Discriminative projection fuzzy K-Means with adaptive neighbors

Fuzzy K-Means (FKM) based on fuzzy theory is a classic method to effectively handle overlapping regions between clusters. However, redundant features and noises brought by increasing data dimensions affect the effectiveness of FKM. To cope with this issue, we propose a Discriminative Projection Fuzzy K-Means with adaptive neighbors (DPFKM) model, which embeds a discriminative subspace into FKM to facilitate learning of global structure and the most discriminative information. Firstly, a novel projection space with uncorrelated constraints are adopted to promote statistical independence among the data in the subspace as well as to enhance the ability of FKM to discern and utilize discriminative information. Secondly, the Frobenius norm is introduced as the regularization term to eliminate discrete solutions, while preserving the fuzziness and enhancing the sparsity of FKM. Finally, we propose a novel optimization method to finetune the model, with a particular focus on adaptive adjustment of the regularization parameter based on the proximity relationship between the samples and clusters. Comprehensive experiments are conducted on multiple data sets, and the results can prove the superiority of the proposed model.