  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 ${\sim}2\%{-}5\%$
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.
