Research On Clustering Validity Evaluation Method Of Fuzzy C-Means Algorithm Based On Components

As the research focus of machine learning,image processing and pattern recognition,fuzzy clustering has been widely concerned by scholars at home and abroad.Because the concept of fuzzy set is introduced,fuzzy clustering can effectively deal with the problem of fuzziness in classification,and has the significance and value of practical application.Fuzzy C-Means（FCM）clustering algorithm is one of the most commonly used algorithms in fuzzy clustering,because there is no need to know the prior knowledge of data set,FCM clustering algorithm is a kind of unsupervised learning way.However,FCM algorithm needs to pass clustering validity verification to judge the best partitioning results of data samples,so fuzzy clustering effectiveness evaluation method is an important research direction of FCM clustering algorithm.At present,the research on the Validity of Fuzzy Clustering is mainly divided into Fuzzy Clustering Validity Function,FCVF and Combined Fuzzy Clustering Validity Function（CFCVF）.However,any FCVF and CFCVF are composed of several sub-parts with different geometric meanings,namely,components（CP）.Therefore,based on the above two aspects,this thesis studies the componentized construction strategy of fuzzy clustering effectiveness and analyzes the research status and composition methods of different fuzzy clustering effectiveness methods.According to the characteristics of typical FCVF,six components are proposed,and based on these six components,a new FCVF and two FCM clustering effectiveness componentized design method is designed to solve the fuzzy clustering problem,as shown below:（1）Combining the fuzzy membership degree and the geometric structure of the data set,six clustering performance evaluation components are proposed that define the compactness,similarity,variation degree within the data set,as well as the separation degree and overlap degree between the data sets.At the same time,the theoretical basis of these 6 components is explained in detail,and finally these 6 components constitute a new FCVF（V_{W G}）.It can suppress the influence of noisy data well and accurately divide high-dimensional data and overlapping data.The comparison results of V_WGand traditional validity function on manual data sets and UCI data sets show that the clustering results of V_WG for different data sets are more accurate.（2）On the basis of V_WG,a new ratio componentized construction method of FCVF is proposed by strengthening the persuasiveness of FCVF constituted by components.The above 6 components types were arranged and combined continuously in the form of ratio in an objective way,and several newly constituted FCVF were verified on UCI data sets to analyze the influence brought by different components and select the best effectiveness function,which was compared with typical effectiveness function on more UCI data sets.The experimental results show that the validity function can obtain correct clustering results on UCI data sets,and can accurately partition high-dimensional data and overlapping data.（3）In order to increase the research depth of the validity function construction method of component-based fuzzy clustering,a new combination weight strategy was proposed by combining the subjective weight method and the coefficient of Variation weight method.Then,the six components defined are continuously combined in weighted form based on the combination weighting strategy,and several validity functions formed are verified by experiments on UCI data sets to select the one with the best classification effect.Finally,this function is compared with typical FCVF and commonly used CFCVF on more UCI data sets.The experimental results show that the validity function can obtain correct clustering results on UCI data sets,which can overcome the shortcomings of other clustering validity functions well,and provide a new solution for the study of fuzzy clustering validity.