{"paper":{"title":"A New Quartet Tree Heuristic for Hierarchical Clustering","license":"","headline":"","cross_cats":["cs.CV","cs.DM","math.ST","physics.data-an","q-bio.QM","stat.TH"],"primary_cat":"cs.DS","authors_text":"Paul M.B. Vitanyi, Rudi Cilibrasi","submitted_at":"2006-06-11T16:05:51Z","abstract_excerpt":"We consider the problem of constructing an an optimal-weight tree from the 3*(n choose 4) weighted quartet topologies on n objects, where optimality means that the summed weight of the embedded quartet topologiesis optimal (so it can be the case that the optimal tree embeds all quartets as non-optimal topologies). We present a heuristic for reconstructing the optimal-weight tree, and a canonical manner to derive the quartet-topology weights from a given distance matrix. The method repeatedly transforms a bifurcating tree, with all objects involved as leaves, achieving a monotonic approximation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0606048","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}