[Paper Review] Few-shot Learning as Cluster-induced Voronoi Diagrams: A Geometric Approach

Chunwei Ma, Ziyun Huang+2 more|arXiv (Cornell University)|Feb 5, 2022

Domain Adaptation and Few-Shot Learning4 citations

TL;DR

This paper proposes DeepVoro, a geometric framework for few-shot learning that leverages Cluster-induced Voronoi Diagrams (CIVD) to improve decision boundary learning by modeling cluster-to-point and cluster-to-cluster influences in feature space. It achieves state-of-the-art performance on mini-ImageNet, CUB, and tiered-ImageNet with 2%–5% accuracy gains over prior methods by enabling robust, fast geometric ensembling and mitigating overfitting in low-data regimes.

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

Motivation & Objective

• Address the challenge of data insufficiency in few-shot learning by introducing a geometric framework that models complex decision boundaries beyond simple point-based Voronoi diagrams.
• Overcome limitations of existing methods like ProtoNet, which rely on point-to-point distance and linear bisectors, by incorporating cluster-level relationships for finer-grained decision boundary modeling.
• Enhance model robustness and generalization by integrating feature representation, surrogate representation, and multiple heterogeneities (feature, transformation, geometry) into a unified geometric ensemble.
• Achieve state-of-the-art performance across diverse few-shot benchmarks while maintaining computational efficiency and interpretability.

Proposed method

• Adopt Cluster-induced Voronoi Diagrams (CIVD) as the core geometric structure, generalizing traditional Voronoi Diagrams from point-to-point to cluster-to-point and cluster-to-cluster influence-based space partitioning.
• Integrate CIVD into a multi-stage few-shot learning pipeline to model decision boundaries using both parametric and nonparametric classifiers, improving accuracy and robustness.
• Leverage CIVD to combine feature-level, transformation-level, and geometry-level heterogeneities into a single ensemble framework, enabling fast and effective model combination.
• Use a differentiable CIVD construction process that ensures $(1+\epsilon)$-approximation with nearly linear-size diagrams, balancing accuracy and efficiency.
• Design DeepVoro and DeepVoro++ as end-to-end models that use CIVD for prediction, with hyperparameters $\beta$, $R$, $\lambda$, and $b$ tuned for optimal performance.
• Apply CIVD to both inductive and transductive settings, demonstrating stability under domain shift and resistance to outlier support sets via geometric variance analysis.

Experimental results

Research questions

• RQ1 Can a geometric framework based on cluster-induced Voronoi diagrams improve decision boundary learning in few-shot classification beyond point-based prototypes?
• RQ2 How does incorporating cluster-to-point and cluster-to-cluster influence relationships enhance robustness and accuracy in low-shot scenarios?
• RQ3 To what extent can CIVD-based models mitigate overfitting and handle data insufficiency in few-shot learning?
• RQ4 How does the proposed method perform under domain shift and in the presence of outlier support sets?
• RQ5 Can CIVD enable effective geometric ensembling across diverse feature extractors and meta-training schemes?

Key findings

• DeepVoro achieves 68.80% accuracy on 1-shot mini-ImageNet and 85.70% on 5-shot, outperforming DC (66.43% and 82.61%) and S2M2_R (58.33% and 79.26%) under rotation loss.
• With manifold mixup training, DeepVoro reaches 65.00% on 1-shot and 83.19% on 5-shot, surpassing DC (62.61% and 78.62%) and S2M2_R (48.11% and 72.74%).
• On cross-domain few-shot learning, DeepVoro improves by 6.68% on 1-shot (CUB → mini-ImageNet) and 6.51% on 5-shot over S2M2_R, showing strong domain generalization.
• DeepVoro++ reduces the performance gap between rotation loss and manifold mixup from 10.22% (1-shot) to 3.98%, indicating better utilization of diverse pretraining schemes.
• The method demonstrates superior resistance to outliers: episodes with high geometric variance (indicating outlier presence) show significantly lower accuracy for baselines, but DeepVoro maintains performance.
• CIVD-based models achieve state-of-the-art results across all benchmarks, with consistent 2%–5% improvements over the next best method, validating the geometric framework’s effectiveness.