Shock physics experiments are often complicated and expensive. As a result, researchers are unable to conduct as many experiments as they would like - leading to sparse data sets. In this paper, Support Vector Machines for regression are applied to velocimetry data sets for shock damaged and melted tin met al. Some success at interpolating between data sets is achieved. Implications for future work are discussed.
As noted above, SVM for regression (as opposed to SVM classification) is rarely applied in physics. There are, however, several successful examples of the support vector regression application. In @cite_3 introduced the regression type of the SVM technique to the civil engineering community and showed that SVM can be successfully applied to the problem of stream flow data estimation based on records of rainfall and other climatic data. By using three types of kernels, Polynomial, RBF, and Neural Network, and choosing the best values for SVM free parameters via trial and error, the authors point out that the SVM with the RBF kernel performs the best. Finally, this research is the first attempt to apply support vector regression in data analysis of VISAR measurements obtained from experiments on shock melted and damaged met al.
@cite_3
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The Support Vector Machine (SVM) has emerged in recent years as a popular approach to the classification of data. One problem that faces the user of an SVM is how to choose a kernel and the specific parameters for that kernel. Applications of an SVM therefore require a search for the optimum settings for a particular problem. This paper proposes a classification technique, which we call the Genetic Kernel SVM (GK SVM), that uses Genetic Programming to evolve a kernel for a SVM classifier. Results of initial experiments with the proposed technique are presented. These results are compared with those of a standard SVM classifier using the Polynomial, RBF and Sigmoid kernel with various parameter settings Least squares support vector machines (LS-SVM) is an SVM version which involves equality instead of inequality constraints and works with a least squares cost function. In this way, the solution follows from a linear Karush–Kuhn–Tucker system instead of a quadratic programming problem. However, sparseness is lost in the LS-SVM case and the estimation of the support values is only optimal in the case of a Gaussian distribution of the error variables. In this paper, we discuss a method which can overcome these two drawbacks. We show how to obtain robust estimates for regression by applying a weighted version of LS-SVM. We also discuss a sparse approximation procedure for weighted and unweighted LS-SVM. It is basically a pruning method which is able to do pruning based upon the physical meaning of the sorted support values, while pruning procedures for classical multilayer perceptrons require the computation of a Hessian matrix or its inverse. The methods of this paper are illustrated for RBF kernels and demonstrate how to obtain robust estimates with selection of an appropriate number of hidden units, in the case of outliers or non-Gaussian error distributions with heavy tails. c 2002 Elsevier Science B.V. All rights reserved. This paper provides an overview of the support vector machine SVM methodology and its applicability to real-world engineering problems. Specifically, the aim of this study is to review the current state of the SVM technique, and to show some of its latest successful results in real-world problems present in different engineering fields. The paper starts by reviewing the main basic concepts of SVMs and kernel methods. Kernel theory, SVMs, support vector regression SVR, and SVM in signal processing and hybridization of SVMs with meta-heuristics are fully described in the first part of this paper. The adoption of SVMs in engineering is nowadays a fact. As we illustrate in this paper, SVMs can handle high-dimensional, heterogeneous and scarcely labeled datasets very efficiently, and it can be also successfully tailored to particular applications. The second part of this review is devoted to different case studies in engineering problems, where the application of the SVM methodology has led to excellent results. First, we discuss the application of SVR algorithms in two renewable energy problems: the wind speed prediction from measurements in neighbor stations and the wind speed reconstruction using synoptic-pressure data. The application of SVMs in noninvasive cardiac indices estimation is described next, and results obtained there are presented. The application of SVMs in problems of functional magnetic resonance imaging fMRI data processing is further discussed in the paper: brain decoding and mental disorder characterization. The following application deals with antenna array processing, namely SVMs for spatial nonlinear beamforming, and the SVM application in a problem of arrival angle detection. Finally, the application of SVMs to remote sensing image classification and target detection problems closes this review. WIREs Data Mining Knowl Discov 2014, 4:234-267. doi: 10.1002 widm.1125 The support vector machine (SVM) is known for its good performance in two-class classification, but its extension to multiclass classification is still an ongoing research issue. In this article, we propose a new approach for classification, called the import vector machine (IVM), which is built on kernel logistic regression (KLR). We show that the IVM not only performs as well as the SVM in two-class classification, but also can naturally be generalized to the multiclass case. Furthermore, the IVM provides an estimate of the underlying probability. Similar to the support points of the SVM, the IVM model uses only a fraction of the training data to index kernel basis functions, typically a much smaller fraction than the SVM. This gives the IVM a potential computational advantage over the SVM. We investigate the relation of two fundamental tools in machine learning and signal processing, that is the support vector machine (SVM) for classification, and the Lasso technique used in regression. We show that the resulting optimization problems are equivalent, in the following sense. Given any instance of an L2-loss soft-margin (or hard-margin) SVM, we construct a Lasso instance having the same optimal solutions, and vice versa. As a consequence, many existing optimization algorithms for both SVMs and Lasso can also be applied to the respective other problem instances. Also, the equivalence allows for many known theoretical insights for SVM and Lasso to be translated between the two settings. One such implication gives a simple kernelized version of the Lasso, analogous to the kernels used in the SVM setting. Another consequence is that the sparsity of a Lasso solution is equal to the number of support vectors for the corresponding SVM instance, and that one can use screening rules to prune the set of support vectors. Furthermore, we can relate sublinear time algorithms for the two problems, and give a new such algorithm variant for the Lasso. We also study the regularization paths for both methods. Support vector machines (SVMs) have been promising methods for classification and regression analysis because of their solid mathematical foundations which convery several salient properties that other methods hardly provide. However, despite the prominent properties of SVMs, they are not as favored for large-scale data mining as for pattern recognition or machine learning because the training complexity of SVMs is highly dependent on the size of a data set. Many real-world data mining applications involve millions or billions of data records where even multiple scans of the entire data are too expensive to perform. This paper presents a new method, Clustering-Based SVM (CB-SVM), which is specifically designed for handling very large data sets. CB-SVM applies a hierarchical micro-clustering algorithm that scans the entire data set only once to provide an SVM with high quality samples that carry the statistical summaries of the data such that the summaries maximize the benefit of learning the SVM. CB-SVM tries to generate the best SVM boundary for very large data sets given limited amount of resources. Our experiments on synthetic and real data sets show that CB-SVM is highly scalable for very large data sets while also generating high classification accuracy. Straightforward classification using kernelized SVMs requires evaluating the kernel for a test vector and each of the support vectors. For a class of kernels we show that one can do this much more efficiently. In particular we show that one can build histogram intersection kernel SVMs (IKSVMs) with runtime complexity of the classifier logarithmic in the number of support vectors as opposed to linear for the standard approach. We further show that by precomputing auxiliary tables we can construct an approximate classifier with constant runtime and space requirements, independent of the number of support vectors, with negligible loss in classification accuracy on various tasks. This approximation also applies to 1 - chi2 and other kernels of similar form. We also introduce novel features based on a multi-level histograms of oriented edge energy and present experiments on various detection datasets. On the INRIA pedestrian dataset an approximate IKSVM classifier based on these features has the current best performance, with a miss rate 13 lower at 10-6 False Positive Per Window than the linear SVM detector of Dalal & Triggs. On the Daimler Chrysler pedestrian dataset IKSVM gives comparable accuracy to the best results (based on quadratic SVM), while being 15times faster. In these experiments our approximate IKSVM is up to 2000times faster than a standard implementation and requires 200times less memory. Finally we show that a 50times speedup is possible using approximate IKSVM based on spatial pyramid features on the Caltech 101 dataset with negligible loss of accuracy. This paper deals with the application of a novel neural network technique, support vector machine (SVM), in financial time series forecasting. The objective of this paper is to examine the feasibility of SVM in financial time series forecasting by comparing it with a multi-layer back-propagation (BP) neural network. Five real futures contracts that are collated from the Chicago Mercantile Market are used as the data sets. The experiment shows that SVM outperforms the BP neural network based on the criteria of normalized mean square error (NMSE), mean absolute error (MAE), directional symmetry (DS) and weighted directional symmetry (WDS). Since there is no structured way to choose the free parameters of SVMs, the variability in performance with respect to the free parameters is investigated in this study. Analysis of the experimental results proved that it is advantageous to apply SVMs to forecast financial time series. Traditional classification approaches generalize poorly on image classification tasks, because of the high dimensionality of the feature space. This paper shows that support vector machines (SVM) can generalize well on difficult image classification problems where the only features are high dimensional histograms. Heavy-tailed RBF kernels of the form K(x, y)=e sup - spl rho spl Sigma sub i sup |xia-yia|b with a spl les 1 and b spl les 2 are evaluated on the classification of images extracted from the Corel stock photo collection and shown to far outperform traditional polynomial or Gaussian radial basis function (RBF) kernels. Moreover, we observed that a simple remapping of the input x sub i spl rarr x sub i sup a improves the performance of linear SVM to such an extend that it makes them, for this problem, a valid alternative to RBF kernels. Support vector machine (SVM) is a very specific type of learning algorithms characterized by the capacity control of the decision function, the use of the kernel functions and the sparsity of the solution. In this paper, we investigate the predictability of financial movement direction with SVM by forecasting the weekly movement direction of NIKKEI 225 index. To evaluate the forecasting ability of SVM, we compare its performance with those of Linear Discriminant Analysis, Quadratic Discriminant Analysis and Elman Backpropagation Neural Networks. The experiment results show that SVM outperforms the other classification methods. Further, we propose a combining model by integrating SVM with the other classification methods. The combining model performs best among all the forecasting methods. This paper introduces a methodology for the detection of sleep apnea based on single-lead electrocardiogram (ECG) of the patient. In the proposed technique, each QRS complex of the ECG signal is approximated using a linear combination of the lower order Hermite basis functions. The coefficients of the Hermite expansion are then used to discriminate the apnea and normal segments along with three features based on R-R time series (mean of R-R intervals, the standard deviation of R-R intervals) and energy in the error of the QRS approximation. To perform classification between the apnea and normal segments, four different types of classifiers (K-nearest neighbor (KNN), multilayer perceptron neural network (MLPNN), support vector machine (SVM), and least-square support vector machine (LS-SVM)) are used in this work.In total, 70 ECG recordings from Apnea-ECG dataset are used in this study and the performance of the proposed algorithm is evaluated based on the minute-by-minute (per-segment) classification, and per-recording (where the entire ECG recording of a subject is discriminated as the apnea or normal one) classification. By considering the events of apnea and hypopnea together, an accuracy of about 84 is achieved on the minute-by-minute basis classification using the LS-SVM classifier with the Gaussian radial basis function (RBF) kernel.On the other hand, an accuracy of about 97.14 is achieved for per-recording classification using the SVM, and LS-SVM classifiers. From the results, it is observed that the proposed methodology provides comparable accuracy with the methods existing in the literature at reduced computational cost due to the lesser number of features selected for the classification. Sleep apnea detection from single-lead ECG based on QRS morphology.Hermite basis functions for tracking respiratory induced morphological variations in the QRS complexes.We performed the analysis on the Apnea-ECG database. The expected kernel for missing features is introduced and applied to training a support vector machine. The expected kernel is a measure of the mean similarity with respect to the distribution of the missing features. We compare the expected kernel SVM with the robust second-order cone program (SOCP) SVM, which accounts for missing kernel values by estimating the mean and covariance of missing similarities. Further, we extend the SOCP SVM to utilize the expected kernel by deriving the expected kernel variance. Results show that the expected kernel-used with a traditional SVM solver-shows competitive performance on benchmark datasets to the SOCP SVM at a far-reduced computational burden. Least Squares Support Vector Machines (LS-SVM) is aproven method for classification and function approximation. In comparison to the standard Support Vector Machines (SVM) it only requires solving a linear system, but it lacks sparseness in the number of solution terms. Pruning can therefore be applied. Standard ways of pruning the LS-SVM consist of recursively solving the approximation problem and subsequently omitting data that have a small error in the previous pass and are based on support values. We suggest a slightly adapted variant that improves the performance significantly. We assess the relative regression performance of these pruning schemes in a comparison with two (for pruning adapted) subset selection schemes, -one based on the QR decomposition (supervised), one that searches the most representative feature vector span (unsupervised)-, random omission and backward selection on independent test sets in some benchmark experiments. We show that a class of nonlinear kernel SVMs admits approximate classifiers with runtime and memory complexity that is independent of the number of support vectors. This class of kernels, which we refer to as additive kernels, includes widely used kernels for histogram-based image comparison like intersection and chi-squared kernels. Additive kernel SVMs can offer significant improvements in accuracy over linear SVMs on a wide variety of tasks while having the same runtime, making them practical for large-scale recognition or real-time detection tasks. We present experiments on a variety of datasets, including the INRIA person, Daimler-Chrysler pedestrians, UIUC Cars, Caltech-101, MNIST, and USPS digits, to demonstrate the effectiveness of our method for efficient evaluation of SVMs with additive kernels. Since its introduction, our method has become integral to various state-of-the-art systems for PASCAL VOC object detection image classification, ImageNet Challenge, TRECVID, etc. The techniques we propose can also be applied to settings where evaluation of weighted additive kernels is required, which include kernelized versions of PCA, LDA, regression, k-means, as well as speeding up the inner loop of SVM classifier training algorithms. Effective prediction of defect-prone software modules can enable software developers to focus quality assurance activities and allocate effort and resources more efficiently. Support vector machines (SVM) have been successfully applied for solving both classification and regression problems in many applications. This paper evaluates the capability of SVM in predicting defect-prone software modules and compares its prediction performance against eight statistical and machine learning models in the context of four NASA datasets. The results indicate that the prediction performance of SVM is generally better than, or at least, is competitive against the compared models. Effective use of support vector machines (SVMs) in classification necessitates the appropriate choice of a kernel. Designing problem specific kernels involves the definition of a similarity measure, with the condition that kernels are positive semi-definite (PSD). An alternative approach which places no such restrictions on the similarity measure is to construct a set of inputs and let each example be represented by its similarity to all the examples in this set and then apply a conventional SVM to this transformed data. Dynamic time warping (DTW) is a well established distance measure for time series but has been of limited use in SVMs since it is not obvious how it can be used to derive a PSD kernel. The feasibility of the similarity based approach for DTW is investigated by applying the method to a large set of time-series classification problems. Early diagnosis of stroke is essential for timely prevention and treatment. Investigation shows that measures extracted from various risk parameters carry valuable information for the prediction of stroke. This research work investigates the various physiological parameters that are used as risk factors for the prediction of stroke. Data was collected from International Stroke Trial database and was successfully trained and tested using Support Vector Machine (SVM). In this work, we have implemented SVM with different kernel functions and found that linear kernel gave an accuracy of 90 . This paper describes an approach for the problem of face pose discrimination using support vector machines (SVM). Face pose discrimination means that one can label the face image as one of several known poses. Face images are drawn from the standard FERET database. The training set consists of 150 images equally distributed among frontal, approximately 33.75 spl deg rotated left and right poses, respectively, and the test set consists of 450 images again equally distributed among the three different types of poses. SVM achieved perfect accuracy-100 -discriminating between the three possible face poses on unseen test data, using either polynomials of degree 3 or radial basis functions (RBF) as kernel approximation functions. This paper introduces a novel classification approach which improves the performance of support vector machines (SVMs) by learning a distance metric. The metric learned is a Mahalanobis metric previously trained so that examples from different classes are separated with a large margin. The learned metric is used to define a kernel function for SVM classification. In this context, the metric can be seen as a linear transformation of the original inputs before applying an SVM classifier that uses Euclidean distances. This transformation increases the separability of classes in the transformed space where the classification is applied. Experiments demonstrate significant improvements in classification tasks on various data sets. In many problems of machine learning, the data are distributed nonlinearly. One way to address this kind of data is training a nonlinear classifier such as kernel support vector machine (kernel SVM). However, the computational burden of kernel SVM limits its application to large scale datasets. In this paper, we propose a Clustered Support Vector Machine (CSVM), which tackles the data in a divide and conquer manner. More specifically, CSVM groups the data into several clusters, followed which it trains a linear support vector machine in each cluster to separate the data locally. Meanwhile, CSVM has an additional global regularization, which requires the weight vector of each local linear SVM aligning with a global weight vector. The global regularization leverages the information from one cluster to another, and avoids over-fitting in each cluster. We derive a data-dependent generalization error bound for CSVM, which explains the advantage of CSVM over linear SVM. Experiments on several benchmark datasets show that the proposed method outperforms linear SVM and some other related locally linear classifiers. It is also comparable to a fine-tuned kernel SVM in terms of prediction performance, while it is more efficient than kernel SVM.