Partition-distance via the assignment problem

Konovalov, Dmitry A.; Litow, Bruce; Bajema, Nigel

doi:10.1093/bioinformatics/bti373

Cited by 37 publications

(46 citation statements)

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“…Partition distance: The partition distance is the minimum number of individuals that must be removed to make two assignments equivalent (Almudevar and Field 1999;Gusfield 2002;Konovalov et al 2005). For two assignments, with populations represented, respectively, we begin by relabeling each assignment using the restricted growth function (RGF) (e.g., Stanton and White 1986;Huelsenbeck and Andolfatto 2007).…”

Section: Im Models With Assignmentmentioning

confidence: 99%

“…In this article we studied this issue in detail for the case of three-population models. This required that we extend the ideas of partition distance (Almudevar and Field 1999;Gusfield 2002;Konovalov et al 2005) and mean assignment (Huelsenbeck and Andolfatto 2007) to tree-constrained partition distance and tree-constrained mean assignment. We are then able to use tree-constrained partition distances in the JDAP algorithm to jointly estimate assignment, demographic history, and population phylogeny.…”

Section: Assignment and Phylogenymentioning

confidence: 99%

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Joint Inference of Population Assignment and Demographic History

Choi

Hey

2011

Genetics

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A new approach to assigning individuals to populations using genetic data is described. Most existing methods work by maximizing Hardy-Weinberg and linkage equilibrium within populations, neither of which will apply for many demographic histories. By including a demographic model, within a likelihood framework based on coalescent theory, we can jointly study demographic history and population assignment. Genealogies and population assignments are sampled from a posterior distribution using a general isolation-with-migration model for multiple populations. A measure of partition distance between assignments facilitates not only the summary of a posterior sample of assignments, but also the estimation of the posterior density for the demographic history. It is shown that joint estimates of assignment and demographic history are possible, including estimation of population phylogeny for samples from three populations. The new method is compared to results of a widely used assignment method, using simulated and published empirical data sets.T HE assignment of individuals to populations is a common population genetic application (Paetkau et al. 1995;Rannala and Mountain 1997;Pritchard et al. 2000;Dawson and Belkhir 2001;Corander et al. 2003;Baudouin et al. 2004;Guillot et al. 2005;François et al. 2006;Pella and Masuda 2006;Wu et al. 2006;Huelsenbeck and Andolfatto 2007;Zhang 2008;Reeves and Richards 2009). Most methods assume random mating within populations and free recombination between loci to find population assignments that minimize the amount of departure from Hardy-Weinberg equilibrium (HWE) and linkage equilibrium (LE) within populations. The population assignment with the highest likelihood, or highest posterior probability under Bayesian approaches, is taken as the assignment estimate. Generally the true allele frequencies are not known so that methods must either make use of estimated allele frequencies (e.g., Grant et al. 1980) or consider the range of possible allele frequencies (e.g., Pritchard et al. 2000).Methods based on minimizing departure from HWE and LE typically offer little accommodation for the different potential causes of differentiation between populations. They allow populations to differ in allele frequencies, but they do so without including explicit evolutionary models of demography and mutation that cause such differences (Waples and Gaggiotti 2006;Listman et al. 2007). For example, it is possible that a method based on departures from HWE and LE will provide better estimates when divergence arises under an island model than when a similar amount of divergence arises under a phylogenetic branching model or vice versa. To assess such dependencies methods must be run on data simulated under various kinds of demographic histories. Without demographic history as a part of the model implemented in a method, such simulation studies tend to treat the computer program as a "black box" that can reveal interactions between demography and assignment only when observed in operation under ...

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Section: Im Models With Assignmentmentioning

confidence: 99%

Section: Assignment and Phylogenymentioning

confidence: 99%

Joint Inference of Population Assignment and Demographic History

Choi

Hey

2011

Genetics

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“…LSAPs can be found in fields as varied as bioinformatics (Konovalov et al 2005;Zaslavskiy et al 2009;Milenković et al 2010), computer vision (Cheng et al 1996(Cheng et al , 2001Lowe 2004) as well as subproblems within a number of other combinatorial optimisation problems.…”

Section: Introductionmentioning

confidence: 99%

A heuristic for the time constrained asymmetric linear sum assignment problem

et al. 2015

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The linear sum assignment problem is a fundamental combinatorial optimisation problem and can be broadly defined as: given an n × m, m ≥ n benefit matrix B = (b i j ), matching each row to a different column so that the sum of entries at the row-column intersections is maximised. This paper describes the application of a new fast heuristic algorithm, Asymmetric Greedy Search, to the asymmetric version (n = m) of the linear sum assignment problem. Extensive computational experiments, using a range of model graphs demonstrate the effectiveness of the algorithm. The heuristic was also incorporated within an algorithm for the non-sequential protein structure matching problem where non-sequential alignment between two proteins, normally of different numbers of amino acids, needs to be maximised.

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“…How to assess the partitions (partitioning algorithms) and find a consensus partition are important and interesting problems after some partitions have been generated. Hence, methods to compare and validate cluster consensus have been widely studied (Almudevar and Field, 1999;Berman et al, 2007;Butler et al, 2004;Goder and Filkov, 2008;Gusfield, 2002;Hirsch et al, 2007;Konovalov et al, 2005a;Swift et al, 2004;Yeung et al, 2001;Yu et al, 2005). Different distance functions between two or more partitions usually need to be computed by different algorithms.…”

Section: Introductionmentioning

confidence: 99%

The k Partition-Distance Problem

Chen

2012

Journal of Computational Biology

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Many applications of data partitioning (clustering) have been well studied in bioinformatics. Consider, for instance, a set N of organisms (elements) based on DNA marker data. A partition divides all elements in N into two or more disjoint clusters that cover all elements, where a cluster contains a non-empty subset of N. Different partitioning algorithms may produce different partitions. To compute the distance and find the consensus partition (also called consensus clustering) between two or more partitions are important and interesting problems that arise frequently in bioinformatics and data mining, in which different distance functions may be considered in different partition algorithms. In this article, we discuss the k partition-distance problem. Given a set of elements N with k partitions of N, the k partition-distance problem is to delete the minimum number of elements from each partition such that all remaining partitions become identical. This problem is NP-complete for general k > 2 partitions, and no algorithms are known at present. We design the first known heuristic and approximation algorithms with performance ratios 2 to solve the k partition-distance problem in O(k · ρ · |N|) time, where ρ is the maximum number of clusters of these k partitions and |N| is the number of elements in N. We also present the first known exact algorithm in O(ℓ · 2(ℓ)·k(2) · |N|(2)) time, where ℓ is the partition-distance of the optimal solution for this problem. Performances of our exact and approximation algorithms in testing the random data with actual sets of organisms based on DNA markers are compared and discussed. Experimental results reveal that our algorithms can improve the computational speed of the exact algorithm for the two partition-distance problem in practice if the maximum number of elements per cluster is less than ρ. From both theoretical and computational points of view, our solutions are at most twice the partition-distance of the optimal solution. A website offering the interactive service of solving the k partition-distance problem using our and previous algorithms is available (see http://mail.tmue.edu.tw/~yhchen/KPDP.html).

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Partition-distance via the assignment problem

Abstract: Computer code written in java is available upon request from the first author.

Cited by 37 publications

References 8 publications

Joint Inference of Population Assignment and Demographic History

Joint Inference of Population Assignment and Demographic History

A heuristic for the time constrained asymmetric linear sum assignment problem

The k Partition-Distance Problem

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