ESTIMATION OF POSTERIOR PROBABILITIES WITH NEURAL NETWORKS : APPLICATION TO MICROCALCIFICATION DETECTION IN BREAST CANCER DIAGNOSIS

Neural networks (NNs) are customarily used as classifiers aimed at minimizing classification error rates. However, it is known that the NN architectures that compute soft decisions can be used to estimate posterior class probabilities; sometimes, it could be useful to implement general decision rules other than the maximum a posteriori (MAP) decision criterion. In addition, probabilities provide a confidence measure of the classifier decisions, a fact that is essential in applications in which a high risk is involved. This chapter is devoted to the general problem of estimating posterior class probabilities using NNs. Two components of the estimation problem are discussed: Model selection, on one side, and parameter learning, on the other. The analysis assumes an NN model called the generalized softmax perceptron (GSP), although most of the discussion can be easily extended to other schemes, such as the hierarchical mixture of experts (HME) [1], which has inspired part of our work, or even the well-known multilayer perceptron. The use of posterior probability estimates is applied in this chapter to a medical decision support system; the testbed used is the detection of microcalcifications (MCCs) in mammograms, which is a key step in breast cancer early diagnosis. The chapter is organized as follows: Section 3.2 discusses the estimation of posterior class probabilities with NNs, with emphasis in a medical application; Section 3.3 discusses learning and model selection algorithms for the GSP networks; Section 3.4 proposes a system for MCC detection based on the GSP; Section 3.5 shows some simulation results on detection performance using a mammogram database; and Section 3.6 provides some conclusions and future trends.