A nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area with structures based on neural networks, radial basis networks, wavelet networks, hinging hyperplanes, as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules. This paper describes all these approaches in a common framework, from a user's perspective. It focuses on what are the common features in the different approaches, the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques. It is pointed out that the nonlinear structures can be seen as a concatenation of a mapping from observed data to a regression vector and a nonlinear mapping from the regressor space to the output space. These mappings are discussed separately. The latter mapping is usually formed as a basis function e...

Radial wavelet networks have recently been proposed as a method for nonparametric regression. In this paper we analyse their performance within a Bayesian framework. We derive probability distributions over both the dimension of the networks and the network coefficients by placing a prior on the degrees of freedom of the model. This process bypasses the need to test or select a finite number of networks during the modelling process. Predictions are formed by mixing over many models of varying dimension and parameterization. We show that the complexity of the models adapts to the complexity of the data and produces good results on a number of benchmark test series. Keywords: Wavelets, radial basis functions, model choice, Bayesian neural networks, reversible jump Markov chain Monte Carlo, nonparametric regression, splines. 1 Introduction Wavelet networks have previously been studied in relation to nonparametric regression by Zhang (1997), Kugarajah and Zhang (1995), Zhang and Benveni...

This paper presents a new path-tracking scheme for a car-like mobile robot based on neural predictive control. A multi-layer back-propagation neural network is employed to model non-linear kinematics of the robot instead of a linear regression estimator in order to adapt the robot to a large operating range. The neural predictive control for path tracking is a model-based predictive control based on neural network modelling, which can generate its output in term of the robot kinematics and a desired path. The desired path for the robot is produced by a polar polynomial with a simple closed form. The multi-layer back-propagation neural network is constructed by a wavelet orthogonal decomposition to form a wavelet neural network that can overcome the problem caused by the local minima when training the neural network. The wavelet neural network has the advantage of using an explicit way to determine the number of the hidden nodes and initial value of weights. Simulation results for the modelling and control are provided to justify the proposed scheme.

We present an original initialization procedure for the parameters of feedforward wavelet networks, prior to training by gradient-based techniques. It takes advantage of wavelet frames stemming from the discrete wavelet transform, and uses a selection method to determine a set of best wavelets whose centers and dilation parameters are used as initial values for subsequent training. Results obtained for the modeling of two simulated processes are compared to those obtained with a heuristic initialization procedure, and demonstrate the effectiveness of the proposed method.

An approximating neural model, called hierarchical radial basis function (HRBF) network, is presented here. This is a self-organizing (by growing) multiscale version of a radial basis function (RBF) network. It is constituted of hierarchical layers, each containing a Gaussian grid at a decreasing scale. The grids are not completely filled, but units are inserted only where the local error is over threshold. This guarantees a uniform residual error and the allocation of more units with smaller scales where the data contain higher frequencies. Only local operations, which do not require any iteration on the data, are required; this allows to construct the network in quasi-real time. Through harmonic analysis, it is demonstrated that, although a HRBF cannot be reduced to a traditional wavelet-based multiresolution analysis (MRA), it does employ Riesz bases and enjoys asymptotic approximation properties for a very large class of functions. HRBF networks have been extensively applied to the reconstruction of three-dimensional (3-D) models from noisy range data. The results illustrate their power in denoising the original data, obtaining an effective multiscale reconstruction of better quality than that obtained by MRA.

This paper presents reliable techniques for detecting, tracking, and storing keyframes of people in surveillance video. The first component of our system is a novel face detector algorithm, which is based on first learning local adaptive features for each training image, and then using Adaboost learning to select the most general features for detection. This method provides a powerful mechanism for combining multiple features, allowing faster training time and better detection rates. The second component is a face tracking algorithm that interleaves multiple view-based classifiers along the temporal domain in a video sequence. This interleaving technique, combined with a correlation-based tracker, enables fast and robust face tracking over time. Finally, the third component of our system is a keyframe selection method that combines a person classifier with a face classifier. The basic idea is to generate a person keyframe in case the face is not visible, in order to reduce the number of false negatives. We performed quantitatively evaluation of our techniques on standard datasets and on surveillance videos captured by a camera over several days. 1.

Abstract | This paper introduces hardware implementations of Arti cial Neural Networks and Fuzzy Systems. Several implementation methodologies are described, ranging from fully digital to fully analog ones. Advantages and drawbacks are outlined and performance of existing implementations are presented. The paper also analyzes hardware performance parameters and tradeo s, and the bottlenecks intrinsic in several implementation methodologies. The constraints posed by hardware technologies onto algorithms and performance are also clearly described. I.

We survey a number of applications of the wavelet transform in time series prediction.

Human body tracking is useful in applications like medical diagnostic, human computer interface, visual surveillance etc. In this paper, a trajectory-learning algorithm using wavenet is proposed to track human body in real time without sacrificing accuracy. Human body is located within a small searching window using color and shape as heuristic. The location and size of the searching window are estimated using the proposed wavenet-based algorithm. The effectiveness and efficiency of the proposed tracking system were tested. The results show that the proposed system can track the human body in real time under various conditions including clutter background, background with distractor, and scene with object occlusion. 1.

Wavelet Networks (WNs) were introduced in 1992 as a combination of... In this paper, we analyze some of their properties and hightlight their advantages for object representation purposes. We then present a series of experimental results where we have used WNs for face tracking in which we exploit the efficiency due to data reduction, for face recognition and face-pose estimation where we exploit the optimized filter bank principle of the WNs.