Network Unfolding Map by Edge Dynamics Modeling

The emergence of collective dynamics in neural networks is a mechanism of the animal and human brain for information processing. In this paper, we develop a computational technique using distributed processing elements in a complex network, which are called particles, to solve semi-supervised learning problems. Three actions govern the particles' dynamics: generation, walking, and absorption. Labeled vertices generate new particles that compete against rival particles for edge domination. Active particles randomly walk in the network until they are absorbed by either a rival vertex or an edge currently dominated by rival particles. The result from the model evolution consists of sets of edges arranged by the label dominance. Each set tends to form a connected subnetwork to represent a data class. Although the intrinsic dynamics of the model is a stochastic one, we prove there exists a deterministic version with largely reduced computational complexity; specifically, with linear growth. Furthermore, the edge domination process corresponds to an unfolding map in such way that edges "stretch" and "shrink" according to the vertex-edge dynamics. Consequently, the unfolding effect summarizes the relevant relationships between vertices and the uncovered data classes. The proposed model captures important details of connectivity patterns over the vertex-edge dynamics evolution, in contrast to previous approaches which focused on only vertex or only edge dynamics. Computer simulations reveal that the new model can identify nonlinear features in both real and artificial data, including boundaries between distinct classes and overlapping structures of data.