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An enhanced label propagation (LP) method called GraphHop was proposedrecently. It outperforms graph convolutional networks (GCNs) in thesemi-supervised node classification task on various networks. Although theperformance of GraphHop was explained intuitively with joint node attribute andlabel signal smoothening, its rigorous mathematical treatment is lacking. Inthis paper, we propose a label efficient regularization and propagation (LERP)framework for graph node classification, and present an alternate optimizationprocedure for its solution. Furthermore, we show that GraphHop only offers anapproximate solution to this framework and has two drawbacks. First, itincludes all nodes in the classifier training without taking the reliability ofpseudo-labeled nodes into account in the label update step. Second, it providesa rough approximation to the optimum of a subproblem in the label aggregationstep. Based on the LERP framework, we propose a new method, named the LERPmethod, to solve these two shortcomings. LERP determines reliable pseudo-labelsadaptively during the alternate optimization and provides a betterapproximation to the optimum with computational efficiency. Theoreticalconvergence of LERP is guaranteed. Extensive experiments are conducted todemonstrate the effectiveness and efficiency of LERP. That is, LERP outperformsall benchmarking methods, including GraphHop, consistently on five testdatasets and an object recognition task at extremely low label rates (i.e., 1,2, 4, 8, 16, and 20 labeled samples per class).

Label Efficient Regularization and Propagation for Graph Node Classification