Adjacency-constrained hierarchical clustering of a band similarity matrix with application to genomics

Genomic data analyses such as Genome-Wide Association Studies (GWAS) or Hi-C studies are often faced with the problem of partitioning chromosomes into successive regions based on a similarity matrix of high-resolution, locus-level measurements. An intuitive way of doing this is to perform a modified Hierarchical Agglomerative Clustering (HAC), where only adjacent clusters (according to the ordering of positions within a chromosome) are allowed to be merged. But a major practical drawback of this method is its quadratic time and space complexity in the number of loci, which is typically of the order of $$ to $$ for each chromosome.

By assuming that the similarity between physically distant objects is negligible, we are able to propose an implementation of adjacency-constrained HAC with quasi-linear complexity. This is achieved by pre-calculating specific sums of similarities, and storing candidate fusions in a min-heap. Our illustrations on GWAS and Hi-C datasets demonstrate the relevance of this assumption, and show that this method highlights biologically meaningful signals. Thanks to its small time and memory footprint, the method can be run on a standard laptop in minutes or even seconds.

Software and sample data are available as an R package, adjclust, that can be downloaded from the Comprehensive R Archive Network (CRAN).