Hyperspectral data classification using supervised approaches, in general, and the statistical algorithms, in particular, need high quantity and quality training data. However, these limitations, and the high dimensionality of these data, are the most important problems for using the supervised algorithms. As a solution, unsupervised or clustering algorithms can be considered to overcome these problems. One of the emerging clustering algorithms that can be used for this purpose is the kernel-based fuzzy c-means (KFCM), which has been developed by kernelizing the FCM algorithm. Nevertheless, there are some parameters that affect the efficiency of KFCM clustering of hyperspectral data. These parameters include kernel parameters, initial cluster centers, and the number of spectral bands. To address these problems, two new algorithms are developed. In these algorithms, the particle swarm optimization method is employed to optimize the KFCM with respect to these parameters. The first algorithm is designed to optimize the KFCM with respect to kernel parameters and initial cluster centers, while the second one selects the optimum discriminative subset of bands and the former parameters as well. The evaluations of the results of experiments show that the proposed algorithms are more efficient than the standard k-means and FCM algorithms for clustering hyperspectral remotely sensed data.