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.
Highlights
Filtering information out of complex datasets is becoming a central issue and a crucial bottleneck in any scientific endeavor
We apply the DBHT technique to various data sets ranging from artificial data with known clustering and hierarchical structures to real gene expression data
Comparisons are made between the results retrieved by the DBHT technique and some of state-of-the-art cluster analysis techniques such as kmeans++[29], Spectral clustering via Normalized cut on k-nearest neighbor graph [30,31], Self Organizing Map (SOM) [32] and Q-cut [33]
Summary
Filtering information out of complex datasets is becoming a central issue and a crucial bottleneck in any scientific endeavor. The requirement of any prior information is a potential problem because often the filtering is one of the preliminary processing on the data and it is performed at a stage where very little information about the system is available Another difficulty may arise from the fact that, in some cases, the reduction of the system into a set of separated local communities may hide properties associated with the global organization. In the literature there exist several methods which can be used to extract clusters and hierarchies [1,2,3] and the application to biology and gene expression data has attracted a great attention in recent years [4,5,6,7] In these established approaches, to extract discrete clusters, one must input some a priori information about their number or define a thresholding value. We propose an alternative method that overcomes these limitations providing both clustering subdivision and hierarchical organization without the need of any prior information, without demanding supervision and without requiring thresholding
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