A stability-based algorithm to validate hierarchical clusters of genes

Abstract

Stability-based methods have been successfully applied in functional genomics to the analysis of the reliability of clusterings characterised by a relatively low number of examples and clusters. The application of these methods to the validation of gene clusters discovered in biomolecular data may lead to computational problems due to the large amount of possible clusters involved. To address this problem, we present a stability-based algorithm to discover significant clusters in hierarchical clusterings with a large number of examples and clusters. The reliability of clusters of genes discovered in gene expression data of patients affected by human myeloid leukaemia is analysed through the proposed algorithm, and their relationships with specific biological processes are tested by means of Gene Ontology-based functional enrichment methods.

An algorithm to estimate the stability of the individual clusters in the hierarchical context

“…The stability-based algorithm for the estimation of hierarchical clusters in [1] follows the standard scheme, where the multiple hierarchical re-clustering of the perturbed data are performed in order to estimate the reliability of the individual clusters in the hierarchy. A particular concern is paid to the construction of the consensus matrix, which takes into account all the levels of hierarchy.…”

“…After the estimation of all the individual clusters at the different levels of hierarchy it is possible to select the most significant ones and analyze them from the biological point of view. The first approach in this direction, the stability-based algorithm, has been proposed in [1], where the authors directly applied a stability measure that estimated the reliability of each individual cluster in the dendrogram computed by the hierarchical algorithm. In our view, the deficiencies of the stability-based algorithm in [1] are an unsuitable construction of the consensus (stability) matrix, which takes into account all the hierarchy levels to calculate the pairwise similarities of the data objects.…”

“…The first approach in this direction, the stability-based algorithm, has been proposed in [1], where the authors directly applied a stability measure that estimated the reliability of each individual cluster in the dendrogram computed by the hierarchical algorithm. In our view, the deficiencies of the stability-based algorithm in [1] are an unsuitable construction of the consensus (stability) matrix, which takes into account all the hierarchy levels to calculate the pairwise similarities of the data objects. Such an approach might not produce reliable estimations of the cluster stability indices at the higher levels of hierarchy.…”

“…Such an approach might not produce reliable estimations of the cluster stability indices at the higher levels of hierarchy. The main purpose of our research was to overcome the deficiencies of the previous work [1] and to develop a stability-based algorithm for the clustering hierarchy estimation. Such an algorithm must be capable of producing results corresponding to the real structure of the analyzed dataset.…”

“…Such an algorithm must be capable of producing results corresponding to the real structure of the analyzed dataset. The idea of constructing several clustering hierarchies in order to estimate the stability of individual clusters is not original [1], but the calculation of the consensus matrix is innovative. Our HClusterV algorithm improves the reliability of the stability indices' values, especially for the clusters at the higher levels of hierarchy.…”