Study On FCM Algorithm Based On Gravitation And Class Merging

Researchers are getting more and more attentions to cluster analysis, since it involved in many fields such as statistics, data mining, machine learning and image processing, etc. There are many clustering algorithms among which fuzzy c-means (FCM) gets the most concern because of its sound mathematical foundation and complete theory but it is not impeccable. The paper mainly focuses on fuzzy c-means clustering algorithm (FCM), coming up with some improvements. The specifics are as follows:①To relieve the sensitivity of traditional FCM algorithm to outliers, the paper takes advantage of the gravity to remove outliers, preparing for the next cluster steps. Outliers are characterized as its rarefaction and have a long distance between most other objects , but gravity between objects is positively related to the quality of objects, and negatively related to the square of the distance between objects. The processing of noise points by gravity can enlarge the characteristics of outliers,it is much easier to remove the outliers.②The clustering center selection method based on gravity was proposed to overcome the imperfection that the traditional FCM algorithm depends extra on the initial cluster center. Gravity takes account of not only the distance between the objects but also the "quality" of the object. the "quality" of an object in the data sets means the number of objects that its neighborhood contained.Most in the cases,the clustering centers selected by gravity in the class center,not only avoid the algorithm get into the local extremum,but also reduce the number of iteration and optimization.③the number of classes needs to be given in Traditional FCM algorithms, which is difficult for users who lack of experience.To solve this problem , the best number of clustering getted by class merging was propose in this paper.In order to verify the efficiency and feasibility of the improved algorithm, the paper ends with the comparison experiments with the traditional FCM algorithm on several datasets. The results show that the improved algorithm is superior to traditional FCM in both of clustering quality and stability. Therefore, the improved FCM algorithm proposed in this paper is effective and feasible.