We present a new method that we call generalized discriminant analysis (GDA) to deal with nonlinear discriminant analysis using kernel function operator. The underlying theory is close to the support vector machines (SVM) insofar as the GDA method provides a mapping of the input vectors into high-dimensional feature space. In the transformed space, linear properties make it easy to extend and generalize the classical linear discriminant analysis (LDA) to nonlinear discriminant analysis. The formulation is expressed as an eigenvalue problem resolution. Using a different kernel, one can cover a wide class of nonlinearities. For both simulated data and alternate kernels, we give classification results, as well as the shape of the decision function. The results are confirmed using real data to perform seed classification.

/pdf/generalized-discriminant-analysis-using-a-kernel-approach-2p31nwoukr.pdf

Generalized Discriminant Analysis Using a Kernel Approach

Three networks are compared for low false alarm stock trend predictions. Short-term trends, particularly attractive for neural network analysis, can be used profitably in scenarios such as option trading, but only with significant risk. Therefore, we focus on limiting false alarms, which improves the risk/reward ratio by preventing losses. To predict stock trends, we exploit time delay, recurrent, and probabilistic neural networks (TDNN, RNN, and PNN, respectively), utilizing conjugate gradient and multistream extended Kalman filter training for TDNN and RNN. We also discuss different predictability analysis techniques and perform an analysis of predictability based on a history of daily closing price. Our results indicate that all the networks are feasible, the primary preference being one of convenience.

/pdf/comparative-study-of-stock-trend-prediction-using-time-delay-43t3st4s0x.pdf

Comparative study of stock trend prediction using time delay, recurrent and probabilistic neural networks

Network structure determination is an important issue in pattern classification based on a probabilistic neural network. In this study, a supervised network structure determination algorithm is proposed. The proposed algorithm consists of two parts and runs in an iterative way. The first part identifies an appropriate smoothing parameter using a genetic algorithm, while the second part determines suitable pattern layer neurons using a forward regression orthogonal algorithm. The proposed algorithm is capable of offering a fairly small network structure with satisfactory classification accuracy.

/pdf/probabilistic-neural-network-structure-determination-for-1ao4edlt15.pdf

Probabilistic neural-network structure determination for pattern classification

This paper examines how real-time information gathered as part of intelligent transportation systems can be used to predict link travel times for one through five time periods ahead (of 5-min duration). The study employed a spectral basis artificial neural network (SNN) that utilizes a sinusoidal transformation technique to increase the linear separability of the input features. Link travel times from Houston that had been collected as part of the automatic vehicle identification system of the TranStar system were used as a test bed. It was found that the SNN outperformed a conventional artificial neural network and gave similar results to that of modular neural networks. However, the SNN requires significantly less effort on the part of the modeler than modular neural networks. The results, of the best SNN were compared with conventional link travel time prediction techniques including a Kalman filtering model, exponential smoothing model, historical profile, and real-time profile. It was found that the SNN gave the best overall results.

Spectral Basis Neural Networks for Real-Time Travel Time Forecasting

With the advent of route guidance systems (RGS), the prediction of short-term link travel times has become increasingly important. For RGS to be successful, the calculated routes should be based on not only historical and real-time link travel time information but also anticipatory link travel time information. An examination is conducted on how real-time information gathered as part of intelligent transportation systems can be used to predict link travel times for one through five time periods (of 5 minutes' duration). The methodology developed consists of two steps. First, the historical link travel times are classified based on an unsupervised clustering technique. Second, an individual or modular artificial neural network (ANN) is calibrated for each class, and each modular ANN is then used to predict link travel times. Actual link travel times from Houston, Texas, collected as part of the automatic vehicle identification system of the Houston Transtar system were used as a test bed. It was found that the modular ANN outperformed a conventional singular ANN. The results of the best modular ANN were compared with existing link travel time techniques, including a Kalman filtering model, an exponential smoothing model, a historical profile, and a real-time profile, and it was found that the modular ANN gave the best overall results.

Forecasting Multiple-Period Freeway Link Travel Times Using Modular Neural Networks

This correspondence presents a method for evaluation of artificial neural network (ANN) classifiers. In order to find the performance of the network over all possible input ranges, a probabilistic input model is defined. The expected error of the output over this input range is taken as a measure of generalization ability. Two essential elements for carrying out the proposed evaluation technique are estimation of the input probability density and numerical integration. A nonparametric method, which depends on the nearest M neighbors, is used to locally estimate the distribution around each training pattern. An orthogonalization procedure is utilized to determine the covariance matrices of local densities. A Monte Carlo method is used to perform the numerical integration. The proposed evaluation technique has been used to investigate the generalization ability of back propagation (BP), radial basis function (RBF) and probabilistic neural network (PNN) classifiers for three test problems. >

On the generalization ability of neural network classifiers

A probabilistic model for evaluation of neural network classifiers

A minimum error neural network (MNN)

A methodology for selection of appropriate widths or covariance matrices of the Gaussian functions in implementations of PNN (probabilistic neural network) classifiers is presented. The Gram-Schmidt orthogonalization process is employed to find these matrices. It has been shown that the proposed technique improves the generalization ability of the PNN classifiers over the standard approach. The result can be applied to other Gaussian-based classifiers such as the radial basis functions. >

http://ieeexplore.ieee.org/iel2/632/7149/00287147.pdf

Improving the performance of probabilistic neural networks

Summary form only given, as follows. An approach for evaluation of the generalization ability of neural network classifiers is discussed, and a minimum error neural network (MENN) classifier is offered. A probabilistic model and an estimation scheme for the input distribution have been defined. After defining and minimizing an error function for the classifier output, a criterion for the MENN classifier was found. The expected MENN classifier performance was then evaluated. It has been shown that the boundaries of the MENN decision surface, in the sense of least mean square error, are equivalent to the boundaries obtained by the Bayes rule. The proposed technique can be used to evaluate the generalization ability of any supervised learning classifier. >

K. Kalantri

Papers

On the generalization ability of neural network classifiers

A probabilistic model for evaluation of neural network classifiers

A minimum error neural network (MNN)

Improving the performance of probabilistic neural networks

On the generalization ability of neural network classifiers