Identification of nonlinear systems using generalized kernel models

Nonlinear system identification is considered using a generalized kernel regression model. Unlike the standard kernel model, which employs a fixed common variance for all the kernel regressors, each kernel regressor in the generalized kernel model has an individually tuned diagonal covariance matrix that is determined by maximizing the correlation between the training data and the regressor using a repeated guided random search based on boosting optimization. An efficient construction algorithm based on orthogonal forward regression with leave-one-out (LOO) test statistic and local regularization (LR) is then used to select a parsimonious generalized kernel regression model from the resulting full regression matrix. The proposed modeling algorithm is fully automatic and the user is not required to specify any criterion to terminate the construction procedure. Experimental results involving two real data sets demonstrate the effectiveness of the proposed nonlinear system identification approach.

Analysing Google rankings through search engine optimization data

Purpose - The purpose of this paper is to identify the most popular techniques used to rank a web page highly in Google. Design/methodology/approach - The paper presents the results of a study into 50 highly optimized web pages that were created as part of a Search Engine Optimization competition. The study focuses on the most popular techniques that were used to rank highest in this competition, and includes an analysis on the use of PageRank, number of pages, number of in-links, domain age and the use of third party sites such as directories and social bookmarking sites. A separate study was made into 50 non-optimized web pages for comparison. Findings - The paper provides insight into the techniques that successful Search Engine Optimizers use to ensure a page ranks highly in Google. Recognizes the importance of PageRank and links as well as directories and social bookmarking sites. Research limitations/implications - Only the top 50 web sites for a specific query were analyzed. Analysing more web sites and comparing with similar studies in different competition would provide more concrete results. Practical implications - The paper offers a revealing insight into the techniques used by industry experts to rank highly in Google, and the success or other-wise of those techniques. Originality/value - This paper fulfils an identified need for web sites and e-commerce sites keen to attract a wider web audience.

Optimization of apodization functions in terahertz transient spectrometry

A quadratic programming optimization procedure for designing asymmetric apodization windows tailored to the shape of time-domain sample waveforms recorded using a terahertz transient spectrometer is proposed. By artificially degrading the waveforms, the performance of the designed window in both the time and the frequency domains is compared with that of conventional rectangular, triangular (Mertz), and Hamming windows. Examples of window optimization assuming Gaussian functions as the building elements of the apodization window are provided. The formulation is sufficiently general to accommodate other basis functions. (C) 2007 Optical Society of America

Nonlinear channel equalizer design using directional evolutionary multi-objective optimization

In this paper, a new equalizer learning scheme is introduced based on the algorithm of the directional evolutionary multi-objective optimization (EMOO). Whilst nonlinear channel equalizers such as the radial basis function (RBF) equalizers have been widely studied to combat the linear and nonlinear distortions in the modern communication systems, most of them do not take into account the equalizers' generalization capabilities. In this paper, equalizers are designed aiming at improving their generalization capabilities. It is proposed that this objective can be achieved by treating the equalizer design problem as a multi-objective optimization (MOO) problem, with each objective based on one of several training sets, followed by deriving equalizers with good capabilities of recovering the signals for all the training sets. Conventional EMOO which is widely applied in the MOO problems suffers from disadvantages such as slow convergence speed. Directional EMOO improves the computational efficiency of the conventional EMOO by explicitly making use of the directional information. The new equalizer learning scheme based on the directional EMOO is applied to the RBF equalizer design. Computer simulation demonstrates that the new scheme can be used to derive RBF equalizers with good generalization capabilities, i.e., good performance on predicting the unseen samples.

Investigation of liquid MALDI and optimization for instrument tuning and quantitative measurements

The success of Matrix-assisted laser desorption / ionisation (MALDI) in fields such as proteomics has partially but not exclusively been due to the development of improved data acquisition and sample preparation techniques. This has been required to overcome some of the short comings of the commonly used solid-state MALDI matrices such as - cyano-4-hydroxycinnamic acid (CHCA) and 2,5-dihydroxybenzoic acid (DHB). Solid state matrices form crystalline samples with highly inhomogeneous topography and morphology which results in large fluctuations in analyte signal intensity from spot to spot and positions within the spot. This means that efficient tuning of the mass spectrometer can be impeded and the use of MALDI MS for quantitative measurements is severely impeded. Recently new MALDI liquid matrices have been introduced which promise to be an effective alternative to crystalline matrices. Generally the liquid matrices comprise either ionic liquid matrices (ILMs) or a usually viscous liquid matrix which is doped with a UV lightabsorbing chromophore [1-3]. The advantages are that the droplet surface is smooth and relatively uniform with the analyte homogeneously distributed within. They have the ability to replenish a sampling position between shots negating the need to search for sample hot-spots. Also the liquid nature of the matrix allows for the use of additional additives to change the environment to which the analyte is added.

Particle swarm optimization aided orthogonal forward regression for unified data modeling

We propose a unified data modeling approach that is equally applicable to supervised regression and classification applications, as well as to unsupervised probability density function estimation. A particle swarm optimization (PSO) aided orthogonal forward regression (OFR) algorithm based on leave-one-out (LOO) criteria is developed to construct parsimonious radial basis function (RBF) networks with tunable nodes. Each stage of the construction process determines the center vector and diagonal covariance matrix of one RBF node by minimizing the LOO statistics. For regression applications, the LOO criterion is chosen to be the LOO mean square error, while the LOO misclassification rate is adopted in two-class classification applications. By adopting the Parzen window estimate as the desired response, the unsupervised density estimation problem is transformed into a constrained regression problem. This PSO aided OFR algorithm for tunable-node RBF networks is capable of constructing very parsimonious RBF models that generalize well, and our analysis and experimental results demonstrate that the algorithm is computationally even simpler than the efficient regularization assisted orthogonal least square algorithm based on LOO criteria for selecting fixed-node RBF models. Another significant advantage of the proposed learning procedure is that it does not have learning hyperparameters that have to be tuned using costly cross validation. The effectiveness of the proposed PSO aided OFR construction procedure is illustrated using several examples taken from regression and classification, as well as density estimation applications.

Prediction of Parkinson’s Disease tremor onset using a radial basis function neural network based on particle swarm optimization

Deep Brain Stimulation (DBS) has been successfully used throughout the world for the treatment of Parkinson's disease symptoms. To control abnormal spontaneous electrical activity in target brain areas DBS utilizes a continuous stimulation signal. This continuous power draw means that its implanted battery power source needs to be replaced every 18–24 months. To prolong the life span of the battery, a technique to accurately recognize and predict the onset of the Parkinson's disease tremors in human subjects and thus implement an on-demand stimulator is discussed here. The approach is to use a radial basis function neural network (RBFNN) based on particle swarm optimization (PSO) and principal component analysis (PCA) with Local Field Potential (LFP) data recorded via the stimulation electrodes to predict activity related to tremor onset. To test this approach, LFPs from the subthalamic nucleus (STN) obtained through deep brain electrodes implanted in a Parkinson patient are used to train the network. To validate the network's performance, electromyographic (EMG) signals from the patient's forearm are recorded in parallel with the LFPs to accurately determine occurrences of tremor, and these are compared to the performance of the network. It has been found that detection accuracies of up to 89% are possible. Performance comparisons have also been made between a conventional RBFNN and an RBFNN based on PSO which show a marginal decrease in performance but with notable reduction in computational overhead.

Neural networks for identification of nonlinear systems under random piecewise polynomial disturbances

The problem of identification of a nonlinear dynamic system is considered. A two-layer neural network is used for the solution of the problem. Systems disturbed with unmeasurable noise are considered, although it is known that the disturbance is a random piecewise polynomial process. Absorption polynomials and nonquadratic loss functions are used to reduce the effect of this disturbance on the estimates of the optimal memory of the neural-network model.

Use of the statistical properties of the wavelet-transform coefficients for optimization of integration time in Fourier transform spectrometry

We show that an analysis of the mean and variance of discrete wavelet coefficients of coaveraged time-domain interferograms can be used as a specification for determining when to stop coaveraging. We also show that, if a prediction model built in the wavelet domain is used to determine the composition of unknown samples, a stopping criterion for the coaveraging process can be developed with respect to the uncertainty tolerated in the prediction.

Dynamic integrated system optimization and parameter estimation for discrete time optimal control of nonlinear systems

An algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses Dynamic Integrated System Optimization and Parameter Estimation (DISOPE), which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimization procedure. A version of the algorithm with a linear-quadratic model-based problem, implemented in the C+ + programming language, is developed and applied to illustrative simulation examples. An analysis of the optimality and convergence properties of the algorithm is also presented.

Induced random fields in the LiHoxY1-xF4 quantum ising magnet in a transverse magnetic field

The LiHoxY1-xF4 magnetic material in a transverse magnetic field Bxx̂ perpendicular to the Ising spin direction has long been used to study tunable quantum phase transitions in a random disordered system. We show that the Bx-induced magnetization along the x̂ direction, combined with the local random dilution-induced destruction of crystalline symmetries, generates, via the predominant dipolar interactions between Ho3+ ions, random fields along the Ising ẑ direction. This identifies LiHoxY1-xF4 in Bx as a new random field Ising system. The random fields explain the rapid decrease of the critical temperature in the diluted ferromagnetic regime and the smearing of the nonlinear susceptibility at the spin-glass transition with increasing Bx and render the Bx-induced quantum criticality in LiHoxY1-xF4 likely inaccessible.

Random orthogonal matrix simulation

This paper introduces a method for simulating multivariate samples that have exact means, covariances, skewness and kurtosis. We introduce a new class of rectangular orthogonal matrix which is fundamental to the methodology and we call these matrices L matrices. They may be deterministic, parametric or data specific in nature. The target moments determine the L matrix then infinitely many random samples with the same exact moments may be generated by multiplying the L matrix by arbitrary random orthogonal matrices. This methodology is thus termed “ROM simulation”. Considering certain elementary types of random orthogonal matrices we demonstrate that they generate samples with different characteristics. ROM simulation has applications to many problems that are resolved using standard Monte Carlo methods. But no parametric assumptions are required (unless parametric L matrices are used) so there is no sampling error caused by the discrete approximation of a continuous distribution, which is a major source of error in standard Monte Carlo simulations. For illustration, we apply ROM simulation to determine the value-at-risk of a stock portfolio.