Multi-objective artificial immune algorithm for fuzzy clustering based on multiple kernels

This paper presents a multi-objective artificial immune algorithm for fuzzy clustering based on multiple kernels (MAFC). MAFC extends the classical Fuzzy C-Means (FCM) algorithm and overcomes its important limitations, such as limited adaptability, poor handling of non-linear relationships between data, and vulnerability to local optima convergence, which can lead to poor clustering quality. To compensate these limitations, MAFC unifies multi-kernel learning and multi-objective optimization in a joint clustering framework, which preserves the geometric information of the dataset. The multi kernel method maps data from the feature space to kernel space by kernel functions. This approach is effective, not only for spherical clusters, but can also discover the non-linear relationships between data, and adds robustness to the particular choice of kernel functions. Additionally, the introduction of multi-objective optimization can optimize between-cluster separation and within-cluster compactness simultaneously via two different clustering validity criteria. These properties help the proposed algorithm to avoid becoming stuck at local optima. Furthermore, this paper utilizes an artificial immune algorithm to address the multi-objective clustering problem and acquire a Pareto optimal solution set. The solution set is obtained through the process of antibody population initialization, clone proliferation, non-uniform mutation and uniformity maintaining strategy, which avoids the problems of degradation and prematurity which can occur with conventional genetic algorithms. Finally, we choose the best solution, from the Pareto optimal solution set, using a semi-supervised method, to achieve the final clustering results. We compare our method against three state-of-the-art methods from the literature by performing experiments with both UCI datasets and face datasets. The results suggest that MAFC is significantly more efficient for clustering and has a wider scope of application.