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

arXiv: https://arxiv.org/abs/2202.02471 · HTML: https://mlsanity.com/paper/2202.02471/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 66 references that are in the map.
- First posted on arXiv 5 Feb 2022.

## Builds on (most cited first, 30 of 38)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [A Closer Look at Few-shot Classification](https://mlsanity.com/paper/1904.04232/) (2019)
- [Meta-Learning with Latent Embedding Optimization](https://mlsanity.com/paper/1807.05960/) (2018)
- [Meta-Learning with Differentiable Convex Optimization](https://mlsanity.com/paper/1904.03758/) (2019)
- [Meta-Learning for Semi-Supervised Few-Shot Classification](https://mlsanity.com/paper/1803.00676/) (2018)
- [Meta-SGD: Learning to Learn Quickly for Few-Shot Learning](https://mlsanity.com/paper/1707.09835/) (2017)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Learning to Propagate Labels: Transductive Propagation Network for Few-shot Learning](https://mlsanity.com/paper/1805.10002/) (2018)
- [SimpleShot: Revisiting Nearest-Neighbor Classification for Few-Shot Learning](https://mlsanity.com/paper/1911.04623/) (2019)
- [Free Lunch for Few-shot Learning: Distribution Calibration](https://mlsanity.com/paper/2101.06395/) (2021)
- [Charting the Right Manifold: Manifold Mixup for Few-shot Learning](https://mlsanity.com/paper/1907.12087/) (2019)
- [Negative Margin Matters: Understanding Margin in Few-shot Classification](https://mlsanity.com/paper/2003.12060/) (2020)
- [Adversarial Feature Hallucination Networks for Few-Shot Learning](https://mlsanity.com/paper/2003.13193/) (2020)
- [Delta-encoder: an effective sample synthesis method for few-shot object recognition](https://mlsanity.com/paper/1806.04734/) (2018)
- [Boosting Few-Shot Learning With Adaptive Margin Loss](https://mlsanity.com/paper/2005.13826/) (2020)
- [Leveraging the Feature Distribution in Transfer-based Few-Shot Learning](https://mlsanity.com/paper/2006.03806/) (2020)
- [Diversity with Cooperation: Ensemble Methods for Few-Shot Classification](https://mlsanity.com/paper/1903.11341/) (2019)
- [Multi-level Semantic Feature Augmentation for One-shot Learning](https://mlsanity.com/paper/1804.05298/) (2018)
- [The Geometry of Deep Networks: Power Diagram Subdivision](https://mlsanity.com/paper/1905.08443/) (2019)
- [Prototype Completion with Primitive Knowledge for Few-Shot Learning](https://mlsanity.com/paper/2009.04960/) (2020)
- [Bridging Multi-Task Learning and Meta-Learning: Towards Efficient Training and Effective Adaptation](https://mlsanity.com/paper/2106.09017/) (2021)
- [DeepEMD: Differentiable Earth Mover's Distance for Few-Shot Learning](https://mlsanity.com/paper/2003.06777/) (2020)

## Built on by (most cited first, 3 of 3)

- [Robust Few-Shot Ensemble Learning with Focal Diversity-Based Pruning](https://mlsanity.com/paper/2404.04434/) (2024)
- [TTVD: Towards a Geometric Framework for Test-Time Adaptation Based on Voronoi Diagram](https://mlsanity.com/paper/2412.07980/) (2024)
- [P3DC-Shot: Prior-Driven Discrete Data Calibration for Nearest-Neighbor Few-Shot Classification](https://mlsanity.com/paper/2301.00740/) (2023)

## Abstract (arXiv)

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.