Clustering Accuracies on Concepts of Nursing

Abstract

The purpose of this study is to integrate fuzzy clustering algorithm based on common Mahalanobis distance. Fuzzy clustering could distinguish characteristics of concept structures on nursing. Finally, some limitations and suggestions of this study are discussed. It shows that knowledge structures will be feasible for remedial instruction and help students get more chance to get professional certification on nurses. Based on the findings and results, combined with fuzzy clustering algorithm based on normalized Mahalanobis distance could be very feasible for cognition diagnosis in the future. The algorithm provided by Bezdek (1) is used in this study. Fuzzy c-mean algorithm based on Euclidean distance function converges to a local minimum of the objective function, which can only be used to detect spherical structural clusters. Gustafson-Kessel clustering algorithm and Gath-Geva clustering algorithm were developed to detect non-spherical structural clusters. Gustafson-Kessel clustering algorithm needs added constraint of fuzzy covariance matrix, whereas Gath-Geva 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. The fuzzy covariance matrices in the Mahalanobis distance can be directly derived by minimizing the objective function. II. LITERATURE REVIEW FCM can only work well for spherical shaped clusters. In the objective function the distances between data points to the centers of the clusters are calculated by Euclidian distances. To overcome the above drawback, we could try to extend the distance measure to Mahalanobis distance (MD). However, Krishnapuram and Kim (1999) pointed out that the Mahalanobis distance can not be used directly in clustering algorithm. Gustafson and Kessel (1979) extended the Euclidian distances of the standard FCM by employing an adaptive norm, in order to detect clusters of different geometrical shape without changing the clusters' sizes in one data set. Gath-Geva (GG) fuzzy clustering algorithm is an extension of Gustafson-Kessel (GK) fuzzy clustering algorithm, and also takes the size and density of clusters for classification. Hence, it has better behaviors for irregular features. For improving the limitation of GK algorithm and GG algorithm, we added a regulating factor of covariance matrix to each class in the objective function, and deleted the constraint of the determinant of covariance matrices. We can obtain the Fuzzy C-Means based on adaptive Mahalanobis distance (FCM-M) as following (2, 3). For improving the stability of the clustering results, we replace all of the covariance matrices with the same common covariance matrix in the objective function in the FCM-M algorithm, and then, an improved fuzzy clustering method, called the Fuzzy C-Means algorithm based on common Mahalanobis distance (FCM-CM) is proposed.