We study the problem of finding the maximum of a function defined on the nodes of a connected graph. The goal is to identify a node where the function obtains its maximum. We focus on local iterative algorithms, which traverse the nodes of the graph along a path, and the next iterate is chosen from the neighbors of the current iterate with probability distribution determined by the function values at the current iterate and its neighbors. We study two algorithms corresponding to a Metropolis-Hastings random walk with different transition kernels: (i) The first algorithm is an exponentially weighted random walk governed by a parameter $γ$. (ii) The second algorithm is defined with respect to the graph Laplacian and a smoothness parameter $k$. We derive convergence rates for the two algorithms in terms of total variation distance and hitting times. We also provide simulations showing the relative convergence rates of our algorithms in comparison to an unbiased random walk, as a function of the smoothness of the graph function. Our algorithms may be categorized as a new class of "descent-based" methods for function maximization on the nodes of a graph.
Monash University（莫纳什大学）；RMIT University（皇家墨尔本理工大学）；Max Planck Institute for Software Systems（马克斯·普朗克软件系统研究所）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Cambridge（剑桥大学）；Alan Turing Institute（艾伦·图灵研究所）
Influence maximization is a widely studied topic in network science, where the aim is to reach the maximum possible number of nodes, while only targeting a small initial set of individuals. It has critical applications in many fields, including viral marketing, information propagation, news dissemination, and vaccinations. However, the objective does not usually take into account whether the final set of influenced nodes is fair with respect to sensitive attributes, such as race or gender. Here we address fair influence maximization, aiming to reach minorities more equitably. We introduce Adve…
IBM Research（IBM研究院）；IISc（印度科学学院）；Indian Institute of Science（印度科学学院）
Deep representation learning on non-Euclidean data types, such as graphs, has gained significant attention in recent years. Invent of graph neural networks has improved the state-of-the-art for both node and the entire graph representation in a vector space. However, for the entire graph representation, most of the existing graph neural networks are trained on a graph classification loss in a supervised way. But obtaining labels of a large number of graphs is expensive for real world applications. Thus, we aim to propose an unsupervised graph neural network to generate a vector representation …
This paper considers the problem of randomized influence maximization over a Markovian graph process: given a fixed set of nodes whose connectivity graph is evolving as a Markov chain, estimate the probability distribution (over this fixed set of nodes) that samples a node which will initiate the largest information cascade (in expectation). Further, it is assumed that the sampling process affects the evolution of the graph i.e. the sampling distribution and the transition probability matrix are functionally dependent. In this setup, recursive stochastic optimization algorithms are presented t…
We propose a generalized framework for influence maximization in large-scale, time evolving networks. Many real-life influence graphs such as social networks, telephone networks, and IP traffic data exhibit dynamic characteristics, e.g., the underlying structure and communication patterns evolve with time. Correspondingly, we develop a dynamic framework for the influence maximization problem, where we perform effective local updates to quickly adjust the top-k influencers, as the structure and communication patterns in the network change. We design a novel N-Family approach (N=1, 2, 3, ...) ba…
In network analysis and graph mining, closeness centrality is a popular measure to infer the importance of a vertex. Computing closeness efficiently for individual vertices received considerable attention. The NP-hard problem of group closeness maximization, in turn, is more challenging: the objective is to find a vertex group that is central as a whole and state-of-the-art heuristics for it do not scale to very big graphs yet. In this paper, we present new local search heuristics for group closeness maximization. By using randomized approximation techniques and dynamic data structures, our al…
Viral marketing on social networks, also known as Influence Maximization (IM), aims to select k users for the promotion of a target item by maximizing the total spread of their influence. However, most previous works on IM do not explore the dynamic user perception of promoted items in the process. In this paper, by exploiting the knowledge graph (KG) to capture dynamic user perception, we formulate the problem of Influence Maximization with Dynamic Personal Perception (IMDPP) that considers user preferences and social influence reflecting the impact of relevant item adoptions. We prove the ha…
For clustering of an undirected graph, this paper presents an exact algorithm for the maximization of modularity density, a more complicated criterion to overcome drawbacks of the well-known modularity. The problem can be interpreted as the set-partitioning problem, which reminds us of its integer linear programming (ILP) formulation. We provide a branch-and-price framework for solving this ILP, or column generation combined with branch-and-bound. Above all, we formulate the column generation subproblem to be solved repeatedly as a simpler mixed integer linear programming (MILP) problem. Accel…
Influence maximization (IM) is a combinatorial problem of identifying a subset of nodes called the seed nodes in a network (graph), which when activated, provide a maximal spread of influence in the network for a given diffusion model and a budget for seed set size. IM has numerous applications such as viral marketing, epidemic control, sensor placement and other network-related tasks. However, the uses are limited due to the computational complexity of current algorithms. Recently, learning heuristics for IM have been explored to ease the computational burden. However, there are serious limit…
Social networks represent nowadays in many contexts the main source of information transmission and the way opinions and actions are influenced. For instance, generic advertisements are way less powerful than suggestions from our contacts. However, this process hugely depends on the influence of people who disseminate these suggestions. Therefore modern marketing often involves paying some targeted users, or influencers, for advertising products or ideas. Finding the set of nodes in a social network that lead to the highest information spread -- the so-called Influence Maximization (IM) proble…
The study of vertex centrality measures is a key aspect of network analysis. Naturally, such centrality measures have been generalized to groups of vertices; for popular measures it was shown that the problem of finding the most central group is $\mathcal{NP}$-hard. As a result, approximation algorithms to maximize group centralities were introduced recently. Despite a nearly-linear running time, approximation algorithms for group betweenness and (to a lesser extent) group closeness are rather slow on large networks due to high constant overheads. That is why we introduce GED-Walk centrality, …
Modularity maximization is one of the state-of-the-art methods for community detection that has gained popularity in the last decade. Yet it suffers from the resolution limit problem by preferring under certain conditions large communities over small ones. To solve this problem, we propose to expand the meaning of the edges that are currently used to indicate propensity of nodes for sharing the same community. In our approach this is the role of edges with positive weights while edges with negative weights indicate aversion for putting their end-nodes into one community. We also present a nove…
SP-GCRL: Influence Maximization on Incomplete Social Graphs
School of Systems Science and Engineering（系统科学与工程学院）；Sun Yat-sen University（中山大学）；Jiangxi University of Finance and Economics（江西财经大学）；The Hong Kong Polytechnic University（香港理工大学）；Anhui University of Science and Technology（安徽理工大学）
Influence diffusion and influence maximization in large-scale online social networks (OSNs) have been extensively studied, because of their impacts on enabling effective online viral marketing. Existing studies focus on social networks with only friendship relations, whereas the foe or enemy relations that commonly exist in many OSNs, e.g., Epinions and Slashdot, are completely ignored. In this paper, we make the first attempt to investigate the influence diffusion and influence maximization in OSNs with both friend and foe relations, which are modeled using positive and negative edges on sign…
Institute of Information Engineering, Chinese Academy of Sciences（中国科学院信息工程研究所）；School of Cyber Security, University of Chinese Academy of Sciences（中国科学院大学网络空间安全学院）；National Computer Network Emergency Response Technical Team/Coordination Center of China（国家计算机网络应急技术处理协调中心）；Xiaomi AI Lab, Xiaomi Inc.（小米公司小米人工智能实验室）
Bipartite graph embedding has recently attracted much attention due to the fact that bipartite graphs are widely used in various application domains. Most previous methods, which adopt random walk-based or reconstruction-based objectives, are typically effective to learn local graph structures. However, the global properties of bipartite graph, including community structures of homogeneous nodes and long-range dependencies of heterogeneous nodes, are not well preserved. In this paper, we propose a bipartite graph embedding called BiGI to capture such global properties by introducing a novel lo…
A social network (SN) is a social structure consisting of a group representing the interaction between them. SNs have recently been widely used and, subsequently, have become suitable and popular platforms for product promotion and information diffusion. People in an SN directly influence each other's interests and behavior. One of the most important problems in SNs is to find people who can have the maximum influence on other nodes in the network in a cascade manner if they are chosen as the seed nodes of a network diffusion scenario. Influential diffusers are people who, if they are chosen a…
Influence maximization (IM) is the problem of finding a seed vertex set which is expected to incur the maximum influence spread on a graph. It has various applications in practice such as devising an effective and efficient approach to disseminate information, news or ad within a social network. The problem is shown to be NP-hard and approximation algorithms with provable quality guarantees exist in the literature. However, these algorithms are computationally expensive even for medium-scaled graphs. Furthermore, graph algorithms usually suffer from spatial and temporal irregularities during m…
In signed networks, each edge is labeled as either positive or negative. The edge sign captures the polarity of a relationship. Balance of signed networks is a well-studied property in graph theory. In a balanced (sub)graph, the vertices can be partitioned into two subsets with negative edges present only across the partitions. Balanced portions of a graph have been shown to increase coherence among its members and lead to better performance. While existing works have focused primarily on finding the largest balanced subgraph inside a graph, we study the network design problem of maximizing ba…
Indian Institute of Technology Madras（印度理工学院马德拉斯分校）；McGill University（麦吉尔大学）；Mila（米拉魁北克人工智能研究所）；Harvard University（哈佛大学）
A serious challenge when finding influential actors in real-world social networks is the lack of knowledge about the structure of the underlying network. Current state-of-the-art methods rely on hand-crafted sampling algorithms; these methods sample nodes and their neighbours in a carefully constructed order and choose opinion leaders from this discovered network to maximize influence spread in the (unknown) complete network. In this work, we propose a reinforcement learning framework for network discovery that automatically learns useful node and graph representations that encode important st…
A popular model to measure the stability of a network is k-core - the maximal induced subgraph in which every vertex has at least k neighbors. Many studies maximize the number of vertices in k-core to improve the stability of a network. In this paper, we study the edge k-core problem: Given a graph G, an integer k and a budget b, add b edges to non-adjacent vertex pairs in G such that the k-core is maximized. We prove the problem is NP-hard and APX-hard. A heuristic algorithm is proposed on general graphs with effective optimization techniques. Comprehensive experiments on 9 real-life datasets…
Graph Bayesian Optimization for Multiplex Influence Maximization
School of New Media and Communication, Tianjin University（天津大学新媒体与传播学院）；Department of Computer Science and Engineering, Mississippi State University（密西西比州立大学计算机科学与工程系）
Reliable propagation of information through large networks, e.g., communication networks, social networks or sensor networks is very important in many applications concerning marketing, social networks, and wireless sensor networks. However, social ties of friendship may be obsolete, and communication links may fail, inducing the notion of uncertainty in such networks. In this paper, we address the problem of optimizing information propagation in uncertain networks given a constrained budget of edges. We show that this problem requires to solve two NP-hard subproblems: the computation of expec…
As a widely observable social effect, influence diffusion refers to a process where innovations, trends, awareness, etc. spread across the network via the social impact among individuals. Motivated by such social effect, the concept of influence maximization is coined, where the goal is to select a bounded number of the most influential nodes (seed nodes) from a social network so that they can jointly trigger the maximal influence diffusion. A rich body of research in this area is performed under statistical diffusion models with provable submodularity, which essentially simplifies the problem…
Finding influential users in social networks is a fundamental problem with many possible useful applications. Viewing the social network as a graph, the influence of a set of users can be measured by the number of neighbors located within a given number of hops in the network, where each hop marks a step of influence diffusion. In this paper, we reduce the problem of IM to a budget-constrained d-hop dominating set problem (kdDSP). We propose a unified machine learning (ML) framework, FastCover, to solve kdDSP by learning an efficient greedy strategy in an unsupervised way. As one critical comp…
