# An Efficient Semismooth Newton Based Algorithm for Convex Clustering

arXiv: https://arxiv.org/abs/1802.07091 · HTML: https://mlsanity.com/paper/1802.07091/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2018.

## Built on by (most cited first, 5 of 5)

- [On Convex Clustering Solutions](https://mlsanity.com/paper/2105.08348/) (2021)
- [Sum-of-norms regularized Nonnegative Matrix Factorization](https://mlsanity.com/paper/2407.00706/) (2024)
- [Randomly Projected Convex Clustering Model: Motivation, Realization, and Cluster Recovery Guarantees](https://mlsanity.com/paper/2303.16841/) (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)

## Abstract (arXiv)

Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications. Popular methods like K-means, may suffer from instability as they are prone to get stuck in its local minima. Recently, the sum-of-norms (SON) model (also known as clustering path), which is a convex relaxation of hierarchical clustering model, has been proposed in [7] and [5] Although numerical algorithms like ADMM and AMA are proposed to solve convex clustering model [2], it is known to be very challenging to solve large-scale problems. In this paper, we propose a semi-smooth Newton based augmented Lagrangian method for large-scale convex clustering problems. Extensive numerical experiments on both simulated and real data demonstrate that our algorithm is highly efficient and robust for solving large-scale problems. Moreover, the numerical results also show the superior performance and scalability of our algorithm compared to existing first-order methods.