Asymmetry through time dependency

Mantzaris, Alexander V.; Higham, Desmond J.

doi:10.1140/epjb/e2016-60639-0

Cited by 4 publications

(4 citation statements)

References 25 publications

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“…We note that these conclusions are consistent with the results in [28], where an algorithm was proposed to quantify the asymmetry caused by the arrow of time. Our computations also make it clear that, in the Katz setting, use of the supra-centrality matrix also requires a third parameter to be chosen, for the resolvent system involving M.…”

Section: New Block Formulation Vs Supra-centrality Matrixsupporting

confidence: 91%

Block Matrix Formulations for Evolving Networks

Fenu

Higham²

2017

SIAM J. Matrix Anal. & Appl.

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Abstract. Many types of pairwise interaction take the form of a fixed set of nodes with edges that appear and disappear over time. In the case of discrete-time evolution, the resulting evolving network may be represented by a time-ordered sequence of adjacency matrices. We consider here the issue of representing the system as a single, higher dimensional block matrix, built from the individual time-slices. We focus on the task of computing network centrality measures. From a modeling perspective, we show that there is a suitable block formulation that allows us to recover dynamic centrality measures respecting time's arrow. From a computational perspective, we show that the new block formulation leads to the design of more effective numerical algorithms.

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Section: New Block Formulation Vs Supra-centrality Matrixsupporting

confidence: 91%

Block Matrix Formulations for Evolving Networks

Fenu

Higham²

2017

SIAM J. Matrix Anal. & Appl.

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“…This first example describes a call made the day 1 by the caller #349 to the receiver #23 at a time between 00:00 and 00:59 with a duration of 1634 milliseconds. [38], communication network anomaly detection [39], tracking based on call log analysis [30,31], interactive visual analytics [40], and so on. In this research, the VAST data set has been chosen because it has been used widely in this field and, in our case, the extraction of calling patterns is proposed solely from CDR data.…”

Section: Original Datasetmentioning

confidence: 99%

Real-Time Recognition of Calling Pattern and Behaviour of Mobile Phone Users through Anomaly Detection and Dynamically-Evolving Clustering

et al. 2017

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Abstract:In the competitive telecommunications market, the information that the mobile telecom operators can obtain by regularly analysing their massive stored call logs, is of great interest. Although the data that can be extracted nowadays from mobile phones have been enriched with much information, the data solely from the call logs can give us vital information about the customers. This information is usually related with the calling behaviour of their customers and it can be used to manage them. However, the analysis of these data is normally very complex because of the vast data stream to analyse. Thus, efficient data mining techniques need to be used for this purpose. In this paper, a novel approach to analyse call detail records (CDR) is proposed, with the main goal to extract and cluster different calling patterns or behaviours, and to detect outliers. The main novelty of this approach is that it works in real-time using an evolving and recursive framework.

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“…In ( Taylor et al 2017 ) a block-matrix approach was suggested which allows centrality measures for static networks to be applied. However, as mentioned in ( Mantzaris and Higham 2016 ), that formulation does not fully respect the arrow of time.…”

Section: Introductionmentioning

confidence: 98%

“…In a case study on Twitter data, this approach was seen to be successful, in the sense of correlating well with the independent views of social media experts (Lafin et al 2013 ). It was also found to outperform the crude alternative of simply aggregating all edges into a single static network that forgets the time-ordering of the interactions; see ( Mantzaris and Higham 2016 ) for further discussion. Tests in (Chen et al 2016 ; Mantaris and Higham 2013 ) also showed that dynamic broadcast centrality can be effective at quantifying the potential for the spread of disease across time-ordered interactions.…”

Section: Introductionmentioning

confidence: 99%

Sparse matrix computations for dynamic network centrality

Arrigo

Higham

2017

Appl Netw Sci

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Time sliced networks describing human-human digital interactions are typically large and sparse. This is the case, for example, with pairwise connectivity describing social media, voice call or physical proximity, when measured over seconds, minutes or hours. However, if we wish to quantify and compare the overall time-dependent centrality of the network nodes, then we should account for the global flow of information through time. Because the time-dependent edge structure typically allows information to diffuse widely around the network, a natural summary of sparse but dynamic pairwise interactions will generally take the form of a large dense matrix. For this reason, computing nodal centralities for a time-dependent network can be extremely expensive in terms of both computation and storage; much more so than for a single, static network. In this work, we focus on the case of dynamic communicability, which leads to broadcast and receive centrality measures. We derive a new algorithm for computing time-dependent centrality that works with a sparsified version of the dynamic communicability matrix. In this way, the computation and storage requirements are reduced to those of a sparse, static network at each time point. The new algorithm is justified from first principles and then tested on a large scale data set. We find that even with very stringent sparsity requirements (retaining no more than ten times the number of nonzeros in the individual time slices), the algorithm accurately reproduces the list of highly central nodes given by the underlying full system. This allows us to capture centrality over time with a minimal level of storage and with a cost that scales only linearly with the number of time points. We also describe and test three variants of the proposed algorithm that require fewer parameters and achieve a further reduction in the computational cost.

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Asymmetry through time dependency

Cited by 4 publications

References 25 publications

Block Matrix Formulations for Evolving Networks

Block Matrix Formulations for Evolving Networks

Real-Time Recognition of Calling Pattern and Behaviour of Mobile Phone Users through Anomaly Detection and Dynamically-Evolving Clustering

Sparse matrix computations for dynamic network centrality

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