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This paper addresses 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, the paper proposes to construct a tractable large graph by coupling anchor-based 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.
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