Tracking the states of a nonlinear and nonstationary system in the weight-space of artificial neural networks

We propose a novel interpretation and usage of Neural Network (NN) in modeling physiological signals, which are allowed to be nonlinear and/or nonstationary. The method consists of training a NN for the k-step prediction of a physiological signal, and then examining the connection-weight-space (CWS) of the NN to extract information about the signal generator mechanism. We de. ne a novel feature, Normalized Vector Separation (gamma(ij)), to measure the separation of two arbitrary states i and j in the CWS and use it to track the state changes of the generating system. The performance of the method is examined via synthetic signals and clinical EEG. Synthetic data indicates that gamma(ij) can track the system down to a SNR of 3.5 dB. Clinical data obtained from three patients undergoing carotid endarterectomy of the brain showed that EEG could be modeled (within a root-means-squared-error of 0.01) by the proposed method, and the blood perfusion state of the brain could be monitored via gamma(ij), with small NNs having no more than 21 connection weight altogether.

Two Bayesian treatments of the n-tuple recognition method

Two probabilistic interpretations of the n-tuple recognition method are put forward in order to allow this technique to be analysed with the same Bayesian methods used in connection with other neural network models. Elementary demonstrations are then given of the use of maximum likelihood and maximum entropy methods for tuning the model parameters and assisting their interpretation. One of the models can be used to illustrate the significance of overlapping n-tuple samples with respect to correlations in the patterns.

Instantiating deformable models with a neural net

Deformable models are an attractive approach to recognizing objects which have considerable within-class variability such as handwritten characters. However, there are severe search problems associated with fitting the models to data which could be reduced if a better starting point for the search were available. We show that by training a neural network to predict how a deformable model should be instantiated from an input image, such improved starting points can be obtained. This method has been implemented for a system that recognizes handwritten digits using deformable models, and the results show that the search time can be significantly reduced without compromising recognition performance. © 1997 Academic Press.

Topographic mappings and feed-forward neural networks

This thesis is a study of the generation of topographic mappings - dimension reducing transformations of data that preserve some element of geometric structure - with feed-forward neural networks. As an alternative to established methods, a transformational variant of Sammon's method is proposed, where the projection is effected by a radial basis function neural network. This approach is related to the statistical field of multidimensional scaling, and from that the concept of a 'subjective metric' is defined, which permits the exploitation of additional prior knowledge concerning the data in the mapping process. This then enables the generation of more appropriate feature spaces for the purposes of enhanced visualisation or subsequent classification. A comparison with established methods for feature extraction is given for data taken from the 1992 Research Assessment Exercise for higher educational institutions in the United Kingdom. This is a difficult high-dimensional dataset, and illustrates well the benefit of the new topographic technique. A generalisation of the proposed model is considered for implementation of the classical multidimensional scaling (¸mds}) routine. This is related to Oja's principal subspace neural network, whose learning rule is shown to descend the error surface of the proposed ¸mds model. Some of the technical issues concerning the design and training of topographic neural networks are investigated. It is shown that neural network models can be less sensitive to entrapment in the sub-optimal global minima that badly affect the standard Sammon algorithm, and tend to exhibit good generalisation as a result of implicit weight decay in the training process. It is further argued that for ideal structure retention, the network transformation should be perfectly smooth for all inter-data directions in input space. Finally, there is a critique of optimisation techniques for topographic mappings, and a new training algorithm is proposed. A convergence proof is given, and the method is shown to produce lower-error mappings more rapidly than previous algorithms.

First year qualifying report: neural networks for extracting wind vectors from satellite scatterometer data

The ERS-1 Satellite was launched in July 1991 by the European Space Agency into a polar orbit at about km800, carrying a C-band scatterometer. A scatterometer measures the amount of radar back scatter generated by small ripples on the ocean surface induced by instantaneous local winds. Operational methods that extract wind vectors from satellite scatterometer data are based on the local inversion of a forward model, mapping scatterometer observations to wind vectors, by the minimisation of a cost function in the scatterometer measurement space.par This report uses mixture density networks, a principled method for modelling conditional probability density functions, to model the joint probability distribution of the wind vectors given the satellite scatterometer measurements in a single cell (the `inverse' problem). The complexity of the mapping and the structure of the conditional probability density function are investigated by varying the number of units in the hidden layer of the multi-layer perceptron and the number of kernels in the Gaussian mixture model of the mixture density network respectively. The optimal model for networks trained per trace has twenty hidden units and four kernels. Further investigation shows that models trained with incidence angle as an input have results comparable to those models trained by trace. A hybrid mixture density network that incorporates geophysical knowledge of the problem confirms other results that the conditional probability distribution is dominantly bimodal.par The wind retrieval results improve on previous work at Aston, but do not match other neural network techniques that use spatial information in the inputs, which is to be expected given the ambiguity of the inverse problem. Current work uses the local inverse model for autonomous ambiguity removal in a principled Bayesian framework. Future directions in which these models may be improved are given.

CDMA multiuser detection, neural networks, and statistical mechanics

A novel approach, based on statistical mechanics, to analyze typical performance of optimum code-division multiple-access (CDMA) multiuser detectors is reviewed. A `black-box' view ot the basic CDMA channel is introduced, based on which the CDMA multiuser detection problem is regarded as a `learning-from-examples' problem of the `binary linear perceptron' in the neural network literature. Adopting Bayes framework, analysis of the performance of the optimum CDMA multiuser detectors is reduced to evaluation of the average of the cumulant generating function of a relevant posterior distribution. The evaluation of the average cumulant generating function is done, based on formal analogy with a similar calculation appearing in the spin glass theory in statistical mechanics, by making use of the replica method, a method developed in the spin glass theory.

Feed-forward neural networks and topographic mappings for exploratory data analysis

A recent novel approach to the visualisation and analysis of datasets, and one which is particularly applicable to those of a high dimension, is discussed in the context of real applications. A feed-forward neural network is utilised to effect a topographic, structure-preserving, dimension-reducing transformation of the data, with an additional facility to incorporate different degrees of associated subjective information. The properties of this transformation are illustrated on synthetic and real datasets, including the 1992 UK Research Assessment Exercise for funding in higher education. The method is compared and contrasted to established techniques for feature extraction, and related to topographic mappings, the Sammon projection and the statistical field of multidimensional scaling.

Hierarchical Logical Description and Neural Recognition of Complex Patterns

Authors suggested earlier hierarchical method for definition of class description at pattern recognition problems solution. In this paper development and use of such hierarchical descriptions for parallel representation of complex patterns on the base of multi-core computers or neural networks is proposed.

Laser-induced breakdown spectroscopy quantitative analysis method via adaptive analytical line selection and relevance vector machine regression model

Abstract A new LIBS quantitative analysis method based on analytical line adaptive selection and Relevance Vector Machine (RVM) regression model is proposed. First, a scheme of adaptively selecting analytical line is put forward in order to overcome the drawback of high dependency on a priori knowledge. The candidate analytical lines are automatically selected based on the built-in characteristics of spectral lines, such as spectral intensity, wavelength and width at half height. The analytical lines which will be used as input variables of regression model are determined adaptively according to the samples for both training and testing. Second, an LIBS quantitative analysis method based on RVM is presented. The intensities of analytical lines and the elemental concentrations of certified standard samples are used to train the RVM regression model. The predicted elemental concentration analysis results will be given with a form of confidence interval of probabilistic distribution, which is helpful for evaluating the uncertainness contained in the measured spectra. Chromium concentration analysis experiments of 23 certified standard high-alloy steel samples have been carried out. The multiple correlation coefficient of the prediction was up to 98.85%, and the average relative error of the prediction was 4.01%. The experiment results showed that the proposed LIBS quantitative analysis method achieved better prediction accuracy and better modeling robustness compared with the methods based on partial least squares regression, artificial neural network and standard support vector machine.

Neural Control of Chaos and Aplications

Signal processing is an important topic in technological research today. In the areas of nonlinear dynamics search, the endeavor to control or order chaos is an issue that has received increasing attention over the last few years. Increasing interest in neural networks composed of simple processing elements (neurons) has led to widespread use of such networks to control dynamic systems learning. This paper presents backpropagation-based neural network architecture that can be used as a controller to stabilize unsteady periodic orbits. It also presents a neural network-based method for transferring the dynamics among attractors, leading to more efficient system control. The procedure can be applied to every point of the basin, no matter how far away from the attractor they are. Finally, this paper shows how two mixed chaotic signals can be controlled using a backpropagation neural network as a filter to separate and control both signals at the same time. The neural network provides more effective control, overcoming the problems that arise with control feedback methods. Control is more effective because it can be applied to the system at any point, even if it is moving away from the target state, which prevents waiting times. Also control can be applied even if there is little information about the system and remains stable longer even in the presence of random dynamic noise.

Neural Networks: A Diagnostic Tool for Gastric Electrical Uncoupling?

Neural Networks have been successfully employed in different biomedical settings. They have been useful for feature extractions from images and biomedical data in a variety of diagnostic applications. In this paper, they are applied as a diagnostic tool for classifying different levels of gastric electrical uncoupling in controlled acute experiments on dogs. Data was collected from 16 dogs using six bipolar electrodes inserted into the serosa of the antral wall. Each dog underwent three recordings under different conditions: (1) basal state, (2) mild surgically-induced uncoupling, and (3) severe surgically-induced uncoupling. For each condition half-hour recordings were made. The neural network was implemented according to the Learning Vector Quantization model. This is a supervised learning model of the Kohonen Self-Organizing Maps. Majority of the recordings collected from the dogs were used for network training. Remaining recordings served as a testing tool to examine the validity of the training procedure. Approximately 90% of the dogs from the neural network training set were classified properly. However, only 31% of the dogs not included in the training process were accurately diagnosed. The poor neural-network based diagnosis of recordings that did not participate in the training process might have been caused by inappropriate representation of input data. Previous research has suggested characterizing signals according to certain features of the recorded data. This method, if employed, would reduce the noise and possibly improve the diagnostic abilities of the neural network.

Classification of Data to Extract Knowledge from Neural Networks

A major drawback of artificial neural networks is their black-box character. Therefore, the rule extraction algorithm is becoming more and more important in explaining the extracted rules from the neural networks. In this paper, we use a method that can be used for symbolic knowledge extraction from neural networks, once they have been trained with desired function. The basis of this method is the weights of the neural network trained. This method allows knowledge extraction from neural networks with continuous inputs and output as well as rule extraction. An example of the application is showed. This example is based on the extraction of average load demand of a power plant.

A mixture density network approach to modelling and exploiting uncertainty in nonlinear control problems

In nonlinear and stochastic control problems, learning an efficient feed-forward controller is not amenable to conventional neurocontrol methods. For these approaches, estimating and then incorporating uncertainty in the controller and feed-forward models can produce more robust control results. Here, we introduce a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. A nonlinear multi-variable system with different delays between the input-output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non-Gaussian distributions of control signal as well as processes with hysteresis. © 2004 Elsevier Ltd. All rights reserved.

Freeway travel time estimation and prediction using dynamic neural networks

Providing transportation system operators and travelers with accurate travel time information allows them to make more informed decisions, yielding benefits for individual travelers and for the entire transportation system. Most existing advanced traveler information systems (ATIS) and advanced traffic management systems (ATMS) use instantaneous travel time values estimated based on the current measurements, assuming that traffic conditions remain constant in the near future. For more effective applications, it has been proposed that ATIS and ATMS should use travel times predicted for short-term future conditions rather than instantaneous travel times measured or estimated for current conditions. ^ This dissertation research investigates short-term freeway travel time prediction using Dynamic Neural Networks (DNN) based on traffic detector data collected by radar traffic detectors installed along a freeway corridor. DNN comprises a class of neural networks that are particularly suitable for predicting variables like travel time, but has not been adequately investigated for this purpose. Before this investigation, it was necessary to identifying methods for data imputation to account for missing data usually encountered when collecting data using traffic detectors. It was also necessary to identify a method to estimate the travel time on the freeway corridor based on data collected using point traffic detectors. A new travel time estimation method referred to as the Piecewise Constant Acceleration Based (PCAB) method was developed and compared with other methods reported in the literatures. The results show that one of the simple travel time estimation methods (the average speed method) can work as well as the PCAB method, and both of them out-perform other methods. This study also compared the travel time prediction performance of three different DNN topologies with different memory setups. The results show that one DNN topology (the time-delay neural networks) out-performs the other two DNN topologies for the investigated prediction problem. This topology also performs slightly better than the simple multilayer perceptron (MLP) neural network topology that has been used in a number of previous studies for travel time prediction.^

Freeway Travel Time Estimation and Prediction Using Dynamic Neural Networks

Providing transportation system operators and travelers with accurate travel time information allows them to make more informed decisions, yielding benefits for individual travelers and for the entire transportation system. Most existing advanced traveler information systems (ATIS) and advanced traffic management systems (ATMS) use instantaneous travel time values estimated based on the current measurements, assuming that traffic conditions remain constant in the near future. For more effective applications, it has been proposed that ATIS and ATMS should use travel times predicted for short-term future conditions rather than instantaneous travel times measured or estimated for current conditions. This dissertation research investigates short-term freeway travel time prediction using Dynamic Neural Networks (DNN) based on traffic detector data collected by radar traffic detectors installed along a freeway corridor. DNN comprises a class of neural networks that are particularly suitable for predicting variables like travel time, but has not been adequately investigated for this purpose. Before this investigation, it was necessary to identifying methods for data imputation to account for missing data usually encountered when collecting data using traffic detectors. It was also necessary to identify a method to estimate the travel time on the freeway corridor based on data collected using point traffic detectors. A new travel time estimation method referred to as the Piecewise Constant Acceleration Based (PCAB) method was developed and compared with other methods reported in the literatures. The results show that one of the simple travel time estimation methods (the average speed method) can work as well as the PCAB method, and both of them out-perform other methods. This study also compared the travel time prediction performance of three different DNN topologies with different memory setups. The results show that one DNN topology (the time-delay neural networks) out-performs the other two DNN topologies for the investigated prediction problem. This topology also performs slightly better than the simple multilayer perceptron (MLP) neural network topology that has been used in a number of previous studies for travel time prediction.