Michael M. Li

RBF neural networks for solving the inverse problem of backscattering spectra

This paper investigates a new method to solve the inverse problem of Rutherford backscattering (RBS) data. The inverse problem is to determine the sample structure information from measured spectra, which can be defined as a function approximation problem. We propose using radial basis function (RBF) neural networks to approximate an inverse function. Each RBS spectrum, which may contain up to 128 data points, is compressed by the principal component analysis, so that the dimensionality of input data and complexity of the network are reduced significantly. Our theoretical consideration is tested by numerical experiments with the example of the SiGe thin film sample and corresponding backscattering spectra. A comparison of the RBF method with multilayer perceptrons reveals that the former has better performance in extracting structural information from spectra. Furthermore, the proposed method can handle redundancies properly, which are caused by the constraint of output variables. This study is the first method based on RBF to deal with the inverse RBS data analysis problem.

Intelligent methods for solving inverse problems of backscattering spectra with noise: a comparison between neural networks and simulated annealing

This paper investigates two different intelligent techniques—the neural network (NN) method and the simulated annealing (SA) algorithm for solving the inverse problem of Rutherford backscattering (RBS) with noisy data. The RBS inverse problem is to determine the sample structure information from measured spectra, which can be defined as either a function approximation or a non-linear optimization problem. Early studies emphasized on numerical methods and empirical fitting. In this work, we have applied intelligent techniques and compared their performance and effectiveness for spectral data analysis by solving the inverse problem. Since each RBS spectrum may contain up to 512 data points, principal component analysis is used to make the feature extraction so as to ease the complexity of constructing the network. The innovative aspects of our work include introducing dimensionality reduction and noise modeling. Experiments on RBS spectra from SiGe thin films on a silicon substrate show that the SA is more accurate but the NN is faster, though both methods produce satisfactory results. Both methods are resilient to 10% Poisson noise in the input. These new findings indicate that in RBS data analysis the NN approach should be preferred when fast processing is required; whereas the SA method becomes the first choice should the analysis accuracy be targeted.

Mutual complement between statistical and neural network approaches for rock magnetism data analysis

Interpretation of magnetic phenomena in rock magnetism requires a good understanding in relationship between magnetic susceptibility and magnetic minerals, particularly magnetite, contained in rocks. Previous studies emphasized on describing such a correlation using a sole expression through statistical analysis. The resultant correlations are generally useful only in qualitative interpretation, but too coarse to simulate quantitative solutions. In this paper, we combine the correlation analysis with neural network techniques to not only identify the correlations between susceptibility and magnetite in rocks but also simulate accurate susceptibilities with respect to the magnetite contents provided. Our study has demonstrated that multilayer perceptron models are capable of producing accurate mappings between susceptibility and magnetite in rocks. However, correlation analysis provides qualitative interpretation for rock magnetism data in identifying the patterns of magnetic behaviours of the rocks. In quantitative simulation, if the required accuracy is not restricted, a general MLP model with existence of noises in training data is the first choice because it does not require statistical data pre-processing for establishing the NN model. If the simulation is to provide solutions as accurate as possible, the MLP model must be trained by noise-filtered datasets. The noise filtering is based on the preliminary correlation analysis. Therefore, these two approaches are mutually complementary, rather than competitive to each other.

Nonlinear curve fitting to stopping power data using RBF neural networks

We present a novel method using an RBF neural network with an additional linear term.A simple and accurate empirical formula is developed for stopping power data, based on RBF.A benchmark dataset is tested with the new method.Additional linear term improves fitting accuracy.The new method can be used to fit various types of data- many applications in engineering. This paper presents a novel approach for fitting experimental stopping power data to a simple empirical formula. The unknown complex nonlinear stopping power function is approximated by a Radial Basis Function (RBF) neural network with an additional linear neuron. The fitting coefficients are determined by learning algorithms globally. The experiments using the proposed method have been conducted on a benchmark dataset (titanium heat) and a set of stopping power data with implicit noise (MeV projectiles of Li, B, C, O, Al, Si, Ar, Ti and Fe in elemental carbon materials) from high energy physics measurements. The results not only showed the effectiveness of our method but also showed the significant improvement of fitting accuracy over other methods, without increasing computational complexity. The proposed approach allows us to obtain a fast and accurate interpolant that well suits to the situations where no stopping power data exist. It can be used as a standalone method or implemented as a sub-system that can be efficiently embedded in an intelligent system for ion beam analysis techniques.

Approximating nonlinear relations between susceptibility and magnetic contents in rocks using neural networks

Correlations between magnetic susceptibility and contents of magnetic minerals in rocks are important in interpreting magnetic anomalies in geophysical exploration and understanding magnetic behaviors of rocks in rock magnetism studies. Previous studies were focused on describing such correlations using a sole expression or a set of expressions through statistical analysis. In this paper, we use neural network techniques to approximate the nonlinear relations between susceptibility and magnetite and/or hematite contents in rocks. This is the first time that neural networks are used for such study in rock magnetism and magnetic petrophysics. Three multilayer perceptrons are trained for producing the best possible estimation on susceptibility based on magnetic contents. These trained models are capable of producing accurate mappings between susceptibility and magnetite and/or hematite contents in rocks. This approach opens a new way of quantitative simulation using neural networks in rock magnetism and petrophysical research and applications.

Impact of variability in data on accuracy and diversity of neural network based ensemble classifiers

Ensemble classifiers are very useful tools which can be applied for classification and prediction tasks in many real-world applications. There are many popular ensemble classifier generation techniques including neural network based techniques. However, there are many problems with ensemble classifiers when we apply them to real-world data of different size. This paper presents and investigates an approach for finding the impact of various parameters such as attributes, instances, classes on clusters, accuracy and diversity. The primary aim of this research is to see whether there is any link between these parameters and accuracy and diversity. The secondary aim is to see whether we can find any relationship between number of clusters in ensemble classifier and data variables. A series of experiments has been conducted by using different size of UCI machine learning benchmark datasets and neural network ensemble classifiers.

A neural networks-based fitting to high energy stopping power data for heavy ions in solid matter

Neural networks provide an alternative approach for the solution of complex non-linear data fitting problems. In this paper, we propose a novel technique using a multilayer perceptron neural network to fit high energy stopping power data, where the unknown stopping power functional form was fitted to experimental data by a set of linear combination of neurons. The projectiles of Li, B, N, O, Ne and P in the solid matters C, Si, Ti and Ni are illustrated as examples of the application. Using the resilient backpropagation algorithm, it can obtain more accurate fitting coefficients than conventional iterative methods. Our simulations show that a simple, accurate predictor based on neural network fitting can produce reliable predictions of stopping power values either at the energy position or for the projectile-target combination where no measured data currently exist.

An Improved RBF Neural Network Approach to Nonlinear Curve Fitting

This article presents a new framework for fitting measured scientific data to a simple empirical formula by introducing an additional linear neuron to the standard Gaussian kernel radial basis function (RBF) neural networks. The proposed method is first used to evaluate two benchmark datasets (Preschool boy and titanium heat) and then is applied to fit a set of stopping power data (MeV energetic carbon projectiles in elemental target materials C, Al, Si, Ti, Ni, Cu, Ag and Au) from high energy physics experiments. Without increasing computational complexity, the proposed approach significantly improves accuracy of fitting. Based on this type RBF neural network, a simple 6-parameter empirical formula is developed for various potential applications in curve fitting and nonlinear regression problems.

Bayesian Curve Fitting Based on RBF Neural Networks

In this article, we introduce a novel method for solving curve fitting problems. Instead of using polynomials, we extend the base model of radial basis functions (RBF) neural network by adding an extra linear neuron and incorporating the Bayesian learning. The unknown function represented by datasets is approximated by a set of Gaussian basis functions with a linear term. The additional linear term offsets the localized behavior induced by basis functions, while the Bayesian approach effectively reduces overfitting. The presented approach is initially utilized to assess two numerical examples, then further on the method is applied to fit a number of experimental datasets of heavy ion stopping powers (MeV energetic carbon ions in various elemental materials). Due to the linear correction, the proposed method significantly improves accuracy of fitting and outperforms the conventional numerical-based algorithms. Through the theoretical results, the numerical examples and the application of fitting stopping powers data, we demonstrate the suitability of the proposed method.

The Development of a Nonlinear Curve Fitter Using RBF Neural Networks with Hybrid Neurons

This paper investigates a new method using radial basis function (RBF) neural networks with an additional linear neuron for solving nonlinear curve fitting problem. The complicated unknown function to be fitted is approximated by a set of Gaussian basis function with a linear term correction. The proposed new technique is first used to evaluate two benchmark examples and subsequently applied to fit several heavy ion stopping power datasets (MeV energetic projectiles in aluminium). Due to the linear correction effect, the proposed approach significantly improves accuracy of fitting without adding much computational complexity. The developed method can be served as a standalone curve fitter or implemented as a proprietary software module to be embedded in an intelligent data analysis package for applications in regression analysis.