On The Regularization Method Based Fuzzy C-Means Algorithm

With the rapid development of the computer technology, people may have to deal with more and more information every day, which even can be described as mass information. Cluster analysis technique which is a very useful tool in processing information and one of the most important methods in data mining, has become a hot issue in recent years. In this thesis, the study is focused on the fuzzy c-means clustering algorithm which is the most widely used at present. The majority of our contributions can be summarized in the following three aspects:1. Considering the classic fuzzy c-means algorithm is sensitive to the initial cluster centers, and it also has a shortcoming of poor anti-interference ability, we use Tikhonov regularization, which is a classical method in solving the ill-posed problems, to establish a new model by adding a regularizing functional in the objective function of the fuzzy c-means algorithm. Two algorithms, named as REGFCM1 and REGFCM2 are obtained from this model. Experimental results show that REGFCM1 algorithm improves the anti-noise ability and clustering accuracy, and REGFCM2 algorithm has faster convergence speed.2. A new measure is proposed, which can give the information that whether the fuzzy partitions have been divided clearly. Furthermore, a new cluster validity index is presented, which combines the compactness measure and separation measure of fuzzy clustering. The index function has been optimized and has extensive suitability. Experimental results indicate that this new index function can give the optimal number of clusters for fuzzy partitions even under the condition of overlapping clusters and including isolated points clusters.3. At last, we combined the REGFCM1 algorithm and REGFCM2 algorithm with the new validity index and used them to solve Takagi-Sugeno model based systems identification problems. Two algorithms are stated for this type of problems. Illustrative examples show that the presented algorithms not only have higher identification precision but the target system can be reconstructed with less fuzzy rules as well.