  Few-shot learning can find the latent structure information between the prior
knowledge and the queried data by the similarity metric of meta-learning to
construct the discriminative model for recognizing the new categories with the
rare labeled samples. Most existing methods try to model the similarity
relationship of the samples in the intra tasks, and generalize the model to
identify the new categories. However, the relationship of samples between the
separated tasks is difficultly considered because of the different metric
criterion in the respective tasks. In contrast, the proposed high-order
structure preserving graph neural network(HOSP-GNN) can further explore the
rich structure of the samples to predict the label of the queried data on graph
that enables the structure evolution to explicitly discriminate the categories
by iteratively updating the high-order structure relationship (the relative
metric in multi-samples,instead of pairwise sample metric) with the manifold
structure constraints. HOSP-GNN can not only mine the high-order structure for
complementing the relevance between samples that may be divided into the
different task in meta-learning, and but also generate the rule of the
structure updating by manifold constraint. Furthermore, HOSP-GNN doesn't need
retrain the learning model for recognizing the new classes, and HOSP-GNN has
the well-generalizable high-order structure for model adaptability. Experiments
show that HOSP-GNN outperforms the state-of-the-art methods on supervised and
semi-supervised few-shot learning in three benchmark datasets that are
miniImageNet, tieredImageNet and FC100.
