How Magnification of the Root-Mean-Square Deviation (RMSD) Value Affects the Convergence Speed of Hopfield Neural Network Classifier

The Root Mean Square-Deviation (RMSD) or Root Mean Square Error (RMSE) is the frequently used measure of the difference between values predicted by a model or an estimator and the values actually observed from that which is being modelled or estimated. In this paper, we show that the magnification of the RMSE, when used with the classifier Hopfield Neural Network (HNN), may help the network to converge earlier to the same optima reached using the simple RMSE. The segmentation problem of liver pathological images is formulated in energy function as a magnified sum of all neurons’ deviations from their actual clusters, and HNN iterates with respect to the winner-takes-all rule in order to minimize the energy function to a local optimum close to the global one. Twenty liver color images were used in this study. Their segmentation results with their corresponding quantitative analysis show that our approach makes the results more reliable for use as input data to a computer aided diagnosis of liver cancer. Key-Words: Hopfield Neural Network, Optimization, Mean-Square-Error, Magnification, Segmentation, pathological liver color image