Uncovering overlapping cluster structures via stochastic competitive learning

• Authors: Thiago Christiano Silva;Liang Zhao
• Venue: Information Sciences: an International Journal
• Year: 2013

In this paper, we present a method for determining overlapping cluster structures in a networked environment. The technique is built upon a definition of a stochastic competitive model, which permits one to describe the behavior of the model for different types of networks. In the referred model, several particles navigate in the network and compete with each other with the purpose of occupying as many vertices as possible. While visiting new vertices in the network, the particles mark the vertices with a unique domination signature in an attempt to repel intruder particles from possibly capturing them in future steps. Such an indication is soft, in a way that, according to the network's topology, other particles can eventually nullify this domination and become the new owners of those vertices. With this in mind, we show that the particles' domination levels provide a natural and intuitive indicator of whether or not a specific vertex or cluster structure presents overlapping characteristics. Additionally, as opposed to the majority of the techniques designed for uncovering overlapping structures, we demonstrate that this task can be performed in an efficient manner with the particle competition model, since the underlying stochastic process is able to generate useful dynamical information with no additional computational cost. As a result, the model's computational complexity is maintained low. Thus, this method turns out to be a good alternative for finding overlapping cluster structures in real-world data. Moreover, a convergence analysis of the competitive dynamical system is discussed. We conclude that the model usually does not converge to a fixed point, but instead it is bounded by a time-dependent finite region. Furthermore, an upper bound of this region is estimated. Computer simulations reveal that this overlapping index works well in synthetic and real-world data sets. Finally, in order to show the robustness of the model, an application on handwritten digits and letters recognition is provided, where the model is able to achieve high clustering accuracy and is capable of finding the overlapping structures that match our intuition.