Publications

Researchers in the fields of neural networks, statistics, machine learning, and artificial intelligence have followed three basic approaches to developing new pattern classifiers. Probability Density Function (PDF) classifiers include Gaussian and Gaussian Mixture classifiers which estimate distributions or densities of input features separately for each class. Posterior probability classifiers include multilayer perceptron neural networks with sigmoid nonlinearities and radial basis function networks. These classifiers estimate minimum-error Bayesian a posteriori probabilities (hereafter referred to as posterior probabilities) simultaneously for all classes. Boundary forming classifiers include hard-limiting single-layer perceptrons, hypersphere classifiers, and nearest neighbor classifiers. These classifiers have binary indicator outputs which form decision regions that specify the class of any input pattern. Posterior probability and boundary-forming classifiers are trained using discriminant training. All training data is used simultaneously to estimate Bayesian posterior probabilities or minimize overall classification error rates. PDF classifiers are trained using maximum likelihood approaches which individually model class distributions without regard to overall classification performance. Analytic results are presented which demonstrate that many neural network classifiers can accurately estimate posterior probabilities and that these neural network classifiers can sometimes provide lower error rates than PDF classifiers using the same number of trainable parameters. Experiments also demonstrate how interpretation of network outputs as posterior probabilities makes it possible to estimate the confidence of a classification decision, compensate for differences in class prior probabilities between test and training data, and combine outputs of multiple classifiers over time for speech recognition.

Pattern-classification and clustering algorithms are key components of modern information processing systems used to perform tasks such as speech and image recognition, printed-character recognition, medical diagnosis, fault detection, process control, and financial decision making. To simplify the task of applying these types of algorithms in new application areas, we have developed LNKnet-a software package that provides access to more than 20 pattern-classification, clustering, and feature-selection algorithms. Included are the most important algorithms from the fields of neural networks, statistics, machine learning, and artificial intelligence. The algorithms can be trained and tested on separate data or tested with automatic cross-validation. LNKnet runs under the UNM operating system and access to the different algorithms is provided through a graphical point-and-click user interface. Graphical outputs include two-dimensional (2-D) scatter and decision-region plots and 1-D plots of data histograms, classifier outputs, and error rates during training. Parameters of trained classifiers are stored in files from which the parameters can be translated into source-code subroutines (written in the C programming language) that can then be embedded in a user application program. Lincoln Laboratory and other research laboratories have used LNKnet successfully for many diverse applications.

Many neural network classifiers provide outputs which estimate Bayesian a posteriori probabilities. When the estimation is accurate, network outputs can be treated as probabilities and sum to one. Simple proofs show that Bayesian probabilities are estimated when desired network outputs are 1 of M (one output unity, all others zero) and a squared-error or mss-entropy cost function is used. Results of Monte Carlo simulations performed using multilayer perceptron (MLP) networks trained with backpropagation, radial basis function (RBD networks, and high-order polynomial networks graphically demonstrate that network outputs provide good estimates of Bayesian probabilities. Estimation accuracy depends on network complexity, the amount of training data, and the degree to which training data reflect true likelihood distributions and a priori class probabilities. Interpretation of network outputs as Bayesian probabilities allows outputs from multiple networks to be combined for higher level decision making, simplifies creation of rejection thresholds, makes it possible to compensate for differences between pattern class probabilities in training and test data, allows outputs to be used to minimize alternative risk functions, and suggests alternative measures of network performance.

Artificial neural net models have been studied for many years in the hope of achieving human-like performance in the fields of speech and image recognition. These models are composed of many nonlinear computational elements operating in parallel and arranged in patterns reminiscent of biological neural nets. Computational elements or nodes are connected via weights that are typically adapted during use to improve performance. There has been a recent resurgence in the field of artificial neural nets caused by new net topologies and algorithms, analog VLSI implementation techniques, and the belief that massive parallelism is essential for high performance speech and image recognition. This paper provides an introduction to the field of artificial neural nets by reviewing six important neural net models that can be used for pattern classification. These nets are highly parallel building blocks that illustrate neural net components and design principles and can be used to construct more complex systems. In addition to describing these nets, a major emphasis is placed on exploring how some existing classification and clustering algorithms can be performed using simple neuron-like components. Single-layer nets can implement algorithms required by Gaussian maximum-likelihood classifiers and optimum minimum-error classifiers for binary patterns corrupted by noise. More generally, the decision regions required by any classification algorithm can be generated in a straightforward manner by three-layer feed-forward nets.