用颗粒球结构压缩数据，让量子聚类更省资源且更准。
Granular-Ball Quantum Clustering for Resource-Efficient and Robust Learning
- 先用主成分分析分块生成紧凑颗粒球，减少80%量子核计算
- 在希尔伯特空间过滤噪声颗粒，提升聚类鲁棒性
- 适合做量子机器学习的高效聚类，尤其对复杂数据有效
量子聚类旨在利用量子特征表示揭示超越传统欧氏几何的复杂数据结构。然而，样本级核构造需对n个数据点执行O(n²)次量子电路，受限于近中期量子资源成为主要瓶颈。现有方法难以兼顾效率与精度：经典颗粒球聚类虽降低样本复杂度，但依赖欧氏度量，无法捕捉量子关联；现有量子压缩方案侧重效率，牺牲结构保留，导致非凸或噪声数据上性能下降。本文提出颗粒球量子聚类（GBQC），将颗粒球结构抽象与量子特征学习紧密耦合。首先通过主成分分析引导的分割策略将原始数据压缩为紧凑代表性颗粒球，使核评估减少80%；随后在希尔伯特空间引入量子凝聚机制，滤除噪声颗粒以增强鲁棒性。在合成、含噪、重叠及真实数据集上的实验表明，GBQC显著优于代表性经典与量子聚类方法，在准确率与鲁棒性上均具优势。此外，所提颗粒球压缩大幅降低量子核评估与计算开销，使更大规模数据的量子聚类在参数化量子学习框架中成为可能。结果表明，颗粒球表示不仅作为压缩手段降低量子计算成本，更是一种有效结构抽象机制，通过消除冗余和结构模糊的学习单元提升聚类质量。
原文摘要 · Abstract (English)
Quantum clustering aims to exploit quantum feature representations to uncover complex data structures beyond conventional Euclidean geometry. Yet this sample-level kernel construction requires O(n^2) quantum circuit executions for n data points, creating a major bottleneck under near-term quantum resource constraints. Prior solutions fail to resolve this efficiency-accuracy dilemma: classical granular-ball clustering reduces sample complexity but relies on Euclidean metrics that cannot capture quantum correlations, while existing quantum compression schemes prioritize efficiency over structural preservation, degrading performance on non-convex or noisy data. Here we propose Granular-Ball Quantum Clustering (GBQC), a framework that tightly couples granular-ball structural abstraction with quantum feature learning. GBQC first compresses raw data into compact, representative granular balls via a PCA-guided splitting strategy, reducing kernel evaluations by 80% compared to full-sample methods. A quantum cohesion mechanism then filters noisy granules in Hilbert space to improve clustering robustness. Extensive experiments on synthetic, noisy, overlapping, and real-world datasets demonstrate that GBQC consistently achieves superior clustering accuracy and robustness compared with representative classical and quantum clustering methods. Meanwhile, the proposed granular-ball compression significantly reduces quantum kernel evaluations and computational overhead, enabling quantum clustering experiments on larger datasets within parameterized quantum learning frameworks. These results suggest that granular-ball representations serve not only as a compression mechanism to reduce quantum computational costs but also as an effective structural abstraction mechanism that improves clustering quality by eliminating redundant and structurally ambiguous learning units.
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