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Improved metaheuristics for the quartet method of hierarchical clustering

Author

Listed:
  • Sergio Consoli

    (Philips Research)

  • Jan Korst

    (Philips Research)

  • Steffen Pauws

    (Philips Research
    Tilburg University)

  • Gijs Geleijnse

    (Netherlands Comprehensive Cancer Organisation (IKNL))

Abstract

The quartet method is a novel hierarchical clustering approach where, given a set of n data objects and their pairwise dissimilarities, the aim is to construct an optimal tree from the total number of possible combinations of quartet topologies on n, where optimality means that the sum of the dissimilarities of the embedded (or consistent) quartet topologies is minimal. This corresponds to an NP-hard combinatorial optimization problem, also referred to as minimum quartet tree cost (MQTC) problem. We provide details and formulation of this challenging problem, and propose a basic greedy heuristic that is characterized by some appealing insights and findings for speeding up and simplifying the processes of solution generation and evaluation, such as the use of adjacency-like matrices to represent the topology structures of candidate solutions; fast calculation of coefficients and weights of the solution matrices; shortcuts in the enumeration of all solution permutations for a given configuration; and an iterative distance matrix reduction procedure, which greedily merges together highly connected objects which may bring lower values of the quartet cost function in a given partial solution. It will be shown that this basic greedy heuristic is able to improve consistently the performance of popular quartet clustering algorithms in the literature, namely a reduced variable neighbourhood search and a simulated annealing metaheuristic, producing novel efficient solution approaches to the MQTC problem.

Suggested Citation

  • Sergio Consoli & Jan Korst & Steffen Pauws & Gijs Geleijnse, 2020. "Improved metaheuristics for the quartet method of hierarchical clustering," Journal of Global Optimization, Springer, vol. 78(2), pages 241-270, October.
    • Handle: RePEc:spr:jglopt:v:78:y:2020:i:2:d:10.1007_s10898-019-00871-1
    DOI: 10.1007/s10898-019-00871-1
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    References listed on IDEAS

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    1. George Furnas, 1984. "The generation of random, binary unordered trees," Journal of Classification, Springer;The Classification Society, vol. 1(1), pages 187-233, December.
    2. Sergio Consoli & Jan Korst & Gijs Geleijnse & Steffen Pauws, 2019. "An exact algorithm for the minimum quartet tree cost problem," 4OR, Springer, vol. 17(4), pages 401-425, December.
    3. Michael Steel, 1992. "The complexity of reconstructing trees from qualitative characters and subtrees," Journal of Classification, Springer;The Classification Society, vol. 9(1), pages 91-116, January.
    4. Antonis Rokas & Barry L. Williams & Nicole King & Sean B. Carroll, 2003. "Genome-scale approaches to resolving incongruence in molecular phylogenies," Nature, Nature, vol. 425(6960), pages 798-804, October.
    5. Jun Pei & Zorica Dražić & Milan Dražić & Nenad Mladenović & Panos M. Pardalos, 2019. "Continuous Variable Neighborhood Search (C-VNS) for Solving Systems of Nonlinear Equations," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 235-250, April.
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