Robust jointly sparse semi-supervised fuzzy C-means clustering with asymmetric deviation constraints.

Abstract

Semi-supervised methods improve traditional fuzzy clustering by using limited labeled data and have gained attention in data mining and pattern analysis. However, existing semi-supervised fuzzy clustering techniques are noise-sensitive and offer limited performance gains. This paper critiques current methods' semi-supervised constraint terms and proposes a robust jointly sparse semi-supervised fuzzy C-means clustering algorithm (RSSFCM) and an enhanced version for noisy data. Our approach modifies the membership sparse regularization in robust and sparse fuzzy K-means clustering (RSFKM) with an asymmetric deviation quadratic term, making RSSFCM a generalization of RSFKM. We prove algorithm convergence via Zangwill's theorem. Additionally, we integrate a Gaussian kernel into RSSFCM for noisy numerical data clustering and add a fuzzy local information factor for noisy image segmentation. Experiments demonstrate that our algorithms significantly outperform state-of-the-art methods across various datasets, advancing semi-supervised fuzzy C-means clustering. The source codes for our algorithms are accessible at https://github.com/PIAOLIUPING-clound/.