  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 few-shot 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.
