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.

Application of support vector machines on the basis of the first Hungarian bankruptcy model

In our study we rely on a data mining procedure known as support vector machine (SVM) on the database of the first Hungarian bankruptcy model. The models constructed are then contrasted with the results of earlier bankruptcy models with the use of classification accuracy and the area under the ROC curve. In using the SVM technique, in addition to conventional kernel functions, we also examine the possibilities of applying the ANOVA kernel function and take a detailed look at data preparation tasks recommended in using the SVM method (handling of outliers). The results of the models assembled suggest that a significant improvement of classification accuracy can be achieved on the database of the first Hungarian bankruptcy model when using the SVM method as opposed to neural networks.

Building Support Vector Machines in the Context of Regularised Least Squares

This paper formulates a linear kernel support vector machine (SVM) as a regularized least-squares (RLS) problem. By defining a set of indicator variables of the errors, the solution to the RLS problem is represented as an equation that relates the error vector to the indicator variables. Through partitioning the training set, the SVM weights and bias are expressed analytically using the support vectors. It is also shown how this approach naturally extends to Sums with nonlinear kernels whilst avoiding the need to make use of Lagrange multipliers and duality theory. A fast iterative solution algorithm based on Cholesky decomposition with permutation of the support vectors is suggested as a solution method. The properties of our SVM formulation are analyzed and compared with standard SVMs using a simple example that can be illustrated graphically. The correctness and behavior of our solution (merely derived in the primal context of RLS) is demonstrated using a set of public benchmarking problems for both linear and nonlinear SVMs.

Solar Intensity Forecasting using Artificial Neural Networks and Support Vector Machines

This paper presents several forecasting methodologies based on the application of Artificial Neural Networks (ANN) and Support Vector Machines (SVM), directed to the prediction of the solar radiance intensity. The methodologies differ from each other by using different information in the training of the methods, i.e, different environmental complementary fields such as the wind speed, temperature, and humidity. Additionally, different ways of considering the data series information have been considered. Sensitivity testing has been performed on all methodologies in order to achieve the best parameterizations for the proposed approaches. Results show that the SVM approach using the exponential Radial Basis Function (eRBF) is capable of achieving the best forecasting results, and in half execution time of the ANN based approaches.

Multi-scale support vector algorithms for hot spot detection and modelling

The algorithmic approach to data modelling has developed rapidly these last years, in particular methods based on data mining and machine learning have been used in a growing number of applications. These methods follow a data-driven methodology, aiming at providing the best possible generalization and predictive abilities instead of concentrating on the properties of the data model. One of the most successful groups of such methods is known as Support Vector algorithms. Following the fruitful developments in applying Support Vector algorithms to spatial data, this paper introduces a new extension of the traditional support vector regression (SVR) algorithm. This extension allows for the simultaneous modelling of environmental data at several spatial scales. The joint influence of environmental processes presenting different patterns at different scales is here learned automatically from data, providing the optimum mixture of short and large-scale models. The method is adaptive to the spatial scale of the data. With this advantage, it can provide efficient means to model local anomalies that may typically arise in situations at an early phase of an environmental emergency. However, the proposed approach still requires some prior knowledge on the possible existence of such short-scale patterns. This is a possible limitation of the method for its implementation in early warning systems. The purpose of this paper is to present the multi-scale SVR model and to illustrate its use with an application to the mapping of Cs137 activity given the measurements taken in the region of Briansk following the Chernobyl accident.

Uncertainty Quantification Of A Semi-Supervised Support Vector Regression Reservoir Model

Uncertainty quantification of petroleum reservoir models is one of the present challenges, which is usually approached with a wide range of geostatistical tools linked with statistical optimisation or/and inference algorithms. Recent advances in machine learning offer a novel approach to model spatial distribution of petrophysical properties in complex reservoirs alternative to geostatistics. The approach is based of semisupervised learning, which handles both ?labelled? observed data and ?unlabelled? data, which have no measured value but describe prior knowledge and other relevant data in forms of manifolds in the input space where the modelled property is continuous. Proposed semi-supervised Support Vector Regression (SVR) model has demonstrated its capability to represent realistic geological features and describe stochastic variability and non-uniqueness of spatial properties. On the other hand, it is able to capture and preserve key spatial dependencies such as connectivity of high permeability geo-bodies, which is often difficult in contemporary petroleum reservoir studies. Semi-supervised SVR as a data driven algorithm is designed to integrate various kind of conditioning information and learn dependences from it. The semi-supervised SVR model is able to balance signal/noise levels and control the prior belief in available data. In this work, stochastic semi-supervised SVR geomodel is integrated into Bayesian framework to quantify uncertainty of reservoir production with multiple models fitted to past dynamic observations (production history). Multiple history matched models are obtained using stochastic sampling and/or MCMC-based inference algorithms, which evaluate posterior probability distribution. Uncertainty of the model is described by posterior probability of the model parameters that represent key geological properties: spatial correlation size, continuity strength, smoothness/variability of spatial property distribution. The developed approach is illustrated with a fluvial reservoir case. The resulting probabilistic production forecasts are described by uncertainty envelopes. The paper compares the performance of the models with different combinations of unknown parameters and discusses sensitivity issues.

Uncertainty Quantification with Support Vector Regression Prediction Models

Uncertainty quantification of petroleum reservoir models is one of the present challenges, which is usually approached with a wide range of geostatistical tools linked with statistical optimisation or/and inference algorithms. The paper considers a data driven approach in modelling uncertainty in spatial predictions. Proposed semi-supervised Support Vector Regression (SVR) model has demonstrated its capability to represent realistic features and describe stochastic variability and non-uniqueness of spatial properties. It is able to capture and preserve key spatial dependencies such as connectivity, which is often difficult to achieve with two-point geostatistical models. Semi-supervised SVR is designed to integrate various kinds of conditioning data and learn dependences from them. A stochastic semi-supervised SVR model is integrated into a Bayesian framework to quantify uncertainty with multiple models fitted to dynamic observations. The developed approach is illustrated with a reservoir case study. The resulting probabilistic production forecasts are described by uncertainty envelopes.

Geomodelling of a fluvial system with semi-supervised support vector regression

Fluvial deposits are a challenge for modelling flow in sub-surface reservoirs. Connectivity and continuity of permeable bodies have a major impact on fluid flow in porous media. Contemporary object-based and multipoint statistics methods face a problem of robust representation of connected structures. An alternative approach to model petrophysical properties is based on machine learning algorithm ? Support Vector Regression (SVR). Semi-supervised SVR is able to establish spatial connectivity taking into account the prior knowledge on natural similarities. SVR as a learning algorithm is robust to noise and captures dependencies from all available data. Semi-supervised SVR applied to a synthetic fluvial reservoir demonstrated robust results, which are well matched to the flow performance

Ensemble methods for environmental data modelling with support vector regression

This paper investigates the use of ensemble of predictors in order to improve the performance of spatial prediction methods. Support vector regression (SVR), a popular method from the field of statistical machine learning, is used. Several instances of SVR are combined using different data sampling schemes (bagging and boosting). Bagging shows good performance, and proves to be more computationally efficient than training a single SVR model while reducing error. Boosting, however, does not improve results on this specific problem.

Modelling ecological niches with support vector machines

1. The ecological niche is a fundamental biological concept. Modelling species' niches is central to numerous ecological applications, including predicting species invasions, identifying reservoirs for disease, nature reserve design and forecasting the effects of anthropogenic and natural climate change on species' ranges. 2. A computational analogue of Hutchinson's ecological niche concept (the multidimensional hyperspace of species' environmental requirements) is the support of the distribution of environments in which the species persist. Recently developed machine-learning algorithms can estimate the support of such high-dimensional distributions. We show how support vector machines can be used to map ecological niches using only observations of species presence to train distribution models for 106 species of woody plants and trees in a montane environment using up to nine environmental covariates. 3. We compared the accuracy of three methods that differ in their approaches to reducing model complexity. We tested models with independent observations of both species presence and species absence. We found that the simplest procedure, which uses all available variables and no pre-processing to reduce correlation, was best overall. Ecological niche models based on support vector machines are theoretically superior to models that rely on simulating pseudo-absence data and are comparable in empirical tests. 4. Synthesis and applications. Accurate species distribution models are crucial for effective environmental planning, management and conservation, and for unravelling the role of the environment in human health and welfare. Models based on distribution estimation rather than classification overcome theoretical and practical obstacles that pervade species distribution modelling. In particular, ecological niche models based on machine-learning algorithms for estimating the support of a statistical distribution provide a promising new approach to identifying species' potential distributions and to project changes in these distributions as a result of climate change, land use and landscape alteration.

Comparing Support Vector Machines with Gaussian Kernels to Radial Basis Function Classifiers

The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights and threshold such as to minimize an upper bound on the expected test error. The present study is devoted to an experimental comparison of these machines with a classical approach, where the centers are determined by $k$--means clustering and the weights are found using error backpropagation. We consider three machines, namely a classical RBF machine, an SV machine with Gaussian kernel, and a hybrid system with the centers determined by the SV method and the weights trained by error backpropagation. Our results show that on the US postal service database of handwritten digits, the SV machine achieves the highest test accuracy, followed by the hybrid approach. The SV approach is thus not only theoretically well--founded, but also superior in a practical application.

Measuring time series predictability using support vector regression

Most studies involving statistical time series analysis rely on assumptions of linearity, which by its simplicity facilitates parameter interpretation and estimation. However, the linearity assumption may be too restrictive for many practical applications. The implementation of nonlinear models in time series analysis involves the estimation of a large set of parameters, frequently leading to overfitting problems. In this article, a predictability coefficient is estimated using a combination of nonlinear autoregressive models and the use of support vector regression in this model is explored. We illustrate the usefulness and interpretability of results by using electroencephalographic records of an epileptic patient.

Learning kernels for support vector machines with polynomial powers of sigmoid

In the pattern recognition research field, Support Vector Machines (SVM) have been an effectiveness tool for classification purposes, being successively employed in many applications. The SVM input data is transformed into a high dimensional space using some kernel functions where linear separation is more likely. However, there are some computational drawbacks associated to SVM. One of them is the computational burden required to find out the more adequate parameters for the kernel mapping considering each non-linearly separable input data space, which reflects the performance of SVM. This paper introduces the Polynomial Powers of Sigmoid for SVM kernel mapping, and it shows their advantages over well-known kernel functions using real and synthetic datasets.