Graphic Representation With Knowledge Structure of Mathematics and Clustering With Supervised Algorithm

10.6148/IJITAS.201812_11(4).0003

Yuan-Horng Lin；Jeng-Ming Yih

Gustafson-Kessel algorithm ； Fuzzy c-means ； Interpretive structural modeling ； Supervised algorithm

International Journal of Intelligent Technologies and Applied Statistics

11卷4期（2018 / 12 / 01）

271 - 281

英文

Gustafson-Kessel (GK) clustering algorithm needs added constraint of fuzzy covariance matrix, Gath-Geva (GG) clustering algorithm can only be used for the data with multivariate Gaussian distribution. In GK-algorithm, modified Mahalanobis distance with preserved volume was used. However, the added fuzzy covariance matrices in their distance measure were not directly derived from the objective function. Improved normalized Mahalanobis clustering algorithm based on fuzzy c-means (FCM) by taking a new threshold value and a new convergent process is proposed. The experimental results of real data sets show that our proposed new algorithm has the best performance. Not only replacing the common covariance matrix with the correlation matrix in the objective function in the normalized Mahalanobis clustering algorithm The method of this study is to provide an integrated method of fuzzy theory basis for individualized concept structure analysis. This method integrates fuzzy logic model of perception (FLMP) and interpretive structural modeling (ISM). The combined algorithm could analyze individualized concepts structure based on the comparisons with concept structure of expert. This integrated method should be feasible to represent concept structures. Besides, fuzzy clustering technique is adopted to provide features of concept structures based on homogeneity of sample. Applying the method of the cluster of FCM, we could distinguish characteristics of six groups. We analyzed the whole data and discuss the relationship between knowledge structures of the sample. The result and discoveries from the research can offer pupils' misconception of learning basic mathematics with reference of diagnosis.