A note on the ICS algorithm with corrections and theoretical analysis

In [1], Ozdemir and Akarun proposed an intercluster separation (ICS) fuzzy clustering algorithm. The ICS algorithm is useful in combined quantization and dithering. However, there are two errors in the update equations for the ICS algorithm. This correspondence first points out these errors and gives their corrections. Since the parameters m, c, and gamma are important factors in the performance of ICS, we also conduct a theoretical analysis of these ICS parameters. In order to analyze the parameters in ICS, we devise a theorem for the calculation of the Hessian matrix from the ICS objective function. We establish the fixed-point property of ICS based on the decomposition of the Hessian matrix and then analyze the effect of the parameters. Finally, we propose a numerical approach in choosing the appropriate parameters m and gamma for ICS. These experimental results give a better numerical perspective on the effect of parameters in ICS and have conclusions consistent with our theoretical analysis.