An approximation polynomial-time algorithm for a sequence bi-clustering problem

We consider a strongly NP-hard problem of partitioning a finite sequence of vectors in Euclidean space into two clusters using the criterion of the minimal sum of the squared distances from the elements of the clusters to the centers of the clusters. The center of one of the clusters is to be optimi...

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Veröffentlicht in:Computational mathematics and mathematical physics Jg. 55; H. 6; S. 1068 - 1076
Hauptverfasser: Kel’manov, A. V., Khamidullin, S. A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Moscow Pleiades Publishing 01.06.2015
Springer Nature B.V
Schlagworte:
Algorithms
Approximation
Clustering
Clusters
Computational mathematics
Computational Mathematics and Numerical Analysis
Euclidean geometry
Euclidean space
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Optimization
Polynomials
Sequences
Studies
Vectors (mathematics)
NP-hardness
approximation polynomial-time algorithm
clustering
minimum of the sum of squared distances
sequence of Euclidean vectors
ISSN:0965-5425, 1555-6662
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Zusammenfassung:We consider a strongly NP-hard problem of partitioning a finite sequence of vectors in Euclidean space into two clusters using the criterion of the minimal sum of the squared distances from the elements of the clusters to the centers of the clusters. The center of one of the clusters is to be optimized and is determined as the mean value over all vectors in this cluster. The center of the other cluster is fixed at the origin. Moreover, the partition is such that the difference between the indices of two successive vectors in the first cluster is bounded above and below by prescribed constants. A 2-approximation polynomial-time algorithm is proposed for this problem.
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542515060068