Research And Application Of Fuzzy Clustering Algorithm

Because of the introduction of fuzzy set theory, fuzzy clustering can deal with theuncertainty and fuzziness of things and reflect the real world more objectively. So it becomesan important branch of pattern recognition and has been widely used in many fields, such asdata mining, image processing, etc. At present, the technology of fuzzy clustering has alreadyformed large system. Fuzzy C-Means clustering algorithm (FCM), which is based on theobjective function, is a kind of fuzzy clustering technology and more wide in the practicalapplication. Although FCM algorithm has the advantages of simpleness in design, fast andhigh efficiency, easy to implementation, deep foundation of mathematics, there are still manyweaknesses and shortages, for example, it is unable to automatically determine the number ofclusters, clustering results is influenced by the initial clustering centers, it is sensitive to theisolated points and noises, it is easy to trap in local optimal solution, etc.We study and research deeply FCM algorithm and present the corresponding solutionsrespectively according to two drawbacks that FCM algorithm couldn’t determine the numberof clusters in advance and is sensitive to the initial clustering centers. In this paper, the mainworks are as follows:(1) The problem to determinate the optimal clustering number often be converted into theproblem of clustering validity. In the view of the problem that FCM algorithm automaticallydetermines the optimal clustering number, we put forward a new fuzzy clustering validityindex named COD. Firstly, it has redefined the compactness measure and reduces the amountof calculation; Secondly, it introduces the definition to measure that fuzzy partition is clear ornot; Finally, the index consists of three terms: the compactness, the degree of overlapping, andfuzzy partition definition. The experimental results show that the COD index can effectivelyidentify the optimal clustering number of datasets, especially in the case with well-separatedclusters including subclusters that comprise well-separated or overlapping sub-subclusters.(2) In view of the problem that FCM algorithm is sensitive to the initial clustering center,the proved algorithm is put forward.The algorithm introduces the particle swarm optimizationalgorithm (PSO), by the advantage of the strong global optimization ability and the fastconvergence speed to find the initial clustering center for FCM algorithm, and design thefitness function between compactness and separation factors. The experimental results showthat the improved algorithm, to a certain extent, solves the problems that FCM algorithm issensitive to the initial fuzzy partition matrix and easy to fall into local optimal solution.(3) According to the COD index and the improved FCM algorithm, we propose anautomatic segmentation algorithm based on gray image. The algorithm firstly use COD indexfor effectiveness evaluation to obtain the best image segmentation number, secondly combinethe best image segmentation number with the improved FCM algorithm, and lastly is appliedto image segmentation. The experimental results not only verify the effectiveness of theproposed algorithm, but also have achieved better segmentation effect.