9. Case Study of Network-Based Unsupervised Learning: Stochastic Competitive Learning in Networks

Many business and day-to-day problems that arise in our lives must be dealt with under several constraints, such as the prohibition of external interventions of human beings. This may be due to high operational costs or physical or economical impossibilities that are inherently involved in the process. The unsupervised learning—one of the existing machine learning paradigms—can be employed to address these issues and is the main topic discussed in this chapter. For instance, a possible unsupervised task would be to discover communities in social networks, find out groups of proteins with the same biological functions, among many others. In this chapter, the unsupervised learning is investigated with a focus on methods relying on the complex networks theory. In special, a type of competitive learning mechanism based on a stochastic nonlinear dynamical system is discussed. This model possesses interesting properties, runs roughly in linear time for sparse networks, and also has good performance on artificial and real-world networks. In the initial setup, a set of particles is released into vertices of a network in a random manner. As time progresses, they move across the network in accordance with a convex stochastic combination of random and preferential walks, which are related to the offensive and defensive behaviors of the particles, respectively. The competitive walking process reaches a dynamic equilibrium when each community or data cluster is dominated by a single particle. Straightforward applications are in community detection and data clustering. In essence, data clustering can be considered as a community detection problem once a network is constructed from the original data set. In this case, each vertex corresponds to a data item and pairwise connections are established using a suitable network formation process.