  Fuzzy C-Means (FCM) is a widely used clustering method. However, FCM and its
many accelerated variants have low efficiency in the mid-to-late stage of the
clustering process. In this stage, all samples are involved in the update of
their non-affinity centers, and the fuzzy membership grades of the most of
samples, whose assignment is unchanged, are still updated by calculating the
samples-centers distances. All those lead to the algorithms converging slowly.
In this paper, a new affinity filtering technique is developed to recognize a
complete set of the non-affinity centers for each sample with low computations.
Then, a new membership scaling technique is suggested to set the membership
grades between each sample and its non-affinity centers to 0 and maintain the
fuzzy membership grades for others. By integrating those two techniques, FCM
based on new affinity filtering and membership scaling (AMFCM) is proposed to
accelerate the whole convergence process of FCM. Many experimental results
performed on synthetic and real-world data sets have shown the feasibility and
efficiency of the proposed algorithm. Compared with the state-of-the-art
algorithms, AMFCM is significantly faster and more effective. For example,
AMFCM reduces the number of the iteration of FCM by 80% on average.
