Yumin Chen

The K-means clustering algorithm is widely applied in various clustering tasks due to its high computational efficiency and simple implementation. However, its performance significantly deteriorates when dealing with non-convex structures, fuzzy boundaries, or noisy data, as it relies on the assumption that clusters are spherical or linearly separable. To address these limitations, this paper proposes a Gaussian membership-driven fuzzy granular K-means clustering method. In this approach, multi-function Gaussian membership functions are used for fuzzy granulation at the single-feature level to generate fuzzy granules, while fuzzy granule vectors are constructed in the multi-feature space. A novel distance metric for fuzzy granules is defined along with operational rules, for which axiomatic proof is provided. This Gaussian-based granulation enables effective modeling of nonlinear separability in complex data structures, leading to the development of a new fuzzy granular K-means clustering framework. Experimental results on multiple public UCI datasets demonstrate that the proposed method significantly outperforms traditional K-means and other baseline methods in clustering tasks involving complex geometric data (e.g., circular and spiral structures), showing improved robustness and adaptability. This offers an effective solution for clustering data with intricate distributions.

To address the challenges in network anomaly detection, such as data label imbalance and the poor performance of traditional Support Vector Machines (SVM) in fitting high-dimensional, large-sample datasets, this paper proposes a novel framework for network anomaly detection. The core contribution is the proposal of a Fuzzy Granular Support Vector Machine (FGSVM) based on fuzzy granular vectors. FGSVM constructs fuzzy granular vectors by performing fuzzy granulation on data features, thereby comprehensively capturing both local feature distributions and global data characteristics. This method granulates all data, avoiding the information loss caused by sample compression in traditional methods. To further optimize model performance, this paper also introduces a Noise-Aware Hybrid Weighted Sampling (NA-HWS) method, which optimizes the data distribution by purifying the data and applying weighted sampling to critical boundary regions. This approach combines with FGSVM to form the more powerful S-FGSVM model. Comprehensive experimental results on several internationally recognized benchmark datasets, including NSL-KDD, CIC-IDS-2017, and UNSW-NB15, confirm the significant superiority of the proposed methods. The S-FGSVM model demonstrated outstanding performance on all key metrics, significantly surpassing most baseline algorithms, including both deep learning and classic machine learning models. Compared to deep learning models, which generally have high computational overhead, the model proposed in this study shows a significant advantage in computational efficiency, achieving an ideal balance between detection performance and operational efficiency.

Outlier detection is pivotal in data mining and machine learning, as it focuses on discovering unusual behaviors that deviate substantially from the majority of data samples. Conventional approaches, however, often falter when dealing with complex data that are multimodal or sparse or that exhibit strong nonlinearity. To address these challenges, this paper introduces a novel outlier detection framework named Multimodal Granular Distance-based Outlier Detection (MGDOD), which leverages granular computing principles in conjunction with multimodal granulation techniques. Specifically, similarity measures and granulation methods are employed to generate granules from single-modal data, thereby reducing inconsistencies arising from different data modalities. These granules are then combined to form multimodal granular vectors, whose size, measurement, and operational rules are carefully defined. Building on this conceptual foundation, we propose two multimodal granular distance measures, which are formally axiomatized, and develop an associated outlier detection algorithm. Experimental evaluations on benchmark datasets from UCI, ODDS, and multimodal sources compare the proposed MGDOD method against established outlier detection techniques under various granulation parameters, distance metrics, and outlier conditions. The results confirm the effectiveness and robustness of MGDOD, demonstrating its superior performance in identifying anomalies across diverse and challenging data scenarios.