Few-shot Learning as Cluster-induced Voronoi Diagrams: A Geometric Approach

Abstract

Few-shot learning (FSL) is the process of rapid generalization from abundant base samples to inadequate novel samples. Despite extensive research in recent years, FSL is still not yet able to generate satisfactory solutions for a wide range of real-world applications. To confront this challenge, we study the FSL problem from a geometric point of view in this paper. One observation is that the widely embraced ProtoNet model is essentially a Voronoi Diagram (VD) in the feature space. We retrofit it by making use of a recent advance in computational geometry called Cluster-induced Voronoi Diagram (CIVD). Starting from the simplest nearest neighbor model, CIVD gradually incorporates cluster-to-point and then cluster-to-cluster relationships for space subdivision, which is used to improve the accuracy and robustness at multiple stages of FSL. Specifically, we use CIVD (1) to integrate parametric and nonparametric few-shot classifiers; (2) to combine feature representation and surrogate representation; (3) and to leverage feature-level, transformation-level, and geometry-level heterogeneities for a better ensemble. Our CIVD-based workflow enables us to achieve new state-of-the-art results on mini-ImageNet, CUB, and tiered-ImagenNet datasets, with ∼2%−5% improvements upon the next best. To summarize, CIVD provides a mathematically elegant and geometrically interpretable framework that compensates for extreme data insufficiency, prevents overfitting, and allows for fast geometric ensemble for thousands of individual VD. These together make FSL stronger.

DCPNet: Distribution Calibration Prototypical Network for Few-Shot Image Classification

“…Furthermore, data enhancement for fine-tuning the feature backbone is essential when domain divergence occurs between the training and testing sets. Chunwen Ma et al [25] studied the few-shot classification problem from a geometric perspective and they found that the essence of a prototype network can be regarded as a Voronoi Diagram in the feature space. Based on this perspective, they proposed Cluster-induced Voronoi Diagram to improve the accuracy and robustness of the few-shot image classification.…”