The MinMax k-Means clustering algorithm

Applying k-Means to minimize the sum of the intra-cluster variances is the most popular clustering approach. However, after a bad initialization, poor local optima can be easily obtained. To tackle the initialization problem of k-Means, we propose the MinMax k-Means algorithm, a method that assigns...

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Vydáno v:Pattern recognition Ročník 47; číslo 7; s. 2505 - 2516
Hlavní autoři: Tzortzis, Grigorios, Likas, Aristidis
Médium: Journal Article
Jazyk:angličtina
Vydáno: Kidlington Elsevier Ltd 01.07.2014
Elsevier
Témata:
Algorithms
Applied sciences
Balanced clusters
Cluster analysis
Clustering
Clusters
Emergence
Exact sciences and technology
Information, signal and communications theory
k-Means
k-Means initialization
Pattern recognition
Robustness
Signal and communications theory
Signal representation. Spectral analysis
Signal, noise
Telecommunications and information theory
Variance
Weighting
k-Means initialization
Balanced clusters
Clustering
k-Means
Performance evaluation
Automatic classification
Weighting
Minimax method
Iterative method
K means algorithm
Robustness
Signal classification
ISSN:0031-3203, 1873-5142
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Shrnutí:Applying k-Means to minimize the sum of the intra-cluster variances is the most popular clustering approach. However, after a bad initialization, poor local optima can be easily obtained. To tackle the initialization problem of k-Means, we propose the MinMax k-Means algorithm, a method that assigns weights to the clusters relative to their variance and optimizes a weighted version of the k-Means objective. Weights are learned together with the cluster assignments, through an iterative procedure. The proposed weighting scheme limits the emergence of large variance clusters and allows high quality solutions to be systematically uncovered, irrespective of the initialization. Experiments verify the effectiveness of our approach and its robustness over bad initializations, as it compares favorably to both k-Means and other methods from the literature that consider the k-Means initialization problem. •We propose the MinMax k-Means algorithm to minimize the maximum intra-cluster variance objective.•Weights are assigned to the clusters relative to their intra-cluster variance.•Our method prevents the occurrence of clusters with large intra-cluster variances in the solution.•Our method systematically uncovers high quality solutions, irrespective of the initialization.•MinMax k-Means constitutes a sound approach for initializing k-Means.
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ISSN:0031-3203
1873-5142
DOI:10.1016/j.patcog.2014.01.015