Chapter 4 - Diffusion on a Tensor Product Graph for Semi-Supervised Learning and Interactive Image Segmentation

Abstract

Abstract We derive a novel semi-supervised learning method that propagates label information as a symmetric, anisotropic diffusion process (SADP). Because the influence of label information is strengthened at each iteration, the process is anisotropic and does not blur the label information. We show that SADP converges to a closed-form solution by proving its equivalence to a diffusion process on a tensor product graph. Consequently, we obtain a semi-supervised learning framework on a tensor product graph, which does not require the iteration number as a timescale, stopping parameter. The complexity of SADP is shown to be O ( n 2 ) , for n data points. The theoretical properties of SADP and presented experimecntal results demonstrate several advantages of SADP over previous diffusion-based and other classical graph-based semi-supervised learning algorithms. SADP is less sensitive to noise, outliers, and differences in the number of label data for different classes. In particular, we clearly demonstrate that the diffusion on the tensor product graph is superior to diffusion on the original graph in the context of semi-supervised learning. We also show that the proposed approach can be used in interactive image segmentation, which is also called semi-supervised image segmentation.