A new validity index adapted to fuzzy clustering algorithm

The fuzzy c-means clustering algorithm is the most common clustering algorithm. It solves the unrealistic nature of data by defining the membership matrix. As the fuzzy c-means clustering algorithm needs to set the number of classifications in advance, which is almost impossible in cases with no prior knowledge of the data set, some scholars put forward the concept of the validity index. Because the validity index is related to the distance relation between the membership matrix, the data point in the data set and the center of clustering, it is hoped that the feature weighting method can be used to evaluate all the characteristics of data in a data set to obtain the optimal classification number. Therefore, this paper presents an improved validity index for the comprehensive weight index, compactness index and separability index. This validity index first determines the relationship between the features of the data points and the data point itself. By defining the new compactness function and the separability function, the weight of each feature in the data set is obtained. and then the validity index is combined with the fuzzy c-means clustering algorithm to effectively determine the number of classes to be processed. The proposed algorithm is tested on two artificial data sets and real data sets; the experimental results demonstrated the advantages of this work in image processing and showed that it can effectively obtain reliable data classification results.