Diversity-induced fuzzy clustering with Laplacian regularization

Fuzzy clustering is a fundamental technique in unsupervised learning for exploring data structures. However, fuzzy c-means (FCM), as a representative fuzzy clustering algorithm, performs relatively poorly when handling noisy data and outliers since it only considers global data characteristics while ignoring the local information. Additionally, FCM overlooks data diversity, making it difficult to handle complex data and leading to cluster center overlapping. To address these challenges, this paper proposes a novel approach called diversity-induced fuzzy clustering with Laplacian regularization (DiFCMLR). DiFCMLR incorporates Hilbert-Schmidt Independence Criterion (HSIC) to maximize the independence among clusters, thereby enhancing clustering diversity. In addition, DiFCMLR introduces Laplacian regularization to consider the local information of data and determine the affinity relationship between samples. Furthermore, it corrects the Euclidean distance between samples, thereby reducing the impact of the normal distribution prior assumption of FCM and improving the applicability of algorithm to complex data or size-imbalance problems. During the optimization, DiFCMLR utilizes iterative reweighting and the alternating direction method of multipliers, which enhance robustness against noise and outliers and achieve faster convergence towards better solutions. The effectiveness of DiFCMLR is confirmed through theoretical analysis and experimental evaluation.