Research Of New Fuzzy Clustering Algorithms Based On Objective Function And Its Applications

Cluster analysis is an important branch of unsupervised classification in statistical pattern recognition area. It has grown rapidly in the nearly three decades of research and application. Because of its more accurate description of the uncertainty relation between models, fuzzy clustering algorithm has become popular research field of cluster analysis. Based on objective function, fuzzy clustering algorithm uses a constrained optimization mathematical problem to represent clustering problem, and then determines the division of data sets and fuzzy clustering results by solving the optimization problem. Fuzzy clustering algorithm has been widely applied in image processing, pattern recognition and computer vision.Fuzzy c-means clustering and possibilistic c-means clustering are two typical fuzzy clustering algorithms which are based on objective function. The dissertation overviews the research status of two algorithms, The dissertation studies on four research areas:Fuzzy clustering for balanced/imbalanced dataset, the generalized multi-fuzzy indicators, the generalized PSO algorithm fuzzy indicator and adaptive optimization fuzzy indicator.The main research results achieved in this dissertation are given as follows:1. For classification problem of balanced/imbalanced data set, the dissertation analyses the difference between supervised classification and unsupervised classification about imbalanced dataset. It illustrates the basic properties that the clustering analysis for balanced or unbalanced dataset classification should meet. The dissertation indicates the causes of fuzzy clustering imbalance is due to the missing of sample size, and proposes equalization concept, basic principle and method for fuzzy clustering algorithm. Clustering algorithm can implement equalization by importing the sample size information in the objective function. Based on the principle of equalization, the dissertation equalizes the FCM and PCM algorithm, and obtains the balanced FCM and PCM algorithm. Due to the complexity of the objective function, We cannot use gradient information to obtain iterative formula of fuzzy membership. The dissertation introduces particle swarm optimization algorithm to estimate fuzzy membership and then implements clustering algorithm classification for balanced or unbalanced data sets.2. The dissertation studies the generalized multi-fuzzy indicators of clustering algorithm. It analyzes the basic principle of convergence about the FCM clustering algorithm and illustrates algorithm construction of FCM algorithm that chooses the minimum point iteration for the objective function monotonically decreasing. The study reveals the relationship of multi-fuzzy indicators and original single indicators,that is, the relationship of the non-steepest iterative descent path and the steepest descent iterative path. Based on this research, we propose the concepts of generalized fuzzy indicator for clustering algorithm. We implement generalized fuzzy indicators to FCM and PCM algorithm. We make the original clustering algorithm as a special case and extend the range of fuzzy indicators and obtain a variety of iterative path for fuzzy algorithms. It optimizes clustering results and iterative path for clustering algorithm.3. After studying PSO algorithm-based fuzzy indicator, the dissertation discusses the value range of fuzzy indicators. Subject to the FCM Objective function’s requirements that second-order Hessian matrix about fuzzy membership must be positive definite, fuzzy indicator m in FCM algorithm must be greater than1. After through theoretical analysis we found that fuzzy indicator m may relax the value of m constraints greater than0if we use particle swarm algorithm to estimate the fuzzy membership degree. Based on this assumption, the dissertation proposes fuzzy indicators with generalized particle swarm to generalize FCM and PCM algorithms. The method use particle swarm algorithm to find the optimal solution in fuzzy membership space. It relaxes requirement of gradient method that fuzzy indicator must be greater than1and further expands the value range of fuzzy indicators in clustering algorithm.4. Self-adaptive optimization of fuzzy index is studied. The dissertation first summarizes the traditional methods for determining fuzzy control indicator and analyzes their classification, basic principle and shortcoming. It discusses the relationship of fuzzy indicator, fuzzy membership and cluster center. It illustrates that the fuzzy index values should be interrelated with iterative optimization of fuzzy membership and cluster centers. The study points out that fuzzy indicator value should meet the dynamic, self-adaptive and exist extremum for objective function. The dissertation proposes the method of particle swarm algorithm for fuzzy indicator’s self-adaptive optimization. The objective function of fuzzy algorithms existing extremum through transforming objective function of FCM and PCM algorithms. The method utilizes particle swarm optimization to estimate fuzzy indicator and fuzzy membership, and implements self-adaptive optimization for fuzzy indicator, fuzzy membership and clustering center.