A New Quartet Tree Heuristic for Hierarchical Clustering

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 to the exact single globally optimal tree. This contrasts to other heuristic search methods from biological phylogeny, like DNAML or quartet puzzling, which, repeatedly, incrementally construct a solution from a random order of objects, and subsequently add agreement values.Comment: 22 pages, 14 figure

On the Ancestral Compatibility of Two Phylogenetic Trees with Nested Taxa

Compatibility of phylogenetic trees is the most important concept underlying widely-used methods for assessing the agreement of different phylogenetic trees with overlapping taxa and combining them into common supertrees to reveal the tree of life. The notion of ancestral compatibility of phylogenetic trees with nested taxa was introduced by Semple et al in 2004. In this paper we analyze in detail the meaning of this compatibility from the points of view of the local structure of the trees, of the existence of embeddings into a common supertree, and of the joint properties of their cluster representations. Our analysis leads to a very simple polynomial-time algorithm for testing this compatibility, which we have implemented and is freely available for download from the BioPerl collection of Perl modules for computational biology.Comment: Submitte

Reconciling taxonomy and phylogenetic inference: formalism and algorithms for describing discord and inferring taxonomic roots

Although taxonomy is often used informally to evaluate the results of phylogenetic inference and find the root of phylogenetic trees, algorithmic methods to do so are lacking. In this paper we formalize these procedures and develop algorithms to solve the relevant problems. In particular, we introduce a new algorithm that solves a "subcoloring" problem for expressing the difference between the taxonomy and phylogeny at a given rank. This algorithm improves upon the current best algorithm in terms of asymptotic complexity for the parameter regime of interest; we also describe a branch-and-bound algorithm that saves orders of magnitude in computation on real data sets. We also develop a formalism and an algorithm for rooting phylogenetic trees according to a taxonomy. All of these algorithms are implemented in freely-available software.Comment: Version submitted to Algorithms for Molecular Biology. A number of fixes from previous versio

Tree Contractions and Evolutionary Trees

An evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species. Evolutionary trees are useful for modeling the evolutionary history of species. An agreement subtree of two evolutionary trees is an evolutionary tree which is also a topological subtree of the two given trees. We give an algorithm to determine the largest possible number of leaves in any agreement subtree of two trees T_1 and T_2 with n leaves each. If the maximum degree d of these trees is bounded by a constant, the time complexity is O(n log^2(n)) and is within a log(n) factor of optimal. For general d, this algorithm runs in O(n d^2 log(d) log^2(n)) time or alternatively in O(n d sqrt(d) log^3(n)) time

A Fast Quartet Tree Heuristic for Hierarchical Clustering

The Minimum Quartet Tree Cost problem is to construct 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 topologies is optimal (so it can be the case that the optimal tree embeds all quartets as nonoptimal topologies). We present a Monte Carlo heuristic, based on randomized hill climbing, for approximating the optimal weight tree, given the quartet topology weights. The method repeatedly transforms a dendrogram, with all objects involved as leaves, achieving a monotonic approximation to the exact single globally optimal tree. The problem and the solution heuristic has been extensively used for general hierarchical clustering of nontree-like (non-phylogeny) data in various domains and across domains with heterogeneous data. We also present a greatly improved heuristic, reducing the running time by a factor of order a thousand to ten thousand. All this is implemented and available, as part of the CompLearn package. We compare performance and running time of the original and improved versions with those of UPGMA, BioNJ, and NJ, as implemented in the SplitsTree package on genomic data for which the latter are optimized. Keywords: Data and knowledge visualization, Pattern matching--Clustering--Algorithms/Similarity measures, Hierarchical clustering, Global optimization, Quartet tree, Randomized hill-climbing,Comment: LaTeX, 40 pages, 11 figures; this paper has substantial overlap with arXiv:cs/0606048 in cs.D

An Interpretable Deep Hierarchical Semantic Convolutional Neural Network for Lung Nodule Malignancy Classification

While deep learning methods are increasingly being applied to tasks such as computer-aided diagnosis, these models are difficult to interpret, do not incorporate prior domain knowledge, and are often considered as a "black-box." The lack of model interpretability hinders them from being fully understood by target users such as radiologists. In this paper, we present a novel interpretable deep hierarchical semantic convolutional neural network (HSCNN) to predict whether a given pulmonary nodule observed on a computed tomography (CT) scan is malignant. Our network provides two levels of output: 1) low-level radiologist semantic features, and 2) a high-level malignancy prediction score. The low-level semantic outputs quantify the diagnostic features used by radiologists and serve to explain how the model interprets the images in an expert-driven manner. The information from these low-level tasks, along with the representations learned by the convolutional layers, are then combined and used to infer the high-level task of predicting nodule malignancy. This unified architecture is trained by optimizing a global loss function including both low- and high-level tasks, thereby learning all the parameters within a joint framework. Our experimental results using the Lung Image Database Consortium (LIDC) show that the proposed method not only produces interpretable lung cancer predictions but also achieves significantly better results compared to common 3D CNN approaches