Search problems in the domain of multiplication: Case study on robust anomaly detection using markov chains

Yisroel Mirsky; Aviad Cohen; Roni Stern; Ariel Felner; Lior Rokach; Yuval Elovici; Bracha Shapira

Search problems in the domain of multiplication: Case study on robust anomaly detection using markov chains

Yisroel Mirsky, Aviad Cohen, Roni Stern, Ariel Felner, Lior Rokach, Yuval Elovici, Bracha Shapira

Department of Software and Information Systems Engineering

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

3 Scopus citations

Abstract

Most work in heuristic search focused on path finding problems in which the cost of a path in the state space is the sum of its edges’ weights. This paper addresses a different class of path finding problems in which the cost of a path is the product of its weights. We present reductions from different classes of multiplicative path finding problems to suitable classes of additive path finding problems. As a case study, we consider the problem of finding least and most probable paths in a Markov Chain, where path cost corresponds to the probability of traversing it. The importance of this problem is demonstrated in an anomaly detection application for cyberspace security. Three novel anomaly detection metrics for Markov Chains are presented, where computing these metrics require finding least and most probable paths. The underlying Markov Chain is dynamically changing, and so fast methods for computing least and most probable paths are needed. We propose such methods based on the proposed reductions and using heuristic search algorithms.

Original language	English
Title of host publication	Proceedings of the 8th Annual Symposium on Combinatorial Search, SoCS 2015
Editors	Levi Lelis, Roni Stern
Publisher	AAAI press
Pages	70-77
Number of pages	8
ISBN (Electronic)	9781577357322
State	Published - 1 Jan 2015
Event	8th Annual Symposium on Combinatorial Search, SoCS 2015 - Ein Gedi, Israel Duration: 11 Jun 2015 → 13 Jun 2015

Publication series

Name	Proceedings of the 8th Annual Symposium on Combinatorial Search, SoCS 2015
Volume	2015-January

Conference

Conference	8th Annual Symposium on Combinatorial Search, SoCS 2015
Country/Territory	Israel
City	Ein Gedi
Period	11/06/15 → 13/06/15

Keywords

Anomaly detection
Markov Chains
Multiplication domain search
Network intrusion detection
Search space monotonicity

ASJC Scopus subject areas

Computer Networks and Communications

Cite this

Mirsky, Y., Cohen, A., Stern, R., Felner, A., Rokach, L., Elovici, Y., & Shapira, B. (2015). Search problems in the domain of multiplication: Case study on robust anomaly detection using markov chains. In L. Lelis, & R. Stern (Eds.), Proceedings of the 8th Annual Symposium on Combinatorial Search, SoCS 2015 (pp. 70-77). (Proceedings of the 8th Annual Symposium on Combinatorial Search, SoCS 2015; Vol. 2015-January). AAAI press.

Mirsky, Yisroel ; Cohen, Aviad ; Stern, Roni et al. / Search problems in the domain of multiplication : Case study on robust anomaly detection using markov chains. Proceedings of the 8th Annual Symposium on Combinatorial Search, SoCS 2015. editor / Levi Lelis ; Roni Stern. AAAI press, 2015. pp. 70-77 (Proceedings of the 8th Annual Symposium on Combinatorial Search, SoCS 2015).

@inproceedings{8039891a16fd4f8a8b15218360fbd85c,

title = "Search problems in the domain of multiplication: Case study on robust anomaly detection using markov chains",

abstract = "Most work in heuristic search focused on path finding problems in which the cost of a path in the state space is the sum of its edges{\textquoteright} weights. This paper addresses a different class of path finding problems in which the cost of a path is the product of its weights. We present reductions from different classes of multiplicative path finding problems to suitable classes of additive path finding problems. As a case study, we consider the problem of finding least and most probable paths in a Markov Chain, where path cost corresponds to the probability of traversing it. The importance of this problem is demonstrated in an anomaly detection application for cyberspace security. Three novel anomaly detection metrics for Markov Chains are presented, where computing these metrics require finding least and most probable paths. The underlying Markov Chain is dynamically changing, and so fast methods for computing least and most probable paths are needed. We propose such methods based on the proposed reductions and using heuristic search algorithms.",

keywords = "Anomaly detection, Markov Chains, Multiplication domain search, Network intrusion detection, Search space monotonicity",

author = "Yisroel Mirsky and Aviad Cohen and Roni Stern and Ariel Felner and Lior Rokach and Yuval Elovici and Bracha Shapira",

note = "Publisher Copyright: Copyright {\textcopyright} 2015, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.; 8th Annual Symposium on Combinatorial Search, SoCS 2015 ; Conference date: 11-06-2015 Through 13-06-2015",

year = "2015",

month = jan,

day = "1",

language = "English",

series = "Proceedings of the 8th Annual Symposium on Combinatorial Search, SoCS 2015",

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Mirsky, Y, Cohen, A, Stern, R , Felner, A , Rokach, L , Elovici, Y & Shapira, B 2015, Search problems in the domain of multiplication: Case study on robust anomaly detection using markov chains. in L Lelis & R Stern (eds), Proceedings of the 8th Annual Symposium on Combinatorial Search, SoCS 2015. Proceedings of the 8th Annual Symposium on Combinatorial Search, SoCS 2015, vol. 2015-January, AAAI press, pp. 70-77, 8th Annual Symposium on Combinatorial Search, SoCS 2015, Ein Gedi, Israel, 11/06/15.

Search problems in the domain of multiplication: Case study on robust anomaly detection using markov chains. / Mirsky, Yisroel; Cohen, Aviad; Stern, Roni et al.
Proceedings of the 8th Annual Symposium on Combinatorial Search, SoCS 2015. ed. / Levi Lelis; Roni Stern. AAAI press, 2015. p. 70-77 (Proceedings of the 8th Annual Symposium on Combinatorial Search, SoCS 2015; Vol. 2015-January).

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

TY - GEN

T1 - Search problems in the domain of multiplication

T2 - 8th Annual Symposium on Combinatorial Search, SoCS 2015

AU - Mirsky, Yisroel

AU - Cohen, Aviad

AU - Stern, Roni

AU - Felner, Ariel

AU - Rokach, Lior

AU - Elovici, Yuval

AU - Shapira, Bracha

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Most work in heuristic search focused on path finding problems in which the cost of a path in the state space is the sum of its edges’ weights. This paper addresses a different class of path finding problems in which the cost of a path is the product of its weights. We present reductions from different classes of multiplicative path finding problems to suitable classes of additive path finding problems. As a case study, we consider the problem of finding least and most probable paths in a Markov Chain, where path cost corresponds to the probability of traversing it. The importance of this problem is demonstrated in an anomaly detection application for cyberspace security. Three novel anomaly detection metrics for Markov Chains are presented, where computing these metrics require finding least and most probable paths. The underlying Markov Chain is dynamically changing, and so fast methods for computing least and most probable paths are needed. We propose such methods based on the proposed reductions and using heuristic search algorithms.

AB - Most work in heuristic search focused on path finding problems in which the cost of a path in the state space is the sum of its edges’ weights. This paper addresses a different class of path finding problems in which the cost of a path is the product of its weights. We present reductions from different classes of multiplicative path finding problems to suitable classes of additive path finding problems. As a case study, we consider the problem of finding least and most probable paths in a Markov Chain, where path cost corresponds to the probability of traversing it. The importance of this problem is demonstrated in an anomaly detection application for cyberspace security. Three novel anomaly detection metrics for Markov Chains are presented, where computing these metrics require finding least and most probable paths. The underlying Markov Chain is dynamically changing, and so fast methods for computing least and most probable paths are needed. We propose such methods based on the proposed reductions and using heuristic search algorithms.

KW - Anomaly detection

KW - Markov Chains

KW - Multiplication domain search

KW - Network intrusion detection

KW - Search space monotonicity

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T3 - Proceedings of the 8th Annual Symposium on Combinatorial Search, SoCS 2015

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ER -

Mirsky Y, Cohen A, Stern R , Felner A , Rokach L , Elovici Y et al. Search problems in the domain of multiplication: Case study on robust anomaly detection using markov chains. In Lelis L, Stern R, editors, Proceedings of the 8th Annual Symposium on Combinatorial Search, SoCS 2015. AAAI press. 2015. p. 70-77. (Proceedings of the 8th Annual Symposium on Combinatorial Search, SoCS 2015).

Search problems in the domain of multiplication: Case study on robust anomaly detection using markov chains

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Keywords

ASJC Scopus subject areas

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