Clustering Algorithms: On Learning, Validation, Performance, and Applications to Genomics

Abstract

The development of microarray technology has enabled scientists to measure the expression of thousands of genes simultaneously, resulting in a surge of interest in several disciplines throughout biology and medicine. While data clustering has been used for decades in image processing and pattern recognition, in recent years it has joined this wave of activity as a popular technique to analyze microarrays. To illustrate its application to genomics, clustering applied to genes from a set of microarray data groups together those genes whose expression levels exhibit similar behavior throughout the samples, and when applied to samples it offers the potential to discriminate pathologies based on their differential patterns of gene expression. Although clustering has now been used for many years in the context of gene expression microarrays, it has remained highly problematic. The choice of a clustering algorithm and validation index is not a trivial one, more so when applying them to high throughput biological or medical data. Factors to consider when choosing an algorithm include the nature of the application, the characteristics of the objects to be analyzed, the expected number and shape of the clusters, and the complexity of the problem versus computational power available. In some cases a very simple algorithm may be appropriate to tackle a problem, but many situations may require a more complex and powerful algorithm better suited for the job at hand. In this paper, we will cover the theoretical aspects of clustering, including error and learning, followed by an overview of popular clustering algorithms and classical validation indices. We also discuss the relative performance of these algorithms and indices and conclude with examples of the application of clustering to computational biology.

A general framework for a reliable multivariate analysis and pattern recognition in high-dimensional epidemiological data, based on cluster robustness: A tutorial to enrich the epidemiologists’ toolkit

“…In other words, when re-running the same algorithm on the same data, with the same set of parameters, how sure can we be of obtaining similar results? Here again, different measures of stability can be found in the literature [36][37][38]. A useful approach consists in evaluating the stability of groups while iterating the same method with the same parameter set, on randomly chosen and reshuffled subsamples of the data.…”

Gene expression profiling of Arabidopsis meiocytes

“…This is a pair‐wise average‐linked algorithm (Johnson et al. 2003; Dalton et al. 2009) that sorts through all the data to identify pairs of genes that behave most similarly and then progressively adds other genes to initial pairs to form clusters of genes with a correlated expression profiles.…”

“…To improve the chances of identifying genes involved in meiosis, we next performed hierarchical clustering. This is a pair-wise average-linked algorithm (Johnson et al 2003;Dalton et al 2009) that sorts through all the data to identify pairs of genes that behave most similarly and then progressively adds other genes to initial pairs to form clusters of genes with a correlated expression profiles. Hierarchical clustering results were then analysed in regard to the repartition of the set of 29 (Table S3a) or 47 (Table S3a and b) meiotic genes.…”

Linking Genes to Cardiovascular Diseases: Gene Action and Gene–Environment Interactions

“…A microarray gene expression matrix is a table where rows represent genes, columns represent various samples (or examined conditions), and numbers in each cell denote the expression level of the particular gene in the particular sample. Clustering is a helpful statistical data mining procedure for analyzing such gene expression data; it arranges genes together in groups that have potentially related functions or are co-regulated, thus helping to establish the relationships among them in the form of gene regulatory networks [123, 132, 133]. …”