Multiviewpoint Induced Kernel Fuzzy Clustering With Trapezoidal Information Granules

Knowledge-based fuzzy clustering algorithms can integrate prior knowledge, constraints or expert experience into the clustering process, thereby improving the interpretability and accuracy of the clustering results. Recent research has gradually introduced knowledge in the form of knowledge granules into the fuzzy clustering algorithms. However, during the extraction and granulation process of interval or triangular knowledge granules, the inherent structure of the granular data are not sufficiently captured and a large amount of data information is lost, leading to weak representativeness of the knowledge granules. To solve this issue, in this study, we propose a new granular clustering algorithm called multiviewpoint induced kernel fuzzy clustering with trapezoidal information granules (MVKFC-T). First, based on the principle of justifiable granularity, we redesign the optimization function for trapezoidal granules modeling. By using the concept of a hypercube and an update of objective function, new granule weights are given, which more reasonably represent the quality of the granule data and solved the particle size degradation problem in trapezoidal granules modeling. So we propose a novel approach called volumetric trapezoidal information granules modeling method. Second, we propose a knowledge group extraction and granulation (KGEG) algorithm. In the extraction phase of KGEG, we design a novel clustering method called density-based spatial clustering of applications with noise (DBSCAN) algorithm based on reachability and compactness to generate knowledge group prototypes. In the granulation phase of KGEG, these prototypes are modeled into trapezoidal granules to form the knowledge granule group. Third, we introduce kernel distance into the \alpha-cut distance and further propose the MVKFC-T algorithm, which is guided by the knowledge granule group as viewpoints. Finally through experiments on artificial and UCI datasets and the reconstruction error analysis, the results show that MVKFC-T has stronger reconstruction capabilities compared to other granular clustering algorithms, indicating that the performance of MVKFC-T outperforms others.