Anomaly Detection Based on Hybrid Kernelized Fuzzy Density

Unsupervised anomaly detection has been extensively studied. However, most existing methods are designed for either numerical or nominal data, which struggle to detect anomalies effectively in real-world mixed-type datasets. Fuzzy information granulation is a key concept in granular computing, which offers a potent framework for managing uncertainty in mixed-type data and provides a viable pathway for unsupervised anomaly detection. Nevertheless, conventional fuzzy information granulation-based detection methods often model only simple, linear fuzzy relations between samples. This limitation prevents them from capturing the complex, nonlinear structures inherent in the data, leading to a degradation in detection performance. To address these shortcomings, we propose a Hybrid Kernelized Fuzzy Density-based anomaly detector (HKFD). HKFD pioneers a hybrid kernelized fuzzy relation by integrating a hybrid distance metric with kernel methods. This new relation allows us to define a hybrid kernelized fuzzy density for each sample within every feature subspace, effectively capturing the local data dispersion. Crucially, we introduce an information-theoretic weighting mechanism. By calculating the fuzzy information entropy of each feature’s distribution, HKFD automatically assigns higher weights to more informative feature subspaces that contribute more to identifying anomalies. The final anomaly factor is then calculated by the weighted fusion of these densities. Comprehensive experiments on 20 datasets demonstrate that HKFD significantly outperforms state-of-the-art methods, achieving superior anomaly detection performance.