Novel Two-Dimensional Visualization Approaches for Multivariate Centroids of Clustering Algorithms

The dimensionality reduction and visualization problems associated with multivariate centroids obtained by clustering algorithms are addressed in this paper. Two approaches are used in the literature for the solution of such problems, specifically, the self-organizing map (SOM) approach and mapping selected two features manually (MS2Fs). In addition, principle component analysis (PCA) was evaluated as a component for solving this problem on supervised datasets. Each of these traditional approaches has drawbacks: if SOM runs with a small map size, all centroids are located contiguously rather than at their original distances according to the high-dimensional structure; MS2Fs is not an efficient method because it does not take features outside of the method into account, and lastly, PCA is a supervised method and loses the most valuable feature. In this study, five novel hybrid approaches were proposed to eliminate these drawbacks by using the quantum genetic algorithm (QGA) method and four feature selection methods, Pearson’s correlation, gain ratio, information gain, and relief methods. Experimental results demonstrate that, for 14 datasets of different sizes, the prediction accuracy of the proposed weighted clustering approaches is higher than the traditional K-means++ clustering approach. Furthermore, the proposed approach combined with K-means++ and QGA shows the most efficient placements of the centroids on a two-dimensional map for all the test datasets.