A distance-based point-reassignment heuristic for the k-hyperplane clustering problem

Edoardo Amaldi and Stefano Coniglio

European Journal of Operational Research, 2013, vol. 227, issue 1, 22-29

Abstract: We consider the k-Hyperplane Clustering problem where, given a set of m points in Rn, we have to partition the set into k subsets (clusters) and determine a hyperplane for each of them, so as to minimize the sum of the squares of the Euclidean distances between the points and the hyperplane of the corresponding clusters. We give a nonconvex mixed-integer quadratically constrained quadratic programming formulation for the problem. Since even very small-size instances are challenging for state-of-the-art spatial branch-and-bound solvers like Couenne, we propose a heuristic in which many “critical” points are reassigned at each iteration. Such points, which are likely to be ill-assigned in the current solution, are identified using a distance-based criterion and their number is progressively decreased to zero. Our algorithm outperforms the best available one proposed by Bradley and Mangasarian on a set of real-world and structured randomly generated instances. For the largest instances, we obtain an average improvement in the solution quality of 54%.

Keywords: Data mining; Nonlinear programming; Heuristics (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:227:y:2013:i:1:p:22-29

DOI: 10.1016/j.ejor.2012.09.026

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