Clustering partitions a data set S = fs1;:::;sng < m into groups of nearby points. Distance-based clustering uses op-timisation criteria for deening the quality of the partition. Formulations using representatives (means or medians of groups) have received much more attention than minimisa-tion of the total within group distance (TWGD). However, this non-representative approach has attractive p...

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 cl...

We propose techniques of convex optimization for information theoretical clustering. The clustering objective is to maximize the mutual information between data points and cluster assignments. We formulate this problem first as an instance of max k cut on weighted graphs. We then apply the technique of semidefinite programming (SDP) relaxation to obtain a convex SDP problem. We show how the sol...

Clustering, like covariate selection for classification, is an important step to compress and interpret the data. However, clustering of covariates often performed independently classification step, which can lead undesirable results that harm interpretability compression rate. Therefore, we propose a method cluster while taking into account class label information samples. We formulate problem...