Deep learning has made remarkable achievement in many fields. However, learning
 the parameters of neural networks usually demands a large amount of labeled
 data. The algorithms of deep learning, therefore, encounter difficulties when applied
 to supervised learning where only little data are available. This specific task
 is called few-shot learning. To address it, we propose a novel algorithm for fewshot
 learning using discrete geometry, in the sense that the samples in a class are
 modeled as a reduced simplex. The volume of the simplex is used for the measurement
 of class scatter. During testing, combined with the test sample and the
 points in the class, a new simplex is formed. Then the similarity between the test
 sample and the class can be quantized with the ratio of volumes of the new simplex
 to the original class simplex. Moreover, we present an approach to constructing
 simplices using local regions of feature maps yielded by convolutional neural networks.
 Experiments on Omniglot and miniImageNet verify the effectiveness of
 our simplex algorithm on few-shot learning.
A simplex-based geometric method is proposed to cope with few-shot learning problems.