Abstract: Imbalanced image classification remains a formidable challenge in computer vision, where deep learning has been extensively applied but still struggles with class imbalance, causing models to bias towards the majority class and overlook the minority class. Traditional data sampling techniques can introduce noise or omit essential information, thus impeding model generalization. Integrating geometric concepts into deep learning has emerged as an effective solution, improving the classification performance by restructuring feature space, refining decision boundaries, and diversifying data.This paper introduces a novel geometric deep learning method that combines Kernel-based Hierarchical Feature Scaling (KHFS) with Relative Neighborhood Boundary Mining (RNBM). Inspired by Support Vector Data Description (SVDD), KHFS utilizes kernel functions to hierarchically cluster and identify class centroids, scaling feature vectors based on the radius of hyper-spheres centered at these centroids to enhance the representation of minority class samples.RNBM constructs a relative neighborhood graph to identify boundary samples at class intersections, promoting intra-class compactness and inter-class separation. Furthermore, the Convolutional Block Self-Attention (CBSA) mechanism is integrated into the CNN feature extraction module to concentrate on salient input features.Comprehensive experiments on CIFAR-10, CIFAR-100, and CINIC-10 datasets demonstrate the proposed geometric deep learning method's superior performance in mitigating data imbalance compared to existing models.

Key words: Imbalanced Image Classification, Geometric Methods, Feature Scaling, Boundary Sample Mining, Support Vector Data Description

摘要： 不平衡图像分类是计算机视觉领域的一大挑战。尽管深度学习技术已被广泛应用，但类别不平衡问题仍然显著，导致模型偏向多数类而忽视少数类。传统的数据采样方法易引入噪声或丢失关键信息，限制了模型的泛化能力。研究表明，将几何思想融入深度学习方法中是一种有效且创新的解决方案。几何思想通过优化特征空间结构、改进决策边界和增强数据多样性，显著提升了不平衡图像分类的性能。本文提出了一种新的几何深度学习方法，该方法集成了基于核函数的层次特征缩放技术(KHFS)和相对邻域边界样本挖掘手段(RNBM)。KHFS借鉴了基于核函数的支持向量数据描述(SVDD)，通过层次聚类确定每类的中心点，并计算以中心点为球心的超球体半径，对各类特征向量进行相应缩放，从而增强少数类样本的表示能力。RNBM方法则通过构建相对邻域图来捕捉样本间的邻域关系，从中挖掘出不同类别交界处的边界样本，以约束类内样本的紧凑性和类间样本的分散性。此外，本文也引入了卷积块自注意力机制(CBSA)机制，应用于卷积神经网络(CNN)特征提取模块，旨在关注输入数据中的关键信息。在CIFAR-10、CIFAR-100、CINIC-10三个基准数据集上的大量实验验证了该几何深度学习方法在解决数据不平衡问题方面优于现有模型的显著性能。

关键词: 不平衡图像分类, 几何方法, 特征缩放, 边界样本挖掘, 支持向量数据描述