mlsanity.com/paper/2604.03936/) (2026)
- [Affinity Graph Connectivity in Convex Clustering](https://mlsanity.com/paper/2605.24673/) (2026)

## Abstract (arXiv)

In this manuscript, we study the statistical properties of convex clustering. We establish that convex clustering is closely related to single linkage hierarchical clustering and k-means clustering. In addition, we derive the range of tuning parameter for convex clustering that yields a non-trivial solution. We also provide an unbiased estimate of the degrees of freedom, and provide a finite sample bound for the prediction error for convex clustering. We compare convex clustering to some traditional clustering methods in simulation studies.