Structural and functional discovery in dynamic networks with non-negative matrix factorization

Mankad, Shawn; Michailidis, George

doi:10.1103/physreve.88.042812

Cited by 52 publications

(27 citation statements)

References 52 publications

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“…It is straightforward to interpret B ik L kj as the contribution, in terms of model fitting, of the k -th community to the edge W ij . In other words, the interaction B ik L kj between nodes i and j is the result of the sum of their participation in the same communities [25], [35]. Therefore, is a summation of K rank-1 matrices and each denotes the number of pairwise interactions in the context of community k .…”

Section: Methodsmentioning

confidence: 99%

Discovering SIFIs in Interbank Communities

2016

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This paper proposes a new methodology based on non-negative matrix factorization to detect communities and to identify central nodes in a network as well as within communities. The method is specifically designed for directed weighted networks and, consequently, it has been applied to the interbank network derived from the e-MID interbank market. In an interbank network indeed links are directed, representing flows of funds between lenders and borrowers. Besides distinguishing between Systemically Important Borrowers and Lenders, the technique complements the detection of systemically important banks, revealing the community structure of the network, that proxies the most plausible areas of contagion of institutions’ distress.

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Section: Methodsmentioning

confidence: 99%

Discovering SIFIs in Interbank Communities

2016

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“…The Non-negative Matrix Factorization (NMF) has been successfully applied as a clustering tool in various fields such as document clustering ( Xu et al, 2003 ), community detection ( Mankad and Michailidis, 2013 ), and transportation networks ( Han and Moutarde, 2013 ). However, in this paper, we utilize SNMF approach which is more appropriate for clustering, as it gives us the flexibility to define any kind of similarity matrix.…”

Section: Algorithm 1: 'Snake' Algorithmmentioning

confidence: 99%

Clustering of heterogeneous networks with directional flows based on “Snake” similarities

Saeedmanesh

Geroliminis

2016

Transportation Research Part B: Methodological

195

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a b s t r a c tAggregated network level modeling and control of traffic in urban networks have recently gained a lot of interest due to unpredictability of travel behaviors and high complexity of physical modeling in microscopic level. Recent research has shown the existence of well-defined Macroscopic Fundamental Diagrams (MFDs) relating average flow and density in homogeneous networks. The concept of MFD allows to design real-time traffic control schemes specifically hierarchical perimeter control approaches to alleviate or postpone congestion. Considering the fact that congestion is spatially correlated in adjacent roads and it propagates spatiotemporaly with finite speed, describing the main pockets of congestion in a heterogeneous city with small number of clusters is conceivable. In this paper, we propose a three-step clustering algorithm to partition heterogeneous networks into connected homogeneous regions, which makes the application of perimeter control feasible. The advantages of the proposed method compared to the existing ones are the ability of finding directional congestion within a cluster, robustness with respect to parameters calibration, and its good performance for networks with low connectivity and missing data. Firstly, we start to find a connected homogeneous area around each road of the network in an iterative way (i.e. it forms a sequence of roads). Each sequence of roads, defined as 'snake', is built by starting from a single road and iteratively adding one adjacent road based on its similarity to join previously added roads in that sequence. Secondly, based on the obtained sequences from the first step, a similarity measure is defined between each pair of the roads in the network. The similarities are computed in a way that put more weight on neighboring roads and facilitate connectivity of the clusters. Finally, Symmetric Non-negative Matrix Factorization (SNMF) framework is utilized to assign roads to proper clusters with high intra-similarity and low inter-similarity. SNMF partitions the data by providing a lower rank approximation of the similarity matrix. The proposed clustering framework is applied in medium and large-size networks based on micro-simulation and empirical data from probe vehicles. In addition, the extension of the algorithm is proposed to deal with the networks with sparse measurements where information of some links is missing. The results show the effectiveness and robustness of the extended algorithm applied to simulated network under different penetration rates (percentage of links with data).

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“…The problem of community detection in dynamic networks has been studied in recent years [3,5,7,8,18,22,27]. Compared with static networks, the clustering on dynamic networks should consider historical conformity and temporal factors.…”

Section: Related Workmentioning

confidence: 99%

Analysis on Community Variational Trend in Dynamic Networks

Jia

Gao

et al. 2014

Proceedings of the 23rd ACM International Conference on Conference on Information and Knowledge Management

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Temporal analysis on dynamic networks has become a popularly discussed topic today, with more and more emerging data over time. In this paper we investigate the problem of detecting and tracking the variational communities within a given time period. We first define a metric to measure the strength of a community, called the normalized temporal community strength. And then, we propose our analysis framework. The community may evolve over time, either split to multiple communities or merge with others. We address the problem of evolutionary clustering with requirement on temporal smoothness and propose a revised soft clustering method based on non-negative matrix factorization. Then we use a clustering matching method to find the soft correspondence between different community distribution structures. This matching establishes the connection between consecutive snapshots. To estimate the variational rate and meanwhile address the smoothness during continuous evolution, we propose an objective function that combines the conformity of current variation and historical variational trend. In addition, we integrate the weights to the objective function to identify the temporal outliers. An iterative coordinate descent method is proposed to solve the optimization framework. We extensively evaluate our method with a synthetic dataset and several real datasets. The experimental results demonstrate the effectiveness of our method, which is greatly superior to the baselines on detection of the communities with significant variation over time.

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Structural and functional discovery in dynamic networks with non-negative matrix factorization

Cited by 52 publications

References 52 publications

Discovering SIFIs in Interbank Communities

Discovering SIFIs in Interbank Communities

Clustering of heterogeneous networks with directional flows based on “Snake” similarities

Analysis on Community Variational Trend in Dynamic Networks

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