Semi-Supervised Learning with Spectral Graph Wavelets
We consider the transductive learning problem when the labels belong to a continuous space. Through the use of spectral graph wavelets, we explore the benefits of multiresolution analysis on a graph constructed from the labeled and unlabeled data. The spectral graph wavelets behave like discrete multiscale differential operators on graphs, and thus can sparsely approximate piecewise smooth signals. Therefore, rather than enforce a prior belief that the labels are globally smooth with respect to the intrinsic structure of the graph, we enforce sparse priors on the spectral graph wavelet coefficients. One issue that arises when the proportion of data with labels is low is that the fine scale wavelets that are useful in sparsely representing discontinuities are largely masked, making it difficult to recover the high frequency components of the label sequence. We discuss this challenge, and propose one method to use the structured sparsity of the wavelet coefficients to aid label reconstruction.