Kernelised Relaxation Labelling using Fokker-Planck Diffusion

This paper shows how the relaxation labelling problem can be formulated as a diffusion process on a support graph using the Fokker-Planck equation. We abstract the labelling problem using a support graph with each graph node representing a possible object-label assignment and the edge weights representing label compatibilities. Initial object-label probabilities are updated using a relaxation-like process. The update equation is the solution of the Fokker-Planck equation, and is governed by an infinitesimal generator matrix computed from the edge-weights of the support graph. Iterative updating of the label probabilities can be effected using the eigenvalues and eigenvectors of the generator matrix. We illustrate the newly developed relaxation process for the applications of data classification.