On the eigen‐functions of dynamic graphs: Fast tracking and attribution algorithms

Chen, Chen; Tong, Hanghang

doi:10.1002/sam.11310

Cited by 11 publications

(7 citation statements)

References 62 publications

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“…Aggarwal and Li [3] proposed a random-walk based method to perform dynamic classification in content-based networks. In [9,10], a fast eigen-tracking algorithm is proposed which is essential for many graph mining algorithms involving adjacency matrix. Li et al [25] studied how to perform unsupervised feature selection in a dynamic and connected environment.…”

Section: Related Workmentioning

confidence: 99%

Attributed Network Embedding for Learning in a Dynamic Environment

Dani

et al. 2017

Proceedings of the 2017 ACM on Conference on Information and Knowledge Management

332

188

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Network embedding leverages the node proximity manifested to learn a low-dimensional node vector representation. e learned embeddings could advance various learning tasks such as node classi cation, network clustering, and link prediction. Most, if not all, of the existing work, is overwhelmingly performed in the context of plain and static networks. Nonetheless, in reality, network structure o en evolves over time with addition/deletion of links and nodes. Also, a vast majority of real-world networks are associated with a rich set of node a ributes, and their a ribute values are also naturally changing, with the emerging of new content and the fading of old content. ese changing characteristics motivate us to seek an e ective embedding representation to capture network and a ribute evolving pa erns, which is of fundamental importance for learning in a dynamic environment. To our best knowledge, we are the rst to tackle this problem with the following two challenges: (1) the inherently correlated network and node attributes could be noisy and incomplete, it necessitates a robust consensus representation to capture their individual properties and correlations; (2) the embedding learning needs to be performed in an online fashion to adapt to the changes accordingly. In this paper, we tackle this problem by proposing a novel dynamic a ributed network embedding framework -DANE. In particular, DANE provides an o ine method for a consensus embedding rst and then leverages matrix perturbation theory to maintain the freshness of the end embedding results in an online manner. We perform extensive experiments on both synthetic and real a ributed networks to corroborate the e ectiveness and e ciency of the proposed framework.

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Section: Related Workmentioning

confidence: 99%

Attributed Network Embedding for Learning in a Dynamic Environment

Dani

et al. 2017

Proceedings of the 2017 ACM on Conference on Information and Knowledge Management

332

188

View full text Add to dashboard Cite

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“…(1) Degree: selecting top-k nodes (edges) with the largest degrees; specifically, for edge u, v , let d u and d v denote the degrees for its endpoints respectively, the score for u, v is min{d u , d v } 4 . (2) PageRank: selecting top-k nodes (edges) with the largest PageRank scores [29] (the corresponding edge score is the minimum PageRank score among its two endpoints); (3) Eigenvector: selecting top-k nodes (edges) with the largest eigenvector centrality scores [28] (the corresponding edge score is the minimum eigenvector centrality score among its endpoints); (4) Netshield/Netmelt: selecting top-k nodes (edges) that minimize the leading eigenvalue of the network [9,10]; (5) MIOBI : a greedy algorithm that employs first-order matrix perturbation method to estimate element impact score and update eigen-pairs [5]; (6) MIOBI-S: a variant of miobi that selects top-k nodes (edges) in one batch without updating the eigen-pairs of the network; (7) MIOBI-H : a variant of miobi that employs high order matrix perturbation method to update eigen-pairs [8]; (8) Exact: a greedy algorithm that recomputes the top-r eigen-pairs to estimate the impact score for each candidate node/edge. For the results reported in this paper, we set rank r = 80 for all the top-r eigen-pairs based approximation methods (methods (5)-(8) and the proposed CONTAIN method).…”

Section: Datasetsmentioning

confidence: 99%

“…On one hand, although there exist tractable greedy algorithms for some special connectivity measures, they do not scale to large networks because of their super-linear complexity [25]. On the other hand, although matrix perturbation methods offer a linear time complexity, their optimization quality is largely dependent on the spectrum of the underlying network (e.g., the optimization quality would deteriorate quickly in small eigen-gap networks [8,20]).…”

Section: Introductionmentioning

confidence: 99%

Network Connectivity Optimization

Chen

Peng²,

Lü

et al. 2018

Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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Network connectivity optimization, which aims to manipulate network connectivity by changing its underlying topology, is a fundamental task behind a wealth of high-impact data mining applications, ranging from immunization, critical infrastructure construction, social collaboration mining, bioinformatics analysis, to intelligent transportation system design. To tackle its exponential computation complexity, greedy algorithms have been extensively used for network connectivity optimization by exploiting its diminishing returns property. Despite the empirical success, two key challenges largely remain open. First, on the theoretic side, the hardness, as well as the approximability of the general network connectivity optimization problem are still nascent except for a few special instances. Second, on the algorithmic side, current algorithms are often hard to balance between the optimization quality and the computational efficiency. In this paper, we systematically address these two challenges for the network connectivity optimization problem. First, we reveal some fundamental limits by proving that, for a wide range of network connectivity optimization problems, (1) they are NP-hard and (2) (1 − 1/e) is the optimal approximation ratio for any polynomial algorithms. Second, we propose an effective, scalable and general algorithm (CONTAIN) to carefully balance the optimization quality and the computational efficiency.where π is a subgraph of G, f is a non-negative function that maps any subgraph in G to a non-negative real number (i.e. f : π → R + ) [7]. Specifically, we have f (ϕ) = 0 for empty set ϕ; when f (π ) > 0, we call subgraph π as a valid subgraph. In other words, the network connectivity C(G) can be viewed as a weighted aggregation of the connectivities of all valid subgraphs in the network.By choosing an appropriate f () function (please refer to [7] for details), Eq. (1) includes several prevalent network connectivity measures, e.g., path capacity (which is in close relation to the epidemic threshold), triangle capacity (which is rooted in social balance theory) and natural connectivity (which is closely related to network robustness). In terms of computation, it is often much more efficient to either approximate or compute these connectivity measures by the associated eigen-function F (Λ (r ) ), where Λ (r ) represents the top-r eigenvalues of A. For example, the path capacity converges to the leading eigenvalue of the adjacency matrix of the network [4], the triangle capacity can be approximated by the sum of cubes of the eigenvalues [33], and the natural connectivity is calculated by the sum of exponentials of the eigenvalues [16]. Network Connectivity OptimizationWith the network connectivity measure in Eq. (1), we formally define network connectivity optimization problem as follows.Problem 1. Network Connectivity Optimization (NETCOP) Given: (1) a network G; (2) a connectivity mapping function f : π → R + which defines C(G); (3) a type of network operation (node deletion vs. edge deletion) and (4) a...

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“…Another important aspect of network connectivity optimization problem lies in the network dynamics. Chen et al proposed an efficient online algorithm to track some important network connectivity measures (e.g., the leading eigenvalue, the robustness measure) on a temporal dynamic network in [31], [32]. …”

Section: Related Workmentioning

confidence: 99%

Towards Optimal Connectivity on Multi-Layered Networks

Chen

Bliss

et al. 2017

IEEE Trans. Knowl. Data Eng.

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Networks are prevalent in many high impact domains. Moreover, cross-domain interactions are frequently observed in many applications, which naturally form the dependencies between different networks. Such kind of highly coupled network systems are referred to as multi-layered networks, and have been used to characterize various complex systems, including critical infrastructure networks, cyber-physical systems, collaboration platforms, biological systems and many more. Different from single-layered networks where the functionality of their nodes is mainly affected by within-layer connections, multi-layered networks are more vulnerable to disturbance as the impact can be amplified through cross-layer dependencies, leading to the cascade failure to the entire system. To manipulate the connectivity in multi-layered networks, some recent methods have been proposed based on two-layered networks with specific types of connectivity measures. In this paper, we address the above challenges in multiple dimensions. First, we propose a family of connectivity measures (SUBLINE) that unifies a wide range of classic network connectivity measures. Third, we reveal that the connectivity measures in SUBLINE family enjoy diminishing returns property, which guarantees a near-optimal solution with linear complexity for the connectivity optimization problem. Finally, we evaluate our proposed algorithm on real data sets to demonstrate its effectiveness and efficiency.

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On the eigen‐functions of dynamic graphs: Fast tracking and attribution algorithms

Cited by 11 publications

References 62 publications

Attributed Network Embedding for Learning in a Dynamic Environment

Attributed Network Embedding for Learning in a Dynamic Environment

Network Connectivity Optimization

Towards Optimal Connectivity on Multi-Layered Networks

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