QGB-W$k$NN：用于鲁棒分类的量子粒球学习

中文摘要 AI 辅助

最近邻分类在机器学习中被广泛使用，然而现有方法在噪声环境中常常面临计算效率低和鲁棒性有限的问题。为了联合解决这些挑战，本文提出了一种基于量子粒球的高效且可靠的加权$K$近邻分类框架，称为QGB-W$k$NN。该框架通过将量子增强的粒球表示与层次最近邻搜索相结合来提高计算效率，同时通过纯度感知的加权决策机制增强分类可靠性。具体而言，构建量子核粒球以减少检索冗余，并在有限的量子资源下增强非线性特征表示。开发了一种粒球纯度引导的HNSW优化策略，以利用结构可靠性进行邻居检索过程中的层次图构建，缓解传统随机分层导致的局部最优问题。最后，引入了一种联合考虑粒球相似性和纯度的加权投票机制，以在噪声环境中产生更可靠的分类决策。在基准数据集上的大量实验表明，QGB-W$k$NN在实现竞争性分类精度的同时，在分类性能与计算成本之间表现出良好的帕累托权衡。此外，该框架在各种噪声条件下持续提高了鲁棒性，表明可靠性感知的量子粒球学习为高效且鲁棒的最近邻分类提供了一种有前景的范式。

英文摘要

Nearest-neighbor classification is widely used in machine learning, yet existing methods often suffer from low computational efficiency and limited robustness in noisy environments. To jointly address these challenges, this paper proposes an efficient and reliable weighted $K$-nearest neighbor classification framework based on quantum granular balls, termed QGB-W$k$NN. The proposed framework improves computational efficiency by integrating quantum-enhanced granular-ball representation with hierarchical nearest-neighbor search, while enhancing classification reliability through a purity-aware weighted decision mechanism. Specifically, quantum-kernel granular balls are constructed to reduce retrieval redundancy and strengthen nonlinear feature representation under limited quantum resources. A granular-ball purity-guided HNSW optimization strategy is developed to exploit structural reliability for hierarchical graph construction during neighbor retrieval, alleviating the local optimality issue caused by conventional random layering. Finally, a weighted voting mechanism jointly incorporating granular-ball similarity and purity is introduced to produce more reliable classification decisions in noisy environments. Extensive experiments on benchmark datasets demonstrate that QGB-W$k$NN achieves competitive classification accuracy while exhibiting favorable Pareto trade-offs between classification performance and computational cost. Moreover, the proposed framework consistently improves robustness under various noisy conditions, suggesting that reliability-aware quantum granular-ball learning provides a promising paradigm for efficient and robust nearest-neighbor classification.

发表机构

• Chongqing University of Posts and Telecommunications（重庆邮电大学）
• University of Otago（奥塔哥大学）

机构由 AI 辅助整理，请以论文原文为准。