Hamish Burke | 2025-04-03

Related to: #bigData

Convex Clustering

Penalised method for clustering that has elements of K-means and Hierarchical Clustering
Goal is to minimise:

\sum_{i = 1}^{n} (x_{i} - u_{i})^{2} + λ \sum_{i < j}^{n} w_{i j} (u_{i} - u_{j})^{2}

$u_{i}$ is the clustering centroid for observation $i$
$λ$ is a penalty parameter
$w_{i j}$ are non-negative weights

If $λ = 0$ , $u_{i} = x_{i}$ , so that every observation is its own cluster
If $λ \to \infty$ , every observations is one big cluster
As $λ$ increases, centroids fuse

Choosing the weights

Unsupervised learning