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.
