Abstract: Clustering analysis is widely applied to engineering fields, such as biology sequence analysis, image segmentation, text analysis. Currently there have been many clustering methods and statistical learning based methods constitute a class of them. This paper started from FCM, introduced classical methods, such as potential and mountain functions,entropy method, and then analyzed their properties and applicability. Moreover, we also introduced the stat}of-art clustering techniqucs,such as kernel clustering, spectral clustering and Gaussian mixture model based clustering, narrated the solving process and analyzed their properties, computation complexity. At last, this paper presented several research directions.

Key words: Clustering analysis, Statistical machine learning, Gaussian mixture models, Spectral clustering, Kernel clustering