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Farthest Centroids Divisive Clustering ∗
, 2008
"... A method is presented to partition a given set of data entries embedded in Euclidean space by recursively bisecting clusters into smaller ones. The initial set is subdivided into two subsets whose centroids are farthest from each other, and the process is repeated recursively on each subset. The bis ..."
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A method is presented to partition a given set of data entries embedded in Euclidean space by recursively bisecting clusters into smaller ones. The initial set is subdivided into two subsets whose centroids are farthest from each other, and the process is repeated recursively on each subset. The bisection task can be formulated as an integer programming problem, which is NPhard. Instead, an approximate algorithm based on a spectral approach is given. Experimental evidence shows that the clustering method often outperforms a standard spectral clustering method, but at a higher computational cost. The paper also discusses how to improve the standard Kmeans algorithm, a successful clustering method that is sensitive to initialization. It is shown that the quality of clustering resulting from the Kmeans technique can be enhanced by using the proposed algorithm for its initialization. Keywords: graph partitioning, Kmeans algorithm, Lanczos method, spectral bisection, unsupervised clustering 1
SWARM DIRECTIONS EMBEDDED DIFFERENTIAL EVOLUTION FOR FASTER CONVERGENCE OF GLOBAL OPTIMIZATION PROBLEMS
"... In the present study we propose a new hybrid version of Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms called Hybrid DE or HDE for solving continuous global optimization problems. In the proposed HDE algorithm, information sharing mechanism of PSO is embedded in the con ..."
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In the present study we propose a new hybrid version of Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms called Hybrid DE or HDE for solving continuous global optimization problems. In the proposed HDE algorithm, information sharing mechanism of PSO is embedded in the contracted search space obtained by the basic DE algorithm. This is done to maintain a balance between the two antagonist factors; exploration and exploitation thereby obtaining a faster convergence. The embedding of swarm directions to the basic DE algorithm is done with the help of a “switchover constant ” called α which keeps a record of the contraction of search space. The proposed HDE algorithm is tested on a set of 10 unconstrained benchmark problems and four constrained real life, mechanical design problems. Empirical studies show that the proposed scheme helps in improving the convergence rate of the basic DE algorithm without compromising with the quality of solution.