Variable neighborhood search for harmonic means clustering

Harmonic means clustering is a variant of minimum sum of squares clustering (which is sometimes called K-means clustering), designed to alleviate the dependance of the results on the choice of the initial solution. In the harmonic means clustering problem, the sum of harmonic averages of the distances from the data points to all cluster centroids is minimized. In this paper, we propose a variable neighborhood search heuristic for solving it. This heuristic has been tested on numerous datasets from the literature. It appears that our results compare favorably with recent ones from tabu search and simulated annealing heuristics.

[1]  Pierre Hansen,et al.  J-MEANS: a new local search heuristic for minimum sum of squares clustering , 1999, Pattern Recognit..

[2]  Nenad Mladenovic,et al.  Degeneracy in the multi-source Weber problem , 1999, Math. Program..

[3]  Pierre Hansen,et al.  An Interior Point Algorithm for Minimum Sum-of-Squares Clustering , 1997, SIAM J. Sci. Comput..

[4]  Pierre Hansen,et al.  Fuzzy J-Means: a new heuristic for fuzzy clustering , 2001, Pattern Recognit..

[5]  Boris Mirkin,et al.  Clustering For Data Mining: A Data Recovery Approach (Chapman & Hall/Crc Computer Science) , 2005 .

[6]  Pierre Hansen,et al.  Cluster analysis and mathematical programming , 1997, Math. Program..

[7]  Gerhard Reinelt,et al.  TSPLIB - A Traveling Salesman Problem Library , 1991, INFORMS J. Comput..

[8]  Peter J. Rousseeuw,et al.  Finding Groups in Data: An Introduction to Cluster Analysis , 1990 .

[9]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[10]  Zülal Güngör,et al.  K-Harmonic means data clustering with tabu-search method , 2008 .

[11]  Pierre Hansen,et al.  Variable neighbourhood search: methods and applications , 2010, Ann. Oper. Res..

[12]  E. Forgy,et al.  Cluster analysis of multivariate data : efficiency versus interpretability of classifications , 1965 .

[13]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[14]  Pierre Hansen,et al.  Variable Neighborhood Search : Methods and Applications , 2008 .

[15]  Kenneth H. Rosen.  Handbook of Discrete and Combinatorial Mathematics , 1999 .

[16]  Bin Zhang,et al.  Genera lized K- Harmonic Means - - Boosting in Unsupervised Learnin g , 2000 .

[17]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[18]  Pierre Hansen,et al.  Variable Neighborhood Decomposition Search , 1998, J. Heuristics.

[19]  Pierre Hansen,et al.  Variable neighborhood search: Principles and applications , 1998, Eur. J. Oper. Res..

[20]  Zülal Güngör,et al.  K-harmonic means data clustering with simulated annealing heuristic , 2007, Appl. Math. Comput..

[21]  Giuseppe Patanè,et al.  The enhanced LBG algorithm , 2001, Neural Networks.

[22]  Pierre Hansen,et al.  NP-hardness of Euclidean sum-of-squares clustering , 2008, Machine Learning.