Chen

FASCINATE: Fast Cross-Layer Dependency Inference on Multi-layered Networks

Multi-layered networks have recently emerged as a new network model, which naturally finds itself in many high-impact application domains, ranging from critical inter-dependent infrastructure networks, biological systems, organization-level collaborations, to cross-platform e-commerce, etc. Cross-layer dependency, which describes the dependencies or the associations between nodes across different layers/networks, often plays a central role in many data mining tasks on such multi-layered networks. Yet, it remains a daunting task to accurately know the cross-layer dependency a prior. In this paper, we address the problem of inferring the missing cross-layer dependencies on multi-layered networks. The key idea behind our method is to view it as a collective collaborative filtering problem. By formulating the problem into a regularized optimization model, we propose an effective algorithm to find the local optima with linear complexity. Furthermore, we derive an online algorithm to accommodate newly arrived nodes, whose complexity is just linear wrt the size of the neighborhood of the new node. We perform extensive empirical evaluations to demonstrate the effectiveness and the efficiency of the proposed methods.

On the Connectivity of Multi-layered Networks: Models, Measures and Optimal Control

Networks appear naturally in many high-impact real-world applications. In an increasingly connected and coupled world, the networks arising from many application domains are often collected from different channels, forming the so-called multi-layered networks, such as cyber-physical systems, organization-level collaboration platforms, critical infrastructure networks and many more. Compared with single-layered networks, multi-layered networks are more vulnerable as even a small disturbance on one supporting layer/network might cause a ripple effect to all the dependent layers, leading to a catastrophic/cascading failure of the entire system. The state-of-the-art has been largely focusing on modeling and manipulating the cascading effect of two-layered interdependent network systems for some specific type of network connectivity measure. This paper generalizes the challenge to multiple dimensions. First, we propose a new data model for multi-layered networks MULAN, which admits an arbitrary number of layers with a much more flexible dependency structure among different layers, beyond the current pair-wise dependency. Second, we unify a wide range of classic network connectivity measures SUBLINE. Third, we show that for any connectivity measure in the SUBLINE family, it enjoys the diminishing returns property which in turn lends itself to a family of provable near-optimal control algorithms with linear complexity. Finally, we conduct extensive empirical evaluations on real network data, to validate the effectiveness of the proposed algorithms.

Eigen-Optimization on Large Graphs by Edge Manipulation

Large graphs are prevalent in many applications and enable a variety of information dissemination processes, e.g., meme, virus, and influence propagation. How can we optimize the underlying graph structure to affect the outcome of such dissemination processes in a desired way (e.g., stop a virus propagation, facilitate the propagation of a piece of good idea, etc)? Existing research suggests that the leading eigenvalue of the underlying graph is the key metric in determining the so-called epidemic threshold for a variety of dissemination models. In this paper, we study the problem of how to optimally place a set of edges (e.g., edge deletion and edge addition) to optimize the leading eigenvalue of the underlying graph, so that we can guide the dissemination process in a desired way. We propose effective, scalable algorithms for edge deletion and edge addition, respectively. In addition, we reveal the intrinsic relationship between edge deletion and node deletion problems. Experimental results validate the effectiveness and efficiency of the proposed algorithms.

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

Eigen-functions are of key importance in graph mining since they can be used to approximate many graph parameters, such as node centrality, epidemic threshold, graph robustness, with high accuracy. As real-world graphs are changing over time, those parameters may get sharp changes correspondingly. Taking virus propagation network for example, new connections between infected and susceptible people appear all the time, and some of the crucial infections may lead to large decreasing on the epidemic threshold of the network. As a consequence, the virus would spread around the network quickly. However, if we can keep track of the epidemic threshold as the graph structure changes, those crucial infections would be identified timely so that counter measures can be taken proactively to contain the spread process. In our paper, we propose two online eigen-functions tracking algorithms which can effectively monitor those key parameters with linear complexity. Furthermore, we propose a general attribution analysis framework which can be used to identify important structural changes in the evolving process. In addition, we introduce an error estimation method for the proposed eigen-functions tracking algorithms to estimate the tracking error at each time stamp. Finally, extensive evaluations are conducted to validate the effectiveness and efficiency of the proposed algorithms.

Towards Optimal Connectivity on Multi-Layered Networks

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 the 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.

Connectivity in Complex Networks: Measures, Inference and Optimization

Networks are ubiquitous in many high impact domains. Among the various aspects of network studies, connectivity is the one that plays important role in many applications (e.g., information dissemination, robustness analysis, community detection, etc.). The diversified applications have spurred numerous connectivity measures. Accordingly, ad-hoc connectivity optimization methods are designed for each measure, making it hard to model and control the connectivity of the network in a uniformed framework. On the other hand, it is often impossible to maintain an accurate structure of the network due to network dynamics and noise in real applications, which would affect the accuracy of connectivity measures and the effectiveness of corresponding connectivity optimization methods. In this work, we aim to address the challenges on network connectivity by (1)unifying a wide range of classic network connectivity measures into one uniform model; (2)proposing effective approaches to infer connectivity measures and network structures from dynamic and incomplete input data, and (3) providing a general framework to optimize the connectivity measures in the network.

Network Connectivity Optimization: Fundamental Limits and Effective Algorithms

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.

Cross-Dependency Inference in Multi-Layered Networks: A Collaborative Filtering Perspective

The increasingly connected world has catalyzed the fusion of networks from different domains, which facilitates the emergence of a new network model—multi-layered networks. Examples of such kind of network systems include critical infrastructure networks, biological systems, organization-level collaborations, cross-platform e-commerce, and so forth. One crucial structure that distances multi-layered network from other network models is its cross-layer dependency, which describes the associations between the nodes from different layers. Needless to say, the cross-layer dependency in the network plays an essential role in many data mining applications like system robustness analysis and complex network control. However, it remains a daunting task to know the exact dependency relationships due to noise, limited accessibility, and so forth. In this article, we tackle the cross-layer dependency inference problem by modeling it as a collective collaborative filtering problem. Based on this idea, we propose an effective algorithm Fascinate that can reveal unobserved dependencies with linear complexity. Moreover, we derive Fascinate-ZERO, an online variant of Fascinate that can respond to a newly added node timely by checking its neighborhood dependencies. We perform extensive evaluations on real datasets to substantiate the superiority of our proposed approaches.