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26
Approximability of Adaptive Seeding under Knapsack Constraints
, 2015
"... Adapting Seeding is a key algorithmic challenge of influence maximization in social networks. One seeks to select among certain available nodes in a network, and then, adaptively, among neighbors of those nodes as they become available, in order to maximize influence in the overall network. Despite ..."
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Adapting Seeding is a key algorithmic challenge of influence maximization in social networks. One seeks to select among certain available nodes in a network, and then, adaptively, among neighbors of those nodes as they become available, in order to maximize influence in the overall network. Despite recent strong approximation results [25, 1], very little is known about the problem when nodes can take on different activation costs. Surprisingly, designing adaptive seeding algorithms that can appropriately incentivize users with heterogeneous activation costs introduces fundamental challenges that do not exist in the simplified version of the problem. In this paper we study the approximability of adaptive seeding algorithms that incentivize nodes with heterogeneous activation costs. We first show a tight inapproximability result which applies even for a very restricted version of the problem. We then complement this inapproximability with a constantfactor approximation for general submodular functions, showing that the difficulties caused by the stochastic nature of the problem can be overcome. In addition, we show stronger approximation results for additive influence functions and cases where the nodes’ activation costs constitute a small fraction of the budget.
Ranking Mechanisms for Interaction Networks
"... Abstract Interaction networks are prevalent in real world applications and they manifest in several forms such as online social networks, collaboration networks, technological networks, and biological networks. In the analysis of interaction networks, an important aspect is to determine a set of ke ..."
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Abstract Interaction networks are prevalent in real world applications and they manifest in several forms such as online social networks, collaboration networks, technological networks, and biological networks. In the analysis of interaction networks, an important aspect is to determine a set of key nodes either with respect to positional power in the network or with respect to behavioral influence. This calls for designing ranking mechanisms to rank nodes/edges in the networks and there exists several well known ranking mechanisms in the literature such as Google page rank and centrality measures in social sciences. We note that these traditional ranking mechanisms are based on the structure of the underlying network. More recently, we witness applications wherein the ranking mechanisms should take into account not only the structure of the network but also other important aspects of the networks such as the value created by the nodes in the network and the marginal contribution of the nodes in the network. Motivated by this observation, the goal of this tutorial is to provide conceptual understanding of recent advances in designing efficient and scalable ranking mechanisms for large interaction networks along with applications to social network analysis.
1. MINING SEARCH BEHAVIOR
"... In the first part of this presentation, we will overview two systems that gather and display intelligence from search behavior: “Yahoo! Search Clues ” and “Yahoo! Political Insights”. In the second part, we will discuss two realworld problems encounteredwhenminingusergeneratedcontent: determining ..."
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In the first part of this presentation, we will overview two systems that gather and display intelligence from search behavior: “Yahoo! Search Clues ” and “Yahoo! Political Insights”. In the second part, we will discuss two realworld problems encounteredwhenminingusergeneratedcontent: determining which pieces of content are credible, and modeling how users influence each other.
Inferring the Underlying Structure of Information Cascades
"... Abstract—In social networks, information and influence diffuse among users as cascades. While the importance of studying cascades has been recognized in various applications, it is difficult to observe the complete structure of cascades in practice. Moreover, much less is known on how to infer casca ..."
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Abstract—In social networks, information and influence diffuse among users as cascades. While the importance of studying cascades has been recognized in various applications, it is difficult to observe the complete structure of cascades in practice. Moreover, much less is known on how to infer cascades based on partial observations. In this paper we study the cascade inference problem following the independent cascade model, and provide a full treatment from complexity to algorithms: (a) We propose the idea of consistent trees as the inferred structures for cascades; these trees connect source nodes and observed nodes with paths satisfying the constraints from the observed temporal information. (b) We introduce metrics to measure the likelihood of consistent trees as inferred cascades, as well as several optimization problems for finding them. (c) We show that the decision problems for consistent trees are in general NPcomplete, and that the optimization problems are hard to approximate. (d) We provide approximation algorithms with performance guarantees on the quality of the inferred cascades, as well as heuristics. We experimentally verify the efficiency and effectiveness of our inference algorithms, using real and synthetic data. Keywordsinformation diffusion; cascade inference I.
Dynamic Selection of Activation Targets to Boost the Influence Spread in Social Networks
, 2012
"... This paper aims to combine the viral marketing with the idea of direct selling to for influence maximization in a social network. In direct selling, producers can sell the products directly to the consumers without having to go through a cascade of wholesalers. Through direct selling, it is possible ..."
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This paper aims to combine the viral marketing with the idea of direct selling to for influence maximization in a social network. In direct selling, producers can sell the products directly to the consumers without having to go through a cascade of wholesalers. Through direct selling, it is possible to sell the products in a more efficient and economic manner. Motivated by this idea, we propose a targetselecting independent cascade (TIC) model, in which during influence propagation each active node can give up to attempt to influence some neighboring nodes, named victims, who are hard to affect, and try to activate friends of its friends, termed destinations, who could have higher potential to increase the influence spread. The next question to ask is that given a social network and a set of seeds for influence propagation under TIC model, how to effectively select targets (i.e., victims and destinations) for the attempts of activation during propagation to boost the influence spread. We propose and evaluate three heuristics for the target selection. Experiments show that selecting targets based on influence probability between nodes have the highest boost of influence spread.
gSparsify: Graph Motif Based Sparsification for Graph Clustering
"... Graph clustering is a fundamental problem that partitions vertices of a graph into clusters with an objective to optimize the intuitive notions of intracluster density and intercluster sparsity. In many realworld applications, however, the sheer sizes and inherent complexity of graphs may render ..."
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Graph clustering is a fundamental problem that partitions vertices of a graph into clusters with an objective to optimize the intuitive notions of intracluster density and intercluster sparsity. In many realworld applications, however, the sheer sizes and inherent complexity of graphs may render existing graph clustering methods inefficient or incapable of yielding quality graph clusters. In this paper, we propose gSparsify, a graph sparsification method, to preferentially retain a small subset of edges from a graph which are more likely to be within clusters, while eliminating others with less or no structure correlation to clusters. The resultant simplified graph is succinct in size with core cluster structures well preserved, thus enabling faster graph clustering without a compromise to clustering quality. We consider a quantitative approach to modeling the evidence that edges within densely knitted clusters are frequently involved in smallsize graph motifs, which are adopted as prime features to differentiate edges with varied cluster significance. Pathbased indexes and pathjoin algorithms are further designed to compute graphmotif based cluster significance of edges for graph sparsification. We perform experimental studies in realworld graphs, and results demonstrate that gSparsify can bring significant speedup to existing graph clustering methods with an improvement to graph clustering quality.
Structured Prediction of Network Response
"... We introduce the following network response problem: given a complex network and an action, predict the subnetwork that responds to action, that is, which nodes perform the action and which directed edges relay the action to the adjacent nodes. We approach the problem through maxmargin structured ..."
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We introduce the following network response problem: given a complex network and an action, predict the subnetwork that responds to action, that is, which nodes perform the action and which directed edges relay the action to the adjacent nodes. We approach the problem through maxmargin structured learning, in which a compatibility score is learned between the actions and their activated subnetworks. Thus, unlike the most popular influence network approaches, our method, called SPIN, is contextsensitive, namely, the presence, the direction and the dynamics of influences depend on the properties of the actions. The inference problems of finding the highest scoring as well as the worst margin violating networks, are proven to be NPhard. To solve the problems, we present an approximate inference method through a semidefinite programming relaxation (SDP), as well as a more scalable greedy heuristic algorithm. In our experiments, we demonstrate that taking advantage of the context given by the actions and the network structure leads SPIN to a markedly better predictive performance over competing methods. 1.
IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 1 VEGAS: Visual influEnce GrAph Summarization on Citation Networks
"... Abstract—Visually analyzing citation networks poses challenges to many fields of the data mining research. How can we summarize a large citation graph according to the user’s interest? In particular, how can we illustrate the impact of a highly influential paper through the summarization? Can we mai ..."
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Abstract—Visually analyzing citation networks poses challenges to many fields of the data mining research. How can we summarize a large citation graph according to the user’s interest? In particular, how can we illustrate the impact of a highly influential paper through the summarization? Can we maintain the sensory nodelink graph structure in the representation while revealing the flowbased influence patterns and preserving a fine readability? The stateoftheart influence maximization algorithms can detect the most influential node in a citation network, but fail to summarize a graph structure to account for this influence. On the other hand, existing graph summarization methods fold large graphs into clustered views, but can not reveal the hidden influence patterns underneath the citation network. In this paper, we first formally define the Influence Graph Summarization problem on citation networks. Second, we propose a matrix decomposition based algorithm pipeline to solve the IGS problem. Our method can not only highlight the flowbased influence patterns, but also easily extend to support the rich attribute information. A prototype system called VEGAS implementing this pipeline is also developed. Third, we present a theoretical analysis on our main algorithm, which is equivalent to the kernel kmean clustering. It can be proved that the matrix decomposition based algorithm can approximate the objective of the proposed IGS problem. Last, we conduct comprehensive experiments with realworld citation networks to compare the proposed algorithm with classical graph summarization methods. Evaluation results demonstrate that our method significantly outperforms the previous ones in optimizing both the quantitative IGS objective and the quality of the visual summarizations. Index Terms—influence summarization, visualization, citation network. F 1
Backbone discovery in traffic networks
"... We introduce a new computational problem, theBackboneDiscovery problem, which encapsulates both functional and structural aspects of network analysis. For example, while the topology of a typical road network has been available for a long time (e.g., through paper maps), it is only recently that fi ..."
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We introduce a new computational problem, theBackboneDiscovery problem, which encapsulates both functional and structural aspects of network analysis. For example, while the topology of a typical road network has been available for a long time (e.g., through paper maps), it is only recently that finegranularity usage information about the network (like gps traces), is being collected and is readily accessible. By combining functional and structural information, the solution of BackboneDiscovery provides an efficient way to explore and understand usage patterns of networks and aid in design and decision making. To address the BackboneDiscovery problem, we propose two algorithms that make use of the concepts of edge centrality. Our results indicate that it is possible to construct very sparse backbones that summarize the network activity very accurately. We also demonstrate that the usage of edgecentrality measures helps produce backbones of higher quality. 1.