• International Journal of Contents
• /
• v.11 no.2
• /
• pp.57-62
• /
• 2015

Relative entropy is a divergence measure between two probability density functions of a random variable. Assuming that the random variable has only two alphabets, the relative entropy becomes a cross-entropy error function that can accelerate training convergence of multi-layer perceptron neural networks. Also, the n-th order extension of cross-entropy (nCE) error function exhibits an improved performance in viewpoints of learning convergence and generalization capability. In this paper, we derive a new divergence measure between two probability density functions from the nCE error function. And the new divergence measure is compared with the relative entropy through the use of three-dimensional plots.

• International Journal of Contents
• /
• v.8 no.4
• /
• pp.30-35
• /
• 2012

Error surfaces provide us with very important information for training of feed-forward neural networks (FNNs). In this paper, we draw the contour plots of various error or objective functions for training of FNNs. Firstly, when applying FNNs to classifications, the weakness of mean-squared error is explained with the viewpoint of error contour plot. And the classification figure of merit, mean log-square error, cross-entropy error, and n-th order extension of cross-entropy error objective functions are considered for the contour plots. Also, the recently proposed target node method is explained with the viewpoint of contour plot. Based on the contour plots, we can explain characteristics of various error or objective functions when training of FNNs proceeds.

• International Journal of Contents
• /
• v.10 no.1
• /
• pp.23-28
• /
• 2014

When developing a classifier using various objective functions, it is important to compare the performances of the classifiers. Although there are statistical analyses of objective functions for classifiers, simulation results can provide us with direct comparison results and in this case, a comparison criterion is considerably critical. A Receiver Operating Characteristics (ROC) graph is a simulation technique for comparing classifiers and selecting a better one based on a performance. In this paper, we adopt the ROC graph to compare classifiers trained by mean-squared error, cross-entropy error, classification figure of merit, and the n-th order extension of cross-entropy error functions. After the training of feed-forward neural networks using the CEDAR database, the ROC graphs are plotted to help us identify which objective function is better.

• International Journal of Contents
• /
• v.7 no.3
• /
• pp.1-5
• /
• 2011

It has been an interesting challenge to find a good classifier for imbalanced data, since it is pervasive but a difficult problem to solve. However, classifiers developed with the assumption of well-balanced class distributions show poor classification performance for the imbalanced data. Among many approaches to the imbalanced data problems, the algorithmic level approach is attractive because it can be applied to the other approaches such as data level or ensemble approaches. Especially, the error back-propagation algorithm using the target node method, which can change the amount of weight-updating with regards to the target node of each class, attains good performances in the imbalanced data problems. In this paper, we analyze the relationship between two optimal outputs of neural network classifier trained with the target node method. Also, the optimal relationship is compared with those of the other error function methods such as mean-squared error and the n-th order extension of cross-entropy error. The analyses are verified through simulations on a thyroid data set.