Statistical clustering of a random network by extremal properties

Natalia M. Markovich; Maxim S. Ryzhov; Udo R. Krieger

doi:10.1007/978-3-319-99447-5_7

Statistical clustering of a random network by extremal properties

Natalia M. Markovich
, Maxim S. Ryzhov
, Udo R. Krieger

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

3 Scopus citations

Abstract

We propose the new EI-clustering method for random networks. Regarding the underlying graph of a random network, EI-clustering is an advanced statistical tool for community detection and based on the estimation of the extremal index (EI) associated with each node. The EI metric is estimated by samples of indices of the node influences. The latter quantities are determined by the PageRank and a Max-Linear Model. The EI values of both models are estimated by a blocks estimator for each node which is considered as the root of a Thorny Branching Tree. Generations of descendant nodes related to the root node of the tree are used as blocks. The reciprocal of the EI value indicates the average number of influential nodes per generation containing at least one influential node. In the context of random graphs the EI metric indicates the ability of a randomly selected node to attract highly ranked nodes in its orbit. Looking at the changing shape of a plot of the EI metric versus the node number, the node communities are detected. The EI-clustering method is compared with the conductance measure regarding the data set of a real Web graph.

Original language	English
Title of host publication	Distributed Computer and Communication Networks - 21st International Conference, DCCN 2018, Proceedings
Editors	Vladimir M. Vishnevskiy, Dmitry V. Kozyrev, Dmitry V. Kozyrev
Publisher	Springer Verlag
Pages	71-82
Number of pages	12
ISBN (Print)	9783319994468
DOIs	https://doi.org/10.1007/978-3-319-99447-5_7
State	Published - 1 Jan 2018
Externally published	Yes
Event	21st International Conference on Distributed Computer and Communication Networks, DCCN 2018 - Moscow, Russian Federation Duration: 17 Sep 2018 → 21 Sep 2018

Publication series

Name	Communications in Computer and Information Science
Volume	919
ISSN (Print)	1865-0929

Conference

Conference	21st International Conference on Distributed Computer and Communication Networks, DCCN 2018
Country/Territory	Russian Federation
City	Moscow
Period	17/09/18 → 21/09/18

Keywords

Clustering
Extremal index
Max-linear model
Node influence
PageRank
Web graph

ASJC Scopus subject areas

General Computer Science
General Mathematics

Access to Document

10.1007/978-3-319-99447-5_7

Cite this

Markovich, N. M., Ryzhov, M. S., & Krieger, U. R. (2018). Statistical clustering of a random network by extremal properties. In V. M. Vishnevskiy, D. V. Kozyrev, & D. V. Kozyrev (Eds.), Distributed Computer and Communication Networks - 21st International Conference, DCCN 2018, Proceedings (pp. 71-82). (Communications in Computer and Information Science; Vol. 919). Springer Verlag. https://doi.org/10.1007/978-3-319-99447-5_7

Markovich, Natalia M. ; Ryzhov, Maxim S. ; Krieger, Udo R. / Statistical clustering of a random network by extremal properties. Distributed Computer and Communication Networks - 21st International Conference, DCCN 2018, Proceedings. editor / Vladimir M. Vishnevskiy ; Dmitry V. Kozyrev ; Dmitry V. Kozyrev. Springer Verlag, 2018. pp. 71-82 (Communications in Computer and Information Science).

@inproceedings{4a08df9ee1504cb991b92818e98c5f07,

title = "Statistical clustering of a random network by extremal properties",

abstract = "We propose the new EI-clustering method for random networks. Regarding the underlying graph of a random network, EI-clustering is an advanced statistical tool for community detection and based on the estimation of the extremal index (EI) associated with each node. The EI metric is estimated by samples of indices of the node influences. The latter quantities are determined by the PageRank and a Max-Linear Model. The EI values of both models are estimated by a blocks estimator for each node which is considered as the root of a Thorny Branching Tree. Generations of descendant nodes related to the root node of the tree are used as blocks. The reciprocal of the EI value indicates the average number of influential nodes per generation containing at least one influential node. In the context of random graphs the EI metric indicates the ability of a randomly selected node to attract highly ranked nodes in its orbit. Looking at the changing shape of a plot of the EI metric versus the node number, the node communities are detected. The EI-clustering method is compared with the conductance measure regarding the data set of a real Web graph.",

keywords = "Clustering, Extremal index, Max-linear model, Node influence, PageRank, Web graph",

author = "Markovich, \{Natalia M.\} and Ryzhov, \{Maxim S.\} and Krieger, \{Udo R.\}",

note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2018.; 21st International Conference on Distributed Computer and Communication Networks, DCCN 2018 ; Conference date: 17-09-2018 Through 21-09-2018",

year = "2018",

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doi = "10.1007/978-3-319-99447-5\_7",

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Markovich, NM, Ryzhov, MS & Krieger, UR 2018, Statistical clustering of a random network by extremal properties. in VM Vishnevskiy, DV Kozyrev & DV Kozyrev (eds), Distributed Computer and Communication Networks - 21st International Conference, DCCN 2018, Proceedings. Communications in Computer and Information Science, vol. 919, Springer Verlag, pp. 71-82, 21st International Conference on Distributed Computer and Communication Networks, DCCN 2018, Moscow, Russian Federation, 17/09/18. https://doi.org/10.1007/978-3-319-99447-5_7

Statistical clustering of a random network by extremal properties. / Markovich, Natalia M.; Ryzhov, Maxim S.; Krieger, Udo R.
Distributed Computer and Communication Networks - 21st International Conference, DCCN 2018, Proceedings. ed. / Vladimir M. Vishnevskiy; Dmitry V. Kozyrev; Dmitry V. Kozyrev. Springer Verlag, 2018. p. 71-82 (Communications in Computer and Information Science; Vol. 919).

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

TY - GEN

T1 - Statistical clustering of a random network by extremal properties

AU - Markovich, Natalia M.

AU - Ryzhov, Maxim S.

AU - Krieger, Udo R.

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2018.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We propose the new EI-clustering method for random networks. Regarding the underlying graph of a random network, EI-clustering is an advanced statistical tool for community detection and based on the estimation of the extremal index (EI) associated with each node. The EI metric is estimated by samples of indices of the node influences. The latter quantities are determined by the PageRank and a Max-Linear Model. The EI values of both models are estimated by a blocks estimator for each node which is considered as the root of a Thorny Branching Tree. Generations of descendant nodes related to the root node of the tree are used as blocks. The reciprocal of the EI value indicates the average number of influential nodes per generation containing at least one influential node. In the context of random graphs the EI metric indicates the ability of a randomly selected node to attract highly ranked nodes in its orbit. Looking at the changing shape of a plot of the EI metric versus the node number, the node communities are detected. The EI-clustering method is compared with the conductance measure regarding the data set of a real Web graph.

AB - We propose the new EI-clustering method for random networks. Regarding the underlying graph of a random network, EI-clustering is an advanced statistical tool for community detection and based on the estimation of the extremal index (EI) associated with each node. The EI metric is estimated by samples of indices of the node influences. The latter quantities are determined by the PageRank and a Max-Linear Model. The EI values of both models are estimated by a blocks estimator for each node which is considered as the root of a Thorny Branching Tree. Generations of descendant nodes related to the root node of the tree are used as blocks. The reciprocal of the EI value indicates the average number of influential nodes per generation containing at least one influential node. In the context of random graphs the EI metric indicates the ability of a randomly selected node to attract highly ranked nodes in its orbit. Looking at the changing shape of a plot of the EI metric versus the node number, the node communities are detected. The EI-clustering method is compared with the conductance measure regarding the data set of a real Web graph.

KW - Clustering

KW - Extremal index

KW - Max-linear model

KW - Node influence

KW - PageRank

KW - Web graph

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U2 - 10.1007/978-3-319-99447-5_7

DO - 10.1007/978-3-319-99447-5_7

M3 - Conference contribution

AN - SCOPUS:85053903763

SN - 9783319994468

T3 - Communications in Computer and Information Science

SP - 71

EP - 82

BT - Distributed Computer and Communication Networks - 21st International Conference, DCCN 2018, Proceedings

A2 - Vishnevskiy, Vladimir M.

A2 - Kozyrev, Dmitry V.

PB - Springer Verlag

T2 - 21st International Conference on Distributed Computer and Communication Networks, DCCN 2018

Y2 - 17 September 2018 through 21 September 2018

ER -

Markovich NM, Ryzhov MS, Krieger UR. Statistical clustering of a random network by extremal properties. In Vishnevskiy VM, Kozyrev DV, Kozyrev DV, editors, Distributed Computer and Communication Networks - 21st International Conference, DCCN 2018, Proceedings. Springer Verlag. 2018. p. 71-82. (Communications in Computer and Information Science). doi: 10.1007/978-3-319-99447-5_7

Statistical clustering of a random network by extremal properties

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Keywords

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