  An enhanced label propagation (LP) method called GraphHop was proposed
recently. It outperforms graph convolutional networks (GCNs) in the
semi-supervised node classification task on various networks. Although the
performance of GraphHop was explained intuitively with joint node attribute and
label signal smoothening, its rigorous mathematical treatment is lacking. In
this paper, we propose a label efficient regularization and propagation (LERP)
framework for graph node classification, and present an alternate optimization
procedure for its solution. Furthermore, we show that GraphHop only offers an
approximate solution to this framework and has two drawbacks. First, it
includes all nodes in the classifier training without taking the reliability of
pseudo-labeled nodes into account in the label update step. Second, it provides
a rough approximation to the optimum of a subproblem in the label aggregation
step. Based on the LERP framework, we propose a new method, named the LERP
method, to solve these two shortcomings. LERP determines reliable pseudo-labels
adaptively during the alternate optimization and provides a better
approximation to the optimum with computational efficiency. Theoretical
convergence of LERP is guaranteed. Extensive experiments are conducted to
demonstrate the effectiveness and efficiency of LERP. That is, LERP outperforms
all benchmarking methods, including GraphHop, consistently on five test
datasets and an object recognition task at extremely low label rates (i.e., 1,
2, 4, 8, 16, and 20 labeled samples per class).
