Self-reinforced diffusion for graph-based semi-supervised learning

Abstract

Graph construction is the essential component of graph-based semi-supervised learning. Gaussian kernel weighted graph is widely used in this field. The problem of using such kind of graphs is that they are susceptible to data noise. They cannot approximate the geodesic distance on the underlying manifold appropriately, especially for high-dimensional data. Diffusion process has shown its effectiveness of learning pair-wise affinities which is equivalent to a graph, due to its capability of revealing the geometry structure of the manifold. However, data density distribution and label information are ignored in this process, limiting its application for semi-supervised problems. To address these issues, we propose a variant of the diffusion process, named Self-Reinforced Diffusion, which can make use of the label information. As for data density distribution, we introduce an intuitive affinity term, called self-affinity, which can well approximate density distributions and can be directly diffused on the graph. Extensive experiments on noisy synthetic data and various real-world data have demonstrated the effectiveness of the proposed method on semi-supervised learning.