Hierarchical information clustering by means of topologically embedded graphs

TL;DR

This paper presents a novel graph-based method for unsupervised hierarchical clustering that effectively identifies meaningful structures in complex data, including biological gene expression datasets, outperforming existing approaches.

Contribution

It introduces a topologically embedded graph approach for deterministic hierarchical clustering without prior information, applicable to both artificial and real-world data.

Findings

Outperforms other clustering methods on artificial datasets

Successfully identifies biologically relevant gene clusters in lymphoma data

Provides detailed intra- and inter-cluster hierarchies

Abstract

We introduce a graph-theoretic approach to extract clusters and hierarchies in complex data-sets in an unsupervised and deterministic manner, without the use of any prior information. This is achieved by building topologically embedded networks containing the subset of most significant links and analyzing the network structure. For a planar embedding, this method provides both the intra-cluster hierarchy, which describes the way clusters are composed, and the inter-cluster hierarchy which describes how clusters gather together. We discuss performance, robustness and reliability of this method by first investigating several artificial data-sets, finding that it can outperform significantly other established approaches. Then we show that our method can successfully differentiate meaningful clusters and hierarchies in a variety of real data-sets. In particular, we find that the application to gene expression patterns of lymphoma samples uncovers biologically significant groups of genes which play key-roles in diagnosis, prognosis and treatment of some of the most relevant human lymphoid malignancies.