A Graphical method based on the Xie-Beni Validity index to improve the ‘Possibilistic C-Means with Repulsion’ Algorithm

The Possibilistic C-Means clustering algorithm, in its original form, is not very suitable for clustering due to the undesirable tendency to create coincident clusters and to converge to a “worthless” partitions in the case of poor initializations, but it provides robustness to noise and intuitive interpretation of the membership values. Recently, an extension of the PCM has been presented by Timm et al., by introducing a repulsion term and showed a satisfactory performance when a proper value for the weighting factor was used. Our study has shown a correspondence between the Xie-Beni validity function and the range of the weighting factor of , and furthermore a practical graphical method and algorithm to find the suboptimal is presented. The results for the ‘PCM with repulsion’, compared to other possibilistic and probabilistic algorithms, showed quantitative superiority of the ‘PCM with repulsion’ over other methods.