This paper presents a nonlinear supervised feature extraction algorithm that combines Fisher's criterion function with a preliminary perceptron-like nonlinear projection of vectors in pattern space. Its main motivation is to combine the approximation properties of multilayer perceptrons (MLP's) with the target free nature of Fisher's classical discriminant analysis. In fact, although MLP's provide good classifiers for many problems, there may be some situations, such as unequal class sizes with a high degree of pattern mixing among them, that may make difficult the construction of good MLP classifiers. In these instances, the features extracted by our procedure could be more effective. After the description of its construction and the analysis of its complexity, we will illustrate its use over a synthetic problem with the above characteristics.

This letter analyzes the performance of the neural network training method known as optimization layer by layer. We show, from theoretical considerations, that the amount of work required with OLL-Learning scales as the third power of the network size, compared with the square of the network size for commonly used conjugate gradient training algorithms. This theoretical estimate is confirmed through a practical example. Thus, although OLL is shown to function very well for small neural networks (less than about 500 weights per layer), it is slower than CG for large neural networks. Second, we show that OLL does not always improve on the accuracy that can be obtained with CG. It seems that the final accuracy that can be obtained depends strongly on the initial network weights.

This paper presents an online system for fraud detection of credit card operations based on a neural classifier. Since it is installed in a transactional hub for operation distribution, and not on a card-issuing institution, it acts solely on the information of the operation to be rated and of its immediate previous history, and not on historic databases of past cardholder activities. Among the main characteristics of credit card traffic are the great imbalance between proper and fraudulent operations, and a great degree of mixing between both. To ensure proper model construction, a nonlinear version of Fisher's discriminant analysis, which adequately separates a good proportion of fraudulent operations away from other closer to normal traffic, has been used. The system is fully operational and currently handles more than 12 million operations per year with very satisfactory results.