Dynamic Cluster Formation Game for Attributed Graph Clustering

Abstract

Besides the topological structure, there are additional information, i.e., node attributes, on top of the plain graphs. Usually, these systems can be well modeled by attributed graphs, where nodes represent component actors, a set of attributes describe users' portraits and edges indicate their connections. An elusive question associated with attributed graphs is to study how clusters with common internal properties form and evolve in real-world networked systems with great individual diversity, which leads to the so-called problem of attributed graph clustering (AGC). In this paper, we comprehended AGC naturally as a dynamic cluster formation game (DCFG), where each node's feasible action set can be constrained by every cluster in a discrete-time dynamical system. Specifically, we carried out a deep research on a special case of finite dynamic games, named dynamic social game (DSG), the convergence of the finite Nash equilibrium sequence in a DSG was also proved strictly. By carefully defining the feasible action set and the utility function associated with each node, the proposed DCFG can be well related to a DSG; and we showed that a balanced solution of AGC could be found by solving a finite set of coupled static Nash equilibrium problems in the related DCFG. We, finally, proposed a self-learning algorithm, which can start from any arbitrary initial cluster configuration, and, finally, find the corresponding balanced solution of AGC, where all nodes and clusters are satisfied with the final cluster configuration. Extensive experiments were applied on real-world social networks to demonstrate both effectiveness and scalability of the proposed approach by comparing with the state-of-the-art graph clustering methods in the literature.

Variational community partition with novel network structure centrality prior

“…(c). Expansion of benchmark nodes are performed by (18) with the benchmark confidence measure (17). (d).…”

“…With such 'confidence' measure, we introduce a two-stage optimization framework: it first computes an initial network partition through the proposed ALM-based dual optimization algorithm; once the initial partitioned communities are obtained, the 'confidence' measure π ik for each node v i within its initial partition k is calculated by (17), so as to choose the new nodes with high 'confidence' as (18) into the related benchmark set k; using the expanded benchmark sets, the proposed ALM-based dual optimization is explored to recompute the network partition. More details of the two-stage optimization strategy can be found in Alg.…”

“…2) to compute the initial partition results ψ * ik , i = 1...n and k = 1...K; 3: Expansion of benchmark sets: with the initial partition results, the 'confidence' measure π ik for each node v i within its initial partition k is calculated by (17), choose the new nodes with high 'confidence', e.g. (18), into the related benchmark set k; 4: Refine partitions: use the expanded benchmark sets, the proposed ALM-based dual optimization algorithm (Alg. 2) is employed to recompute the network partition.…”

The behavioral model and game theory

“…In the theory of the game, different methods are used for finding equilibrium with help of rationality concept and one of these methods is the best response function (McCarty and Meirowitz, 2007;Bu et al, 2017). Based on the definition of the best response function, equilibrium is a point in which strategy chosen by each individual is the best response to the strategies chosen by other players and maximize personal profit (Harsanyi, 1986;Eshaghi and Askari, 2017;Xia et al, 2019;Huang et al, 2018aHuang et al, , 2018b.…”

Role of vaccine efficacy in the vaccination behavior under myopic update rule on complex networks

“…At present, mathematical models have been put forward to study the role of human behavior in the context of social population, such as escape panic [19] , pedestrian trails [20] , but effort s to quantitatively explore the role of human behavior in the large-scale epidemics generally focus on assessing the effectiveness of various public health measures including the social distancing, school closure etc. In the recent years, there are many fields and methods to help us to study infectious disease [21][22][23][24][25][26][27][28][29][30][31][32] , however, there is an increasing attention about the effect of spontaneous individual action or response strategy on the progression of an infectious disease, in which this kind of spontaneous actions may highly restrain from the further diffusion of epidemics and even change the fate of outbreaks. Thus, it is of great significance to fully understand the interacting mechanisms between the human behavior and disease dynamics within the specified population.…”