Few Shot Learning with Simplex

TL;DR

This paper introduces a novel few-shot learning algorithm that models class samples as simplices in discrete geometry, using volume ratios to measure similarity, and demonstrates its effectiveness on standard datasets.

Contribution

The paper proposes a new geometric approach for few-shot learning based on simplices and volume ratios, integrating with CNN feature maps for improved performance.

Findings

Effective on Omniglot and miniImageNet datasets.

Outperforms some existing few-shot learning methods.

Utilizes local feature regions for simplex construction.

Abstract

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.