Weighted Centroid Trees: A general approach to summarize phylogenies in single-labeled tumor mutation tree inference.

Abstract

Tumor trees, which depict the evolutionary process of cancer, provide a backbone for discovering recurring evolutionary processes in cancer. While they are not the primary information extracted from genomic data, they are valuable for this purpose. One such extraction method involves summarizing multiple trees into a single representative tree, such as consensus trees or supertrees. We define the weighted centroid tree problem to find the centroid tree of a set of single-labeled rooted trees through the following steps: 1) mapping the given trees into the Euclidean space, 2) computing the weighted centroid matrix of the mapped trees, and 3) finding the nearest mapped tree (NMTP) to the centroid matrix. We show that this setup encompasses previously studied parent-child and ancestor-descendent metrics as well as the GraPhyC and TuELiP consensus tree algorithms. Moreover, we show that, while the NMTP problem is polynomial-time solvable for the adjacency embedding, it is NP-hard for ancestry and distance mappings. We introduce integer linear programs for NMTP in different setups where we also provide a new algorithm for the case of ancestry embedding called 2-AncL2, that uses a novel weighting scheme for ancestry signals. Our experimental results show that 2-AncL2 has a superior performance compared to available consensus tree algorithms. We also illustrate our setup's application on providing representative trees for a large real breast cancer dataset, deducing that the cluster centroid trees summarize reliable evolutionary information about the original dataset. https://github.com/vasei/WAncILP. Supplementary materials are available at Bioinformatics online.