The primary goal in cluster analysis is to discover natural groupings of objects. The field of cluster analysis is crowded with diverse methods that make special assumptions about data and address different scientific aims. Despite its shortcomings in accuracy, hierarchical clustering is the dominant clustering method in bioinformatics. Biologists find the trees constructed by hierarchical clus...

We present an extension of convex-hull non-negative matrix factorization (CH-NMF) which was recently proposed as a large scale variant of convex non-negative matrix factorization or Archetypal Analysis. CH-NMF factorizes a non-negative data matrix V into two nonnegative matrix factors V ≈ WH such that the columns of W are convex combinations of certain data points so that they are readily inter...

Cluster analysis aims at identifying groups of similar objects and, therefore helps to discover distribution of patterns and interesting correlations in the data sets. In this paper, we propose to provide a consistent partitioning of a dataset which allows identifying any shape of cluster patterns in case of numerical clustering, convex or non-convex. The method is based on layered structure re...

We formulate ensemble clustering as a regularization problem over nuclear norm and cluster-wise group norm, and present an efficient optimization algorithm, which we call Robust Convex Ensemble Clustering (RCEC). A key feature of RCEC allows to remove anomalous cluster assignments obtained from component clustering methods by using the group-norm regularization. Moreover, the proposed method is...

  The clustering problem under the criterion of minimum sum of squares is a non-convex and non-linear program, which possesses many locally optimal values, resulting that its solution often falls into these trap and therefore cannot converge to global optima solution. In this paper, an efficient hybrid optimization algorithm is developed for solving this problem, called Tabu-KM. It gathers the ...

We present a new clustering algorithm by proposing a convex relaxation of hierarchical clustering, which results in a family of objective functions with a natural geometric interpretation. We give efficient algorithms for calculating the continuous regularization path of solutions, and discuss relative advantages of the parameters. Our method experimentally gives state-of-the-art results simila...