Approaches To Knowledge Discovery And Its Application Via Axiomatic Fuzzy Sets And Support Vector Machines

Axiomatic Fuzzy Sets (AFS) theory is a new method to deal with fuzzy information, which provides an effective tool to concert the information in the training examples and databases into the membership functions and their fuzzy logic operations. Support Vec-tor Machine(SVM) is a new supervised pattern recognition method based on Statistical Learning Theory. It has advantages such as high classification accuracies, few parameters, global optimums and strong generalization performances:it becomes a new research area in the field of machine learning research. This thesis focuses on some popular problems which are often encountered in knowledge discovery and representation based on AFS and SVM theory. Main topics include:1. In the framework of AFS theory, this paper firstly proposes a fuzzy feature selection algorithm and a principle concept selection algorithm in unsupervised learning, which can extract the important features and simple concepts for knowledge discovery. Secondly, it presents a concept categorization approach which is a new and important technique in the artificial intelligence area. It can cluster the simple concepts which have the great correlations to one class. Finally, it gives an algorithm for finding the sample characteristic description. It can extract the salient characteristic of sample, such description is very simple and it is more effective and practical than the complex description in pattern recognition issue.2. By an exhaustive study of the clustering algorithm proposed by X. Liu et al. in IEEE Transactions on Systems, Man, Cybernetics,2005 and its effectiveness on real datasets, some drawbacks are discovered. For these drawbacks, firstly, this paper proposes an algorithm to control the rough extent of fuzzy descriptions of objects:secondly, adds a refinement step, i.e.. the clusters can be further refined by the fuzzy description of each cluster; finally, improves the original AFS cluster validity index. The well known real-world Iris data set is used to illustrate the effectiveness of the new clustering algorithm.3. In order to evaluate the effectiveness of the feature selection, the principle concept selection, the concept categorization and the characteristic description algorithm proposed in the framework of AFS theory, a new fuzzy clustering algorithm based on AFS theory is proposed via these new techniques. The fuzzy description of each cluster obtained from the proposed algorithm is simply a conjunction of some simple concepts. Not only the membership degree of a sample belonging to its cluster is large, but also the membership degrees of this sample belonging to other clusters are as small as possible, even close to 0. Thus, the boundary among the clusters is more clearer with such fuzzy descriptions. Such description is very simple, and easily understandable for the users since each class corresponds to much fewer rules. Several benchmark data sets are used for this study. Clustering accuracies are comparable with or superior to the conventional algorithms such as FCM,κ-means. The practical experience has further indicated that our clustering algorithm is not sensitive to parameters if the reasonable parameters are selected.4. A new density-based clustering algorithm via using the Mahalanobis metric is proposed. There are two novelties for the proposed algorithm:One is to adopt the Ma-halanobis metric as distance measurement and the other is its effective merging approach for leaders and followers. In order to overcome the unique density issue in DBSCAN, we propose an approach to merge the sub-clusters by using the local sub-cluster density information. Extensive experiments on some synthetic datasets show the validity of the proposed algorithm. Further the segmentation results on some typical images by using the proposed algorithm and DBSCAN are presented and it is shown that the proposed algorithm can produce much better visual results than DBSCAN.5. A classification method that is based on easily interpretable fuzzy rules is pro-posed, it fully capitalizes on the two key technologies, namely pruning the outliers in the training data by SVMs; finding a fuzzy set with definite linguistic interpretation to describe each class based on AFS theory. Compared with other fuzzy rule-based methods, the proposed models are usually more compact and easily understandable for the users since each class is described by much fewer rules. The proposed method also comes with two other advantages, namely, each rule obtained from the proposed algorithm is simply a conjunction of some linguistic terms, there are no parameters that are required to be tuned. The results show that the fuzzy rule-based classifier presented in this paper, of-fers a compact, understandable and accurate classification scheme. A balance is achieved between the interpretability and the accuracy.