A new weighting fuzzy c-means algorithm

It is always supposed that each cluster has almost equal number of points when carrying out the FCM. However, this assumption may not hold in practice. In this paper, we propose a novel fuzzy c-means algorithm based on the definition of generalized mean, weighting fuzzy c-means algorithms (WFCM). Noticing that the Gath-Geva fuzzy clustering algorithm considers the size of the clusters, we compare the performance between the WFCM and the Gath-Geva fuzzy clustering algorithms by numerical experiments. Moreover, we offer a theoretical threshold to choose an appropriate weighting exponent in the WFCM, which is also valid for the FCM, the numeric experiments verify such conclusion.