  Graph-based semi-supervised learning has been shown to be one of the most
effective approaches for classification tasks from a wide range of domains,
such as image classification and text classification, as they can exploit the
connectivity patterns between labeled and unlabeled samples to improve learning
performance. In this work, we advance this effective learning paradigm towards
a scenario where labeled data are severely limited. More specifically, we
address the problem of graph-based semi-supervised learning in the presence of
severely limited labeled samples, and propose a new framework, called {\em
Shoestring}, that improves the learning performance through semantic transfer
from these very few labeled samples to large numbers of unlabeled samples.
  In particular, our framework learns a metric space in which classification
can be performed by computing the similarity to centroid embedding of each
class. {\em Shoestring} is trained in an end-to-end fashion to learn to
leverage the semantic knowledge of limited labeled samples as well as their
connectivity patterns with large numbers of unlabeled samples simultaneously.
By combining {\em Shoestring} with graph convolutional networks, label
propagation and their recent label-efficient variations (IGCN and GLP), we are
able to achieve state-of-the-art node classification performance in the
presence of very few labeled samples. In addition, we demonstrate the
effectiveness of our framework on image classification tasks in the few-shot
learning regime, with significant gains on miniImageNet ($2.57\%\sim3.59\%$)
and tieredImageNet ($1.05\%\sim2.70\%$).
