论文标题
作为集群诱导的Voronoi图：几何方法
Few-shot Learning as Cluster-induced Voronoi Diagrams: A Geometric Approach
论文作者
论文摘要
几乎没有射击学习（FSL）是从丰富的基本样本到不足的新样品的快速概括的过程。尽管近年来进行了广泛的研究，但FSL仍无法为广泛的现实应用程序产生令人满意的解决方案。为了应对这一挑战，我们从本文的几何学角度研究了FSL问题。一个观察结果是，广泛包含的质子模型本质上是特征空间中的Voronoi图（VD）。我们通过利用称为群集诱导的Voronoi图（CIVD）的近期计算几何形状上的进步来对其进行翻新。从最简单的邻居模型开始，CIVD逐渐结合了群集到点，然后进行群集到群集关系的空间细分，该关系用于提高FSL多个阶段的精度和鲁棒性。具体而言，我们使用CIVD（1）整合参数和非参数分类器； （2）结合特征表示和替代表示； （3）并利用特征级别，转换级和几何级别的异质性，以获得更好的合奏。我们基于CIVD的工作流程使我们能够在Mini-Imagenet，Cub和Tiered-Imagennet数据集上实现新的最新结果，并使用$ {\ sim} 2 \％{ - } 5 \％$改进下一个最好的。总而言之，CIVD提供了一种数学上优雅且可解释的框架，可补偿极端数据不足，防止过度拟合，并允许成千上万个单独的VD快速几何集合。这些共同使FSL更强大。
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.
