Algorithms for clustering data
Algorithms for clustering data
Cluster analysis and mathematical programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Accelerating exact k-means algorithms with geometric reasoning
KDD '99 Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining
Clustering Algorithms
A method for initialising the K-means clustering algorithm using kd-trees
Pattern Recognition Letters
Top 10 algorithms in data mining
Knowledge and Information Systems
Modified global k-means algorithm for minimum sum-of-squares clustering problems
Pattern Recognition
The hyperbolic smoothing clustering method
Pattern Recognition
New and efficient DCA based algorithms for minimum sum-of-squares clustering
Pattern Recognition
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This article considers the minimum sum-of-squares clustering (MSSC) problem. The mathematical modeling of this problem leads to a min-sum-min formulation which, in addition to its intrinsic bi-level nature, has the significant characteristic of being strongly nondifferentiable. To overcome these difficulties, the proposed resolution method, called hyperbolic smoothing, adopts a smoothing strategy using a special C^~ differentiable class function. The final solution is obtained by solving a sequence of low dimension differentiable unconstrained optimization subproblems which gradually approach the original problem. This paper introduces the method of partition of the set of observations into two nonoverlapping groups: ''data in frontier'' and ''data in gravitational regions''. The resulting combination of the two methodologies for the MSSC problem has interesting properties, which drastically simplify the computational tasks.