Design of hybrids for the minimum sum-of-squares clustering problem
Computational Statistics & Data Analysis
A scatter search approach for the minimum sum-of-squares clustering problem
Computers and Operations Research
Modified global k-means algorithm for clustering in gene expression data sets
WISB '06 Proceedings of the 2006 workshop on Intelligent systems for bioinformatics - Volume 73
Modified global k-means algorithm for minimum sum-of-squares clustering problems
Pattern Recognition
The hyperbolic smoothing clustering method
Pattern Recognition
Minimum sum-of-squares clustering by DC programming and DCA
ICIC'09 Proceedings of the Intelligent computing 5th international conference on Emerging intelligent computing technology and applications
Fast modified global k-means algorithm for incremental cluster construction
Pattern Recognition
Evaluating a branch-and-bound RLT-based algorithm for minimum sum-of-squares clustering
Journal of Global Optimization
A clustering method combining differential evolution with the K-means algorithm
Pattern Recognition Letters
Using the primal-dual interior point algorithm within the branch-price-and-cut method
Computers and Operations Research
Optimising sum-of-squares measures for clustering multisets defined over a metric space
Discrete Applied Mathematics
New and efficient DCA based algorithms for minimum sum-of-squares clustering
Pattern Recognition
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An exact algorithm is proposed for minimum sum-of-squares nonhierarchical clustering, i.e., for partitioning a given set of points from a Euclidean m-space into a given number of clusters in order to minimize the sum of squared distances from all points to the centroid of the cluster to which they belong. This problem is expressed as a constrained hyperbolic program in 0-1 variables. The resolution method combines an interior point algorithm, i.e., a weighted analytic center column generation method, with branch-and-bound. The auxiliary problem of determining the entering column (i.e., the oracle) is an unconstrained hyperbolic program in 0-1 variables with a quadratic numerator and linear denominator. It is solved through a sequence of unconstrained quadratic programs in 0-1 variables. To accelerate resolution, variable neighborhood search heuristics are used both to get a good initial solution and to solve quickly the auxiliary problem as long as global optimality is not reached. Estimated bounds for the dual variables are deduced from the heuristic solution and used in the resolution process as a trust region. Proved minimum sum-of-squares partitions are determined for the first time for several fairly large data sets from the literature, including Fisher's 150 iris.