Abstract

In this paper, we address the scalability issue plaguing graph-based semi-supervised learning via a small number of anchor points which adequately cover the entire point cloud. Critically, these anchor points enable nonparametric regression that predicts the label for each data point as a locally weighted average of the labels on anchor points. Because conventional graph construction is inefficient in large scale, we propose to construct a tractable large graph by coupling anchorbased label prediction and adjacency matrix design. Contrary to the Nystrom approximation of adjacency matrices which results in indefinite graph Laplacians and in turn leads to potential non-convex optimization over graphs, the proposed graph construction approach based on a unique idea called AnchorGraph provides nonnegative adjacency matrices to guarantee positive semidefinite graph Laplacians. Our approach scales linearly with the data size and in practice usually produces a large sparse graph. Experiments on large datasets demonstrate the significant accuracy improvement and scalability of the proposed approach.