Novel Validity Index For Fuzzy Clustering Andits Application

Along with the increasing of the data,scholars did a lot of research on data processing,so data mining technology comes into being.C lustering algorithms is one type of the data mining technology.C luster analysis is a method for clustering a data set into groups of similar individuals without prior knowledge.It is meaningful to have this algorithm for reality application.So many scholars have made a lot of research on clustering algorithms.The fuzzy C-means clustering algorithm is the most widely used clustering algorithm.The hard clustering algorithms make every data point either belong to this cluster or that cluster,this is unrealistic in the real world.FCM solves this problem by using membership matrix.But fuzzy c-means clustering algorithm need to set up the number of clusters in advance,this is almost impossible to solve a problem without prior knowledge,so cluster validity index is proposed.A new cluster validity index is proposed in this study.We combine this new validity index with FCM to determinate the number of clusters.As for practical application,we put our new algorithm in color quantization.The performance of this new index is excellent underpinned by the outcomes from the experiments.The main achievements and innovations of this paper are as follows:Firstly,introduce morphology similarity distance.As the validity index uses the membership matrix,the distance between every data point,the distance between data point and cluster center,so the concept of distance is important.We use morphology similarity distance in order to make a comprehensive investigation of distance.It shows better performance by compare with Euclidean distance and Ma nhattan distance.Secondly,We use morphology similarity distance to improve compactness index and separation index.We add feature weighting algorithm ReliefF to our new index.Also,we propose new compactness index and separation index.We combine ReliefF with new compactness index and separation index to build a new validity index.The performance of this new index is excellent underpinned by the outcomes from the experiments based on both artificial datasets and real world datasets.Finally,we use our new validity index in color quantization.The picture we deal with is color image,the new algorithm could cluster the picture and determine the prime number of the color.In this study,we use the pictures of flower and butterfly to do the experiment and shows our new validity index has a better performance.