A spectral clustering method with semantic interpretation based on axiomatic fuzzy set theory

Abstract

Owing to good performance in clustering non-convex datasets, spectral clustering has attracted much attention and become one of the most popular clustering algorithms in the last decades. However, the existing spectral clustering methods are sensitive to parameter settings in building the affinity matrix, which seriously jeopardizes the algorithm's immunity to noise data. Moreover, in many application domains, including credit rating and medical diagnosis, it is very important that the learned model is capable of understandability and interpretability. To make spectral clustering competitive in both classification rate and comprehensibility, we propose a spectral clustering method with semantic interpretation based on axiomatic fuzzy set (AFS) theory, which integrates the representation capability of AFS and the classification competence of spectral clustering (N-cut). The effectiveness of the proposed approach is demonstrated by using real-word datasets, and the experimental results indicate that the performance of our method is comparable with that of classic spectral clustering algorithms (NJW, SM, Diffuzzy, AASC and SOM-SC) and other clustering methods, including K-means, fuzzy c-means, and MinMax K-means. Meanwhile, the proposed method can be used to explore the underlying clusters and give their characteristics in the form of fuzzy descriptions.