A novel specialized single-linkage clustering algorithm for taxonomically ordered data

Similarities among ortholog genes for a given set of species S can be expressed by alignment matrices, where each matrix cell results from aligning a gene transcript against the genome of a species within S. Gene clusters can be computed by using single-linkage clustering in time n × m, where n denotes the number of ortholog genes and m denotes the number of inspected assemblies. Our approach can break the O(n × m) complexity of single-linkage clustering by exploiting an order among species that results from an in-order traversal of a given phylogenetic tree. The order among species allows the reduction of the inspected scope of the matrix to taxonomically related combinations of assemblies and genes, thus lowering the computational efforts necessary for creating the alignment matrix without affecting cluster quality. We present two novel approaches for clustering. First, we introduce a hierarchical clustering with, omitting the initial sorting of |S| elements, amortized O(|S|) time behavior, where it holds |S|≤n+m. Then, we propose a consecutive clustering having a linear time complexity O(|S|). Both approaches compute identical clusters, whereas dendrograms can only be obtained from the hierarchical one. We prove that our approaches deliver higher cluster densities than single linkage clustering. Additionally, we show that we compute clusters of superior quality, which ensures that our approaches are generally less error prone.