摘要： 无监督异常检测需要在缺乏标签信息的条件下识别偏离主体分布或局部结构模式的样本，其难点在于异常样本通常数量少、形态不稳定，且易与正常样本在特征空间中发生重叠。现有方法虽然可以从距离、密度、聚类结构或模糊相似关系等角度构造异常评分，但在复杂数据中仍存在一定局限：不同属性对异常识别的贡献往往并不一致，统一赋权容易使冗余属性或低信息属性削弱有效属性的作用；直接基于实例级相似关系进行计算时，异常评分容易受孤立噪声和局部波动的影响；同时，全局模糊相似信息与局部聚集结构之间缺少有效结合，导致模型难以同时反映样本的整体偏离程度和所在区域的局部稀疏性。针对这些问题，提出一种融合模糊熵与粒球密度的无监督异常检测算法（FEGBAD）。该方法将原始样本组织为粒球结构，使检测过程能够在样本层和局部区域层之间建立联系；在属性层面，采用邻域对称三角模糊相似度计算样本与总体数据之间的模糊支持关系，并通过模糊熵描述不同属性上的分布差异，从而得到属性权重；在局部结构层面，将样本级模糊概率聚合到粒球内部，形成粒球密度，用于刻画样本所在区域与主体分布之间的相似支持强度。最终，算法将属性权重与粒球密度结合起来生成异常得分，使得得分既能反映属性差异，又能体现局部结构信息。为验证算法有效性，在18个公开基准数据集上与8种代表性异常检测方法进行了比较，数据集覆盖数值型、标称型和混合型属性，样本规模和特征维度也具有较大差异。实验结果表明，FEGBAD受试者工作特征曲线下面积（AUC）在18个数据集中取得10次最优或并列最优结果，并在5个数据集上取得次优结果，平均指标达0.9149；平均精度（AP）在 11 个数据集上取得最优或并列最优，2个数据集获得次优，平均AP值为0.6423；两项指标均高于所有对比方法，且与次优算法存在一定差距，说明该方法在不同数据条件下具有较稳定的异常排序能力。消融实验结果表明，完整 FEGBAD 模型的平均 AUC 与平均 AP 分别达 0.8820 与 0.5549；移除模糊熵属性权重、粒球密度模块及同时移除双模块后，两项指标均进一步下降趋势。两个模块均对检测性能具有正向贡献，其中粒球密度模块对异常精度的提升作用更为突出。运行时间分析显示，FEGBAD 平均运行时长为 59.889 s，虽高于部分轻量级方法，但显著低于其他复杂模糊粗糙集类算法。总体而言，FEGBAD 通过模糊熵抑制低信息属性的干扰、借助粒球密度强化局部分布结构刻画，在检测性能与计算开销间取得了较好平衡，适用于静态表格数据场景，但对强非线性结构、流式及图结构数据的适应性仍有待提升。

Abstract: Unsupervised anomaly detection identifies samples deviating from dominant distributions or local structural patterns without label information, yet it faces inherent challenges including scarce anomalies, feature overlap between normal and abnormal samples, and unstable anomaly patterns. Existing methods constructing anomaly scores from distance, density or fuzzy similarity still have notable limitations in complex scenarios: uniform attribute weighting weakens the effect of discriminative features, instance-level similarity computation is susceptible to isolated noise and local fluctuations, and there lacks effective integration between global fuzzy similarity information and local aggregation structures, making it hard to capture both global deviation and local sparsity of samples. To address these issues, this paper proposes FEGBAD, an unsupervised anomaly detection algorithm integrating fuzzy entropy and granular-ball density. It organizes original samples into granular-ball structures to build a connection between sample-level and local-region information, derives attribute weights via fuzzy entropy to measure the contribution of different attributes to anomaly identification, and aggregates sample-level fuzzy probabilities into granular-ball density to characterize the similarity between local regions and the dominant distribution, finally fusing attribute weights and granular-ball density to generate comprehensive anomaly scores. Comparative experiments on 18 public benchmark datasets against 8 representative methods demonstrate that FEGBAD achieves 10 best or tied-best AUC results and 11 best or tied-best AP results, with an average AUC of 0.9149 and an average AP of 0.6423, outperforming all comparative algorithms. Ablation studies verify that both core modules contribute positively to detection performance, with the granular-ball density module exerting a more significant effect on improving anomaly detection accuracy. Runtime analysis shows FEGBAD has an average running time of 59.889 seconds, which is longer than some lightweight baselines but significantly shorter than other complex fuzzy rough set algorithms. Overall, FEGBAD achieves a favorable trade-off between detection performance and computational cost by suppressing interference from low-information attributes and enhancing the characterization of local distribution structures; it is applicable to static tabular data scenarios, while its adaptability to strongly nonlinear structures, streaming data and graph-structured data still needs further improvement.