Progressive Graph Partitioning Based on Information Diffusion

We propose an online deterministic annealing algorithm for progressive graph partitioning based on the spectral information of the underlying graph Laplacian matrix. Online deterministic annealing is a prototype-based unsupervised learning algorithm that progressively adjusts the number of prototypes used with respect to a performance-complexity trade-off. Due to the online nature of the proposed learning algorithm, the structure of the graph need not be known a priori. In this regard, we construct a distributed approximation algorithm to estimate the spectral information of the graph Laplacian, bypassing the exact computation of its eigenvectors. By propagating an impulse through the graph via a diffusion equation, we show that each node can construct a local learning representation which can be used for spectral clustering. As a result, the proposed approach is suitable for large graphs, requires minimal hyper-parameter tuning, and provides online control over the complexity-accuracy trade-off. We illustrate the properties and evaluate the performance of the proposed methodology in graph partition and image segmentation applications.