We propose a clustering algorithm which incorporates a similarity-based fuzzy clustering and principal component analysis. The proposed algorithm is capable of discovering clusters with hyper-spherical, hyperellipsoidal, or oblique hyper-ellipsoidal shapes. Besides, the number of the clusters need not be specified in advance by the user. For a given dataset, the orientation, locations, and the number of clusters obtained can truthfully reflect the characteristics of the dataset. Experimental results, obtained by running on datasets generated synthetically, show that our method performs better than other methods.