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Purpose: Fuzzy algorithms of Gath-Geva (GG) and Gustafson-Kessel (GK) based on Mahalanobis distance can improve those limitations of spherical structural clusters, but GG algorithm can only be used for the data with multivariate normal distribution. GK algorithm is limited by that it must know the distribution of data. An improved supervised clustering algorithm based on fuzzy c-means (FCM) has been proposed. Methodology: We take a new threshold value and a new convergent algorithm to improve those limitations of GG and GK algorithms, delete the constraint of the determinants of covariance matrices in the GK algorithm, and replace the covariance matrix with the correlation matrix which exists in the objective function. Findings: The experimental results of real data sets show that our proposed new algorithm can promote clustering accuracies and get better performance. Value: The popular FCM 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. Adding fuzzy covariance matrices in their distance measure was not directly derived from the objective function. But it is not stable enough when some of its covariance matrices are not equal. Hence, different initializations may lead to different results. [ABSTRACT FROM AUTHOR]

Nowadays, people pay increasing attention to health, and the integrity of medical records has been put into focus. Recently, medical data imputation has become a very active field because medical data usually have missing values. Many imputation methods have been proposed, but many model-based imputation methods such as expectation–maximization and regression-based imputation based on the variables data have a multivariate normal distribution, which assumption can lead to biased results. Sometimes, this becomes a bottleneck, such as computationally more complex than model-free methods. Furthermore, directly removing instances with missing values has several problems, and it is possible to lose the important data, produce ineffective research samples, and cause research deviations. Therefore, this study proposes a novel clustering-based purity and distance imputation method to improve the handling of missing values. In the experiment, we collected eight different medical datasets to compare the proposed imputation methods with the listed imputation methods with regard to the results of different situations. In imputation measures, the area under the curve (AUC) is used to evaluate the performance of the imbalanced class datasets in MAR and MCAR experiments, and accuracy is applied to measure its performance of the balanced class in MNAR experiment. Finally, the root-mean-square error (RMSE) is also used to compare the proposed and the listing imputation methods. In addition, this study utilized the elbow method and the average silhouette method to find the optimal number of clusters for all datasets. Results showed that the proposed imputation method could improve imputation performance in the accuracy, AUC, and RMSE of different missing degrees and missing types. [ABSTRACT FROM AUTHOR]