# Convex Clustering

### ConvexClustering: a MATLAB package for convex clustering

##### Authors: Defeng Sun, Kim-Chuan Toh, Yancheng YuanCorrespondence: K.-C. Toh

The software was first released in June 2021.
The software is designed to solve convex clustering problems of the following form given input data $$(a_1,\ldots,a_n)$$

$$\min \Big\{ \sum_{i=1}^n \|x_i -a_i\|^2 + \gamma \sum_{(i,j)\in \mathcal{E}} w_{ij}\|x_i – x_j\| \;\mid\; x_i\in\mathbb{R}^d, i=1,\ldots,n\Big\}$$
where  $$\gamma$$ is a positive regularization parameter; typically $$w_{ij} = \exp(-\phi\|a_i-a_j\|^2)$$ and $$\phi$$ is a positive constant; $$\mathcal{E}$$ is the $$k$$-nearest neighbors graph that is constructed based on the pairwise distances $$\|a_i-a_j\|$$.

Important note: this is a research software. It is not intended nor designed to be a general purpose software at the moment.

##### Citation:
1. D.F. Sun, K.C. Toh, and Y.C. Yuan, Convex clustering: model, theoretical guarantee and efficient algorithm, Journal of Machine Learning Research, 22(9), 2021.
2. Y.C. Yuan, D.F. Sun, and K.C. Toh, An efficient semismooth Newton based algorithm for convex clustering, ICML 2018.