[PPT]Hierarchical Clustering and Network Topology · Web viewTitle Hierarchical Clustering and...

Hierarchical Clustering and Network Hierarchical Clustering and Network Topology IdentificationTopology Identification

Mark Coates Rob NowakDepartment of Electrical and Computer Engineering

Rui Castro

Copyright © 2004 - Rui Castro

Topology IdentificationTopology Identification

Pairwise delay measurements reveal topology

Ratnasamy & McCanne (1999)Duffield, et al (2000,01,02)

Bestravos, et al (2001)Coates, et al (2001)Shih & Hero (2002)


Topology IdentificationTopology Identification

Challenges: • 12 % never respond,15 % multiple interfaces - Barford et al (2000)

• detect level-2 topology “invisible” to IP layer (e.g., switches)


Relationship between Topology ID Relationship between Topology ID and Hierarchical Clusteringand Hierarchical Clustering


0

1

2

53 4

Do not need clock

synchronization!!

Sandwich ProbingSandwich Probing


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1

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53 4

more shared queues larger

Topology imposesconstraints

we can infer that receivers 3 & 4 have a longer shared path than 3 & 5

Sandwich ProbingSandwich Probing


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Delay CovarianceDelay Covariance

more shared queues larger covarianceCopyright © 2004 - Rui Castro

individual measurement

Multiple measurements

CLT

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Measurement FrameworkMeasurement Framework

Key Assumptions:

• stationarity

• fixed (but unknown) routes

• temporal independence

• spatial independence


The maximum likelihood tree (MLT) is defined as

where

Maximum Likelihood Tree - MLTMaximum Likelihood Tree - MLT

Two Approaches:

• Binary tree construction based on bottom-up, recursive selection and pair-merging process

• Markov Chain Monte Carlo (MCMC) tree search

measurementsunknown similarity metric values,measurement likelihoodforest of possible trees,monotonicity constrain set, for tree

product of Gaussian densities


Traceroute topology

ALT topology

UNO

Internet Experiments – Internet Experiments – Sandwich ProbingSandwich Probing

MCMC topology


Traceroute topology

Estimated topology

Internet Experiments – Internet Experiments – RTT Delay CovarianceRTT Delay Covariance

Thanks toYolanda Tsang & Mehmet Yildiz


• Clever probing and sampling schemes reveal “hidden” network structure and behavior

• Likelihood based methods are a natural choice to account for uncertainty in the data

• Sampling methods relying solely on RTT can be devised

Complex interplay between measurement/probing techniques, statistical modeling, and computational methods for optimization

Final Remarks and CommentsFinal Remarks and Comments

R. Castro, M. Coates and R. Nowak, "Likelihood Based Hierarchical Clustering", IEEE Transactions in Signal Processing, August 2004.

R. Castro, M. Coates, G. Liang, R. Nowak and B. Yu, "Network Tomography: Recent Developments", Statistical Science, 2004 (invited paper, to appear).


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