A heuristic algorithm for solving the minimum sum-of-squares clustering problems

Clustering is an important task in data mining. It can be formulated as a global optimization problem which is challenging for existing global optimization techniques even in medium size data sets. Various heuristics were developed to solve the clustering problem. The global k -means and modified gl...

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Bibliographic Details
Published in:Journal of global optimization Vol. 61; no. 2; pp. 341 - 361
Main Authors: Ordin, Burak, Bagirov, Adil M.
Format: Journal Article
Language:English
Published: Boston Springer US 01.02.2015
Springer
Springer Nature B.V
Subjects:
Algorithms
Cluster analysis
Clustering
Clusters
Computer Science
Data mining
Datasets
Experiments
Heuristic
Integer programming
Mathematical analysis
Mathematical models
Mathematical optimization
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Optimization algorithms
Optimization techniques
Real Functions
Studies
Tasks
Texts
Variables
Global optimization
Nonsmooth optimization
Minimum sum-of-squares clustering
Global
means algorithm
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:Clustering is an important task in data mining. It can be formulated as a global optimization problem which is challenging for existing global optimization techniques even in medium size data sets. Various heuristics were developed to solve the clustering problem. The global k -means and modified global k -means are among most efficient heuristics for solving the minimum sum-of-squares clustering problem. However, these algorithms are not always accurate in finding global or near global solutions to the clustering problem. In this paper, we introduce a new algorithm to improve the accuracy of the modified global k -means algorithm in finding global solutions. We use an auxiliary cluster problem to generate a set of initial points and apply the k -means algorithm starting from these points to find the global solution to the clustering problems. Numerical results on 16 real-world data sets clearly demonstrate the superiority of the proposed algorithm over the global and modified global k -means algorithms in finding global solutions to clustering problems.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-014-0171-5