一种基于核的模块化判别分析框架用于小样本学习

中文摘要 AI 辅助

小样本（SSS）问题在机器学习中仍然是一个基本挑战，当由于成本、可访问性或伦理约束而导致标记数据稀缺时尤为突出。尽管已有许多方法被提出，但现有方法在高维和有限数据条件下往往难以维持稳定且具有判别性的表示。核化线性主成分判别分析（KLPCDA）是一种最近提出的模块化框架，它在统一的核空间中整合了方差保留、类间可分性和类内紧凑性。尽管其公式已显示出有前景的初步结果，但对其组件在不同SSS场景中如何交互的系统性理解仍然缺乏。在本文中，我们对KLPCDA进行了系统的跨领域研究，以表征其核心目标之间的交互机制。我们分析了其七种变体在多个真实世界SSS任务中的行为，包括高光谱图像分类、机械故障诊断、医学诊断和人脸识别。通过大量实验和消融研究，我们调查了不同的目标组合如何在噪声、类不平衡和高维性等不同条件下影响性能。我们的分析揭示了三个核心目标（方差项、类间项和类内项）交互的一致模式，为它们在SSS设置中稳定表示和增强判别性方面的作用提供了统一且可解释的理解。基于这些发现，我们进一步推导出在不同数据特征下选择合适KLPCDA变体的实用指南。实验结果表明，KLPCDA在各领域均实现了强大且稳健的性能，同时保持了适用于资源受限环境的低计算复杂度。

英文摘要

The small-sample-size (SSS) problem remains a fundamental challenge in machine learning when labeled data are scarce due to cost, accessibility, or ethical constraints. While numerous approaches have been proposed, existing methods often struggle to maintain stable and discriminative representations under high-dimensional and limited-data conditions. Kernelized Linear Principal Component Discriminant Analysis (KLPCDA), a recently proposed modular framework, integrates variance preservation, inter-class separability, and intra-class compactness within a unified kernel space. Although its formulation has shown promising initial results, a systematic understanding of how its components interact across diverse SSS scenarios remains lacking. In this paper, we present a systematic cross-domain study of KLPCDA to characterize the interaction mechanisms among its core objectives. We analyze the behavior of its seven variants across multiple real-world SSS tasks, including hyperspectral image classification, mechanical fault diagnosis, medical diagnosis, and face recognition. Through extensive experiments and ablation studies, we investigate how different objective combinations influence performance under varying conditions such as noise, class imbalance, and high dimensionality. Our analysis reveals consistent patterns in the interaction of the three core objectives variance, between-class, and within-class terms, providing a unified and interpretable understanding of their roles in stabilizing representations and enhancing discrimination in SSS settings. Based on these findings, we further derive practical guidelines for selecting appropriate KLPCDA variants under different data characteristics. Experimental results demonstrate that KLPCDA achieves strong and robust performance across domains, while maintaining low computational complexity suitable for resource-constrained environments.

发表机构

• University of Aizu（会津大学）

机构由 AI 辅助整理，请以论文原文为准。