Two new algorithms for fuzzyclustering are presented. convergence of the proposed algorithms is proved. An empirical study of their convergence behavior is discussed. The performance of the new algorithms is compared...
详细信息
Two new algorithms for fuzzyclustering are presented. convergence of the proposed algorithms is proved. An empirical study of their convergence behavior is discussed. The performance of the new algorithms is compared with the fuzzy c-means algorithm by testing them on four published data sets. Experimental results show that the new algorithms are faster and lead to computational savings.
In this paper a new algorithm for fuzzyclustering is presented. The proposed algorithm utilizes the idea of relaxation. convergence of the proposed algorithm is proved and limits on the relaxation parameter are deriv...
详细信息
In this paper a new algorithm for fuzzyclustering is presented. The proposed algorithm utilizes the idea of relaxation. convergence of the proposed algorithm is proved and limits on the relaxation parameter are derived. Stopping criteria and resulting convergence behaviour of the algorithms are discussed. The performance of the new algorithm is compared to the fuzzy c-means algorithm by testing both on three published data sets. Theoretical and empirical results reported in this paper show that the new algorithm is more efficient and leads to significant computational savings.
In this paper, the problem of achieving "semi-fuzzy" or "soft" clustering of multidimensional data is discussed. A technique based on thresholding the results of the fuzzy c-means algorithm is intr...
详细信息
In this paper, the problem of achieving "semi-fuzzy" or "soft" clustering of multidimensional data is discussed. A technique based on thresholding the results of the fuzzy c-means algorithm is introduced. The proposed approach is analysed and contrasted with the soft clustering method (see S. Z. Selim and M. A. Ismail, Pattern Recognition 17, 559-568) showing the merits of the new method. Separation of clusters in the semi-fuzzyclustering context is introduced and the use of the proposed technique to measure the degree of separation is explained.
The fuzzyclustering (Fc) problem is a non-convex mathematical program which usually possesses several local minima. The global minimum solution of the problem is found using a simulated annealing-based algorithm. Som...
详细信息
The fuzzyclustering (Fc) problem is a non-convex mathematical program which usually possesses several local minima. The global minimum solution of the problem is found using a simulated annealing-based algorithm. Some preliminary computational experiments are reported and the solution is compared with that generated by the fuzzy c-means algorithm.
We report a study of the efficiency of 4 classifiers (the K-nearest-neighbor and single-nearest-prototype algorithms, each as parametrized by both fuzzyc-means and fuzzycovariance clustering) in the detection of ven...
详细信息
We report a study of the efficiency of 4 classifiers (the K-nearest-neighbor and single-nearest-prototype algorithms, each as parametrized by both fuzzyc-means and fuzzycovariance clustering) in the detection of ventricular arrhythmias in EcG traces characterized by 4 features derived from 7 spectral parameters. Principal components analysis was used in conjunction with a cardiologist's deterministicclassification of 90 EcG traces to fix the number of trace classes to 5 (ventricular fibrillation/flutter, sinus rhythm, ventricular rhythms with aberrant complexes and 2 classes of artefact). Forty of the 90 traces were then defined as a test set;5 different learning sets (numbering 25, 30, 35, 40 and 45 traces) were randomly selected from the remaining 50 traces;each learning set was used to parametrize both the classification algorithms using both fuzzyclustering algorithms and the parametrized classification algorithms were then applied to the test set. Optimal K for K-nearest-neighbor algorithms and optimal cluster volumes for fuzzycovariance algorithms were sought by trial error to minimize classification differences with respect to the cardiologist's classification. fuzzycovariance clustering afforded significantly better perception of cluster structure than the fuzzy c-means algorithm, and the classifiers performed correspondingly with an overall empirical error ratio of just 0.10 for the K-nearest-neighbor algorithm parametrized by fuzzycovariance.
We present two new fuzzycluster validity functionals (minimum and mean hard tendencies), based on the analysis of the hard tendency of the fuzzyclassification generated by the fuzzyc -meansalgorithm. We have used ...
详细信息
We present two new fuzzycluster validity functionals (minimum and mean hard tendencies), based on the analysis of the hard tendency of the fuzzyclassification generated by the fuzzyc -meansalgorithm. We have used the bootstrap technique, to avoid the possible influence of local minimums, obtained by the fuzzyc -meansalgorithm.
The hard and fuzzy c-means algorithms are widely used, effective tools for the problem of clustering n objects into (hard or fuzzy) groups of similar individuals when the data is available as object data, consisting o...
详细信息
The hard and fuzzy c-means algorithms are widely used, effective tools for the problem of clustering n objects into (hard or fuzzy) groups of similar individuals when the data is available as object data, consisting of a set of n feature vectors in RP. However, object data algorithms are not directly applicable when the n objects are implicitly described in terms of relational data, which consists of a set of n2 measurements of relations between each of the pairs of objects. New relational versions of the hard and fuzzy c-means algorithms are presented here for the case when the relational data can reasonably be viewed as some measure of distance. Some convergence properties of the algorithms are given along with a numerical example.
One of the main techniques embodied in many pattern recognition systems is cluster analysis — the identification of substructure in unlabeled data sets. The fuzzy c-means algorithms (FcM) have often been used to solv...
详细信息
One of the main techniques embodied in many pattern recognition systems is cluster analysis — the identification of substructure in unlabeled data sets. The fuzzy c-means algorithms (FcM) have often been used to solve certain types of clustering problems. During the last two years several new local results concerning both numerical and stochasticconvergence of FcM have been found. Numerical results describe how the algorithms behave when evaluated as optimization algorithms for finding minima of the corresponding family of fuzzyc-means functionals. Stochastic properties refer to the accuracy of minima of FcM functionals as approximations to parameters of statistical populations which are sometimes assumed to be associated with the data. The purpose of this paper is to collect the main global and local, numerical and stochastic, convergence results for FcM in a brief and unified way.
In this paper, the solutions produced by the fuzzy c-means algorithm for a general class of problems are examined and a method to test for the local optimality of such solutions is established. An equivalent mathemati...
详细信息
In this paper, the solutions produced by the fuzzy c-means algorithm for a general class of problems are examined and a method to test for the local optimality of such solutions is established. An equivalent mathematical program is defined for the c-means problem utilizing a generalized norm, then the properties of the resulting optimization problem are investigated. It is shown that the gradient of the resulting objective function at the solution produced by the c-meansalgorithm in this case takes a special structure which can be used in terminating the algorithm. Moreover, the local optimality of the solution obtained is checked utilizing the Hessian of the criterion function. The solution is a local minimum point if the Hessian matrix at this point is positive semidefinite. Simple rules are proposed to help in checking the definiteness of the matrix.
The convergence of the fuzzy ISODATA clustering algorithm was proved by Bezdek [3]. Two sets of conditions were derived and it was conjectured that they are necessary and sufficient for a local minimum point. In this ...
详细信息
The convergence of the fuzzy ISODATA clustering algorithm was proved by Bezdek [3]. Two sets of conditions were derived and it was conjectured that they are necessary and sufficient for a local minimum point. In this paper, we address this conjecture and explore the properties of the underlying optimization problem. The notions of reduced objective function and improving and feasible directions are used to examine this conjecture. Finally, based on the derived properties of the problem, a new stopping criterion for the fuzzy ISODATA algorithm is proposed.
暂无评论