Standard

Randomized Algorithm of Finding the True Number of Clusters Based on Chebychev Polynomial Approximation. / Avros, R.; Granichin, O.; Shalymov, D.; Volkovich, Z.; Weber, G. -W.

DATA MINING: FOUNDATIONS AND INTELLIGENT PARADIGMS, VOL 1: CLUSTERING, ASSOCIATION AND CLASSIFICATION. ed. / DE Holmes; LC Jain. Springer Nature, 2012. p. 131-155 (Intelligent Systems Reference Library; Vol. 23).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

Harvard

Avros, R, Granichin, O, Shalymov, D, Volkovich, Z & Weber, G-W 2012, Randomized Algorithm of Finding the True Number of Clusters Based on Chebychev Polynomial Approximation. in DE Holmes & LC Jain (eds), DATA MINING: FOUNDATIONS AND INTELLIGENT PARADIGMS, VOL 1: CLUSTERING, ASSOCIATION AND CLASSIFICATION. Intelligent Systems Reference Library, vol. 23, Springer Nature, pp. 131-155. <http://link.springer.com/book/10.1007/978-3-642-23166-7/page/1>

APA

Avros, R., Granichin, O., Shalymov, D., Volkovich, Z., & Weber, G. -W. (2012). Randomized Algorithm of Finding the True Number of Clusters Based on Chebychev Polynomial Approximation. In DE. Holmes, & LC. Jain (Eds.), DATA MINING: FOUNDATIONS AND INTELLIGENT PARADIGMS, VOL 1: CLUSTERING, ASSOCIATION AND CLASSIFICATION (pp. 131-155). (Intelligent Systems Reference Library; Vol. 23). Springer Nature. http://link.springer.com/book/10.1007/978-3-642-23166-7/page/1

Vancouver

Avros R, Granichin O, Shalymov D, Volkovich Z, Weber G-W. Randomized Algorithm of Finding the True Number of Clusters Based on Chebychev Polynomial Approximation. In Holmes DE, Jain LC, editors, DATA MINING: FOUNDATIONS AND INTELLIGENT PARADIGMS, VOL 1: CLUSTERING, ASSOCIATION AND CLASSIFICATION. Springer Nature. 2012. p. 131-155. (Intelligent Systems Reference Library).

Author

Avros, R. ; Granichin, O. ; Shalymov, D. ; Volkovich, Z. ; Weber, G. -W. / Randomized Algorithm of Finding the True Number of Clusters Based on Chebychev Polynomial Approximation. DATA MINING: FOUNDATIONS AND INTELLIGENT PARADIGMS, VOL 1: CLUSTERING, ASSOCIATION AND CLASSIFICATION. editor / DE Holmes ; LC Jain. Springer Nature, 2012. pp. 131-155 (Intelligent Systems Reference Library).

BibTeX

@inbook{d7f8d990310c493491500507b62cf0b7,
title = "Randomized Algorithm of Finding the True Number of Clusters Based on Chebychev Polynomial Approximation",
abstract = "One of the important problems arising in cluster analysis is the estimation of the appropriate number of clusters. In the case when the expected number of clusters is sufficiently large, the majority of the existing methods involve high complexity computations. This difficulty can be avoided by using a suitable confidence interval to estimate the number of clusters. Such a method is proposed in the current chapter.The main idea is to allocate the jump position of the within-cluster dispersion function using Chebyshev polynomial approximations. The confidence interval for the true number of clusters can be obtained in this way by means of a comparatively small number of the distortion calculations. a significant computational complexity decreasing is proven. Several examples are given to demonstrate the high ability of the proposed methodology.",
keywords = "Cluster analysis, Clustering, Cluster stability, Randomized algorithms, VALIDATION, MODEL, CONSISTENCY, DENSITY, TREE",
author = "R. Avros and O. Granichin and D. Shalymov and Z. Volkovich and Weber, {G. -W.}",
year = "2012",
language = "Английский",
isbn = "978-3-642-23165-0",
series = "Intelligent Systems Reference Library",
publisher = "Springer Nature",
pages = "131--155",
editor = "DE Holmes and LC Jain",
booktitle = "DATA MINING: FOUNDATIONS AND INTELLIGENT PARADIGMS, VOL 1: CLUSTERING, ASSOCIATION AND CLASSIFICATION",
address = "Германия",

}

RIS

TY - CHAP

T1 - Randomized Algorithm of Finding the True Number of Clusters Based on Chebychev Polynomial Approximation

AU - Avros, R.

AU - Granichin, O.

AU - Shalymov, D.

AU - Volkovich, Z.

AU - Weber, G. -W.

PY - 2012

Y1 - 2012

N2 - One of the important problems arising in cluster analysis is the estimation of the appropriate number of clusters. In the case when the expected number of clusters is sufficiently large, the majority of the existing methods involve high complexity computations. This difficulty can be avoided by using a suitable confidence interval to estimate the number of clusters. Such a method is proposed in the current chapter.The main idea is to allocate the jump position of the within-cluster dispersion function using Chebyshev polynomial approximations. The confidence interval for the true number of clusters can be obtained in this way by means of a comparatively small number of the distortion calculations. a significant computational complexity decreasing is proven. Several examples are given to demonstrate the high ability of the proposed methodology.

AB - One of the important problems arising in cluster analysis is the estimation of the appropriate number of clusters. In the case when the expected number of clusters is sufficiently large, the majority of the existing methods involve high complexity computations. This difficulty can be avoided by using a suitable confidence interval to estimate the number of clusters. Such a method is proposed in the current chapter.The main idea is to allocate the jump position of the within-cluster dispersion function using Chebyshev polynomial approximations. The confidence interval for the true number of clusters can be obtained in this way by means of a comparatively small number of the distortion calculations. a significant computational complexity decreasing is proven. Several examples are given to demonstrate the high ability of the proposed methodology.

KW - Cluster analysis

KW - Clustering

KW - Cluster stability

KW - Randomized algorithms

KW - VALIDATION

KW - MODEL

KW - CONSISTENCY

KW - DENSITY

KW - TREE

M3 - глава/раздел

SN - 978-3-642-23165-0

T3 - Intelligent Systems Reference Library

SP - 131

EP - 155

BT - DATA MINING: FOUNDATIONS AND INTELLIGENT PARADIGMS, VOL 1: CLUSTERING, ASSOCIATION AND CLASSIFICATION

A2 - Holmes, DE

A2 - Jain, LC

PB - Springer Nature

ER -

ID: 4420519