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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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. 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 Support vector machines (SVM) have been highly successful in many machine learning problems. Recently, it is also used for multi-instance (MI) learning by employing a kernel that is defined directly on the bags. As only the bags (but not the instances) have known labels, this MI kernel implicitly assumes all instances in the bag to be equally important. However, a fundamental property of MI learning is that not all instances in a positive bag necessarily belong to the positive class, and thus different instances in the same bag should have different contributions to the kernel. In this paper, we address this instance label ambiguity by using the method of marginalized kernels. It first assumes that all the instance labels are available and defines a label-dependent kernel on the instances. By integrating out the unknown instance labels, a marginalized kernel defined on the bags can then be obtained. A desirable property is that this kernel weights the instance pairs by the consistencies of their probabilistic instance labels. Experiments on both classification and regression data sets show that this marginalized MI kernel, when used in a standard SVM, performs consistently better than the original MI kernel. It also outperforms a number of traditional MI learning methods. This work addresses a data driven approach which employs a machine learning technique known as Support Vector Regression (SVR), to identify the coupled dynamical model of an autonomous underwater vehicle. To train the regressor, we use a dataset collected from the robot's on-board navigation sensors and actuators. To achieve a better fit to the experimental data, a variant of a radial-basis-function kernel is used in combination with the SVR which accounts for the different complexities of each of the contributing input features of the model. We compare our method to other explicit hydrodynamic damping models that were identified using the total least squares method and with less complex SVR methods. To analyze the transferability, we clearly separate training and testing data obtained in real-world experiments. Our presented method shows much better results especially compared to classical approaches. 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. Linear support vector machines (SVM) are useful for classifying large-scale sparse data. Problems with sparse features are common in applications such as document classification and natural language processing. In this paper, we propose a novel coordinate descent algorithm for training linear SVM with the L2-loss function. At each step, the proposed method minimizes a one-variable sub-problem while fixing other variables. The sub-problem is solved by Newton steps with the line search technique. The procedure globally converges at the linear rate. As each sub-problem involves only values of a corresponding feature, the proposed approach is suitable when accessing a feature is more convenient than accessing an instance. Experiments show that our method is more efficient and stable than state of the art methods such as Pegasos and TRON. The Support Vector Machine (SVM) of Vapnik (1998) has become widely established as one of the leading approaches to pattern recognition and machine learning. It expresses predictions in terms of a linear combination of kernel functions centred on a subset of the training data, known as support vectors. Despite its widespread success, the SVM suffers from some important limitations, one of the most significant being that it makes point predictions rather than generating predictive distributions. Recently Tipping (1999) has formulated the Relevance Vector Machine (RVM), a probabilistic model whose functional form is equivalent to the SVM. It achieves comparable recognition accuracy to the SVM, yet provides a full predictive distribution, and also requires substantially fewer kernel functions. The original treatment of the RVM relied on the use of type II maximum likelihood (the evidence framework') to provide point estimates of the hyperparameters which govern model sparsity. In this paper we show how the RVM can be formulated and solved within a completely Bayesian paradigm through the use of variational inference, thereby giving a posterior distribution over both parameters and hyperparameters. We demonstrate the practicality and performance of the variational RVM using both synthetic and real world examples. The kernel support vector machine (SVM) is one of the most widely used classification methods; however, the amount of computation required becomes the bottleneck when facing millions of samples. In this paper, we propose and analyze a novel divide-and-conquer solver for kernel SVMs (DC-SVM). In the division step, we partition the kernel SVM problem into smaller subproblems by clustering the data, so that each subproblem can be solved independently and efficiently. We show theoretically that the support vectors identified by the subproblem solution are likely to be support vectors of the entire kernel SVM problem, provided that the problem is partitioned appropriately by kernel clustering. In the conquer step, the local solutions from the subproblems are used to initialize a global coordinate descent solver, which converges quickly as suggested by our analysis. By extending this idea, we develop a multilevel Divide-and-Conquer SVM algorithm with adaptive clustering and early prediction strategy, which outperforms state-of-the-art methods in terms of training speed, testing accuracy, and memory usage. As an example, on the covtype dataset with half-a-million samples, DC-SVM is 7 times faster than LIBSVM in obtaining the exact SVM solution (to within @math relative error) which achieves 96.15 prediction accuracy. Moreover, with our proposed early prediction strategy, DC-SVM achieves about 96 accuracy in only 12 minutes, which is more than 100 times faster than LIBSVM. Two-category support vector machines (SVM) have been very popular in the machine learning community for classification problems. Solving multicategory problems by a series of binary classifiers is quite common in the SVM paradigm; however, this approach may fail under various circumstances. We propose the multicategory support vector machine (MSVM), which extends the binary SVM to the multicategory case and has good theoretical properties. The proposed method provides a unifying framework when there are either equal or unequal misclassification costs. As a tuning criterion for the MSVM, an approximate leave-one-out cross-validation function, called Generalized Approximate Cross Validation, is derived, analogous to the binary case. The effectiveness of the MSVM is demonstrated through the applications to cancer classification using microarray data and cloud classification with satellite radiance profiles. The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT &T Bell Labs. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and Multi-Layer Perceptron classifiers. An interesting property of this approach is that it is an approximate implementation of the Structural Risk Minimization (SRM) induction principle. The derivation of Support Vector Machines, its relationship with SRM, and its geometrical insight, are discussed in this paper. Training a SVM is equivalent to solve a quadratic programming problem with linear and box constraints in a number of variables equal to the number of data points. When the number of data points exceeds few thousands the problem is very challenging, because the quadratic form is completely dense, so the memory needed to store the problem grows with the square of the number of data points. Therefore, training problems arising in some real applications with large data sets are impossible to load into memory, and cannot be solved using standard non-linear constrained optimization algorithms. We present a decomposition algorithm that can be used to train SVM''s over large data sets. The main idea behind the decomposition is the iterative solution of sub-problems and the evaluation of, and also establish the stopping criteria for the algorithm. We present previous approaches, as well as results and important details of our implementation of the algorithm using a second-order variant of the Reduced Gradient Method as the solver of the sub-problems. As an application of SVM''s, we present preliminary results we obtained applying SVM to the problem of detecting frontal human faces in real images. In the interest of deriving classifiers that are robust to outlier observations, we present integer programming formulations of Vapnik's support vector machine (SVM) with the ramp loss and hard margin loss. The ramp loss allows a maximum error of 2 for each training observation, while the hard margin loss calculates error by counting the number of training observations that are in the margin or misclassified outside of the margin. SVM with these loss functions is shown to be a consistent estimator when used with certain kernel functions. In computational studies with simulated and real-world data, SVM with the robust loss functions ignores outlier observations effectively, providing an advantage over SVM with the traditional hinge loss when using the linear kernel. Despite the fact that training SVM with the robust loss functions requires the solution of a quadratic mixed-integer program (QMIP) and is NP-hard, while traditional SVM requires only the solution of a continuous quadratic program (QP), we are able to find good solutions and prove optimality for instances with up to 500 observations. Solution methods are presented for the new formulations that improve computational performance over industry-standard integer programming solvers alone. Support vector machines (SVM) is originally designed for binary classification. To extend it to multi-class scenario, a typical conventional way is to decompose an M-class problem into a series of two-class problems, for which one-against-all is the earliest and one of the most widely used implementations. However, certain theoretical analysis reveals a drawback, i.e., the competence of each classifier is totally neglected when the results of classification from the multiple classifiers are combined for the final decision. To overcome this limitation, this paper introduces reliability measures into the multi-class framework. Two measures are designed: static reliability measure (SRM) and dynamic reliability measure (DRM). SRM works on a collective basis and yields a constant value regardless of the location of the test sample. DRM, on the other hand, accounts for the spatial variation of the classifier's performance. Based on these two reliability measures, a new decision strategy for the one-against-all method is proposed, which is tested on benchmark data sets and demonstrates its effectiveness. A new regression technique based on Vapnik's concept of support vectors is introduced. We compare support vector regression (SVR) with a committee regression technique (bagging) based on regression trees and ridge regression done in feature space. On the basis of these experiments, it is expected that SVR will have advantages in high dimensionality space because SVR optimization does not depend on the dimensionality of the input space. Creation and selection of relevant features for machine learning applications (including image classification) is typically a process requiring significant involvement of domain knowledge. It is thus desirable to cover at least part of that process with semi-automated techniques capable of discovering and visualizing those geometric characteristics of images that are potentially relevant to the classification objective. In this work, we propose to utilize multi-scale singular value decomposition (MSVD) along with approximate nearest neighbors algorithm: both have been recently realized using the randomized approach, and can be efficiently run on large, high-dimensional datasets (sparse or dense). We apply this technique to create a multi-scale view of every point in a publicly available set of LIDAR data of riparian images, with classification objective being separating ground from vegetation. We perform “centralized MSVD” for every point and its neighborhood generated by an approximate nearest neighbor algorithm. After completion of this procedure, the original set of 3-dimensional data is augmented by 36 dimensions generated by MSVD (in three different scales), which is then processed using a novel discretization pre-processing method and the SVM classification algorithm with RBF kernel. The result is two times better that the one previously obtained (in terms of its classification error level). The generic nature of the MSVD mechanism and standard mechanisms used for classification (SVM) suggest a wider utility of the proposed approach for other problems as well. Agricultural management increasingly uses crop maps based on classification of remotely sensed data. However, classification errors can translate to errors in model outputs, for instance agricultural production monitoring (yield, water demand) or crop acreage calculation. Hence, knowledge on the spatial variability of the classier performance is important information for the user. But this is not provided by traditional assessments of accuracy, which are based on the confusion matrix. In this study, classification uncertainty was analyzed, based on the support vector machines (SVM) algorithm. SVM was applied to multi-spectral time series data of RapidEye from different agricultural landscapes and years. Entropy was calculated as a measure of classification uncertainty, based on the per-object class membership estimations from the SVM algorithm. Permuting all possible combinations of available images allowed investigating the impact of the image acquisition frequency and timing, respectively, on the classification uncertainty. Results show that multi-temporal datasets decrease classification uncertainty for different crops compared to single data sets, but there was no “one-image-combination-fits-all” solution. The number and acquisition timing of the images, for which a decrease in uncertainty could be realized, proved to be specific to a given landscape, and for each crop they differed across different landscapes. For some crops, an increase of uncertainty was observed when increasing the quantity of images, even if classification accuracy was improved. Random forest regression was employed to investigate the impact of different explanatory variables on the observed spatial pattern of classification uncertainty. It was strongly influenced by factors related with the agricultural management and training sample density. Lower uncertainties were revealed for fields close to rivers or irrigation canals. This study demonstrates that classification uncertainty estimates by the SVM algorithm provide a valuable addition to traditional accuracy assessments. This allows analyzing spatial variations of the classifier performance in maps and also differences in classification uncertainty within the growing season and between crop types, respectively. 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. The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and non-separable data, working through a non-trivial example in detail. We describe a mechanical analogy, and discuss when SVM solutions are unique and when they are global. We describe how support vector training can be practically implemented, and discuss in detail the kernel mapping technique which is used to construct SVM solutions which are nonlinear in the data. We show how Support Vector machines can have very large (even infinite) VC dimension by computing the VC dimension for homogeneous polynomial and Gaussian radial basis function kernels. While very high VC dimension would normally bode ill for generalization performance, and while at present there exists no theory which shows that good generalization performance is guaranteed for SVMs, there are several arguments which support the observed high accuracy of SVMs, which we review. Results of some experiments which were inspired by these arguments are also presented. We give numerous examples and proofs of most of the key theorems. There is new material, and I hope that the reader will find that even old material is cast in a fresh light. This paper addresses the problem of the classification of hyperspectral remote sensing images by support vector machines (SVMs). First, we propose a theoretical discussion and experimental analysis aimed at understanding and assessing the potentialities of SVM classifiers in hyperdimensional feature spaces. Then, we assess the effectiveness of SVMs with respect to conventional feature-reduction-based approaches and their performances in hypersubspaces of various dimensionalities. To sustain such an analysis, the performances of SVMs are compared with those of two other nonparametric classifiers (i.e., radial basis function neural networks and the K-nearest neighbor classifier). Finally, we study the potentially critical issue of applying binary SVMs to multiclass problems in hyperspectral data. In particular, four different multiclass strategies are analyzed and compared: the one-against-all, the one-against-one, and two hierarchical tree-based strategies. Different performance indicators have been used to support our experimental studies in a detailed and accurate way, i.e., the classification accuracy, the computational time, the stability to parameter setting, and the complexity of the multiclass architecture. The results obtained on a real Airborne Visible Infrared Imaging Spectroradiometer hyperspectral dataset allow to conclude that, whatever the multiclass strategy adopted, SVMs are a valid and effective alternative to conventional pattern recognition approaches (feature-reduction procedures combined with a classification method) for the classification of hyperspectral remote sensing data. Although a support vector machine (SVM) is one of the most frequently used classifiers in the field of intelligent transportation systems and shows competitive performances in various problems, it has the disadvantage of requiring relatively large computations in the testing phase. To make up for this weakness, diverse methods have been researched to reduce the number of support vectors determining the computations in the testing phase. This paper is intended to help engineers using the SVM to easily apply support vector number reduction to their own particular problems by providing a state-of-the-art survey and quantitatively comparing three implementations belonging to postpruning, which exploits the result of a standard SVM. In particular, this paper confirms that the support vector number of a pedestrian classifier using a histogram-of-oriented-gradient-based feature and a radial-basis-function-kernel-based SVM can be reduced by more than 99.5 without any accuracy degradation using iterative preimage addition, which can be downloaded from the Internet. As our society gains a better understanding of how humans have negatively impacted the environment, research related to reducing carbon emissions and overall energy consumption has become increasingly important. One of the simplest ways to reduce energy usage is by making current buildings less wasteful. By improving energy efficiency, this method of lowering our carbon footprint is particularly worthwhile because it reduces energy costs of operating the building, unlike many environmental initiatives that require large monetary investments. In order to improve the efficiency of the heating, ventilation, and air conditioning (HVAC) system of a Manhattan skyscraper, 345 Park Avenue, a predictive computer model was designed to forecast the amount of energy the building will consume. This model uses Support Vector Machine Regression (SVMR), a method that builds a regression based purely on historical data of the building, requiring no knowledge of its size, heating and cooling methods, or any other physical properties. SVMR employs time-delay coordinates as a representation of the past to create the feature vectors for SVM training. This pure dependence on historical data makes the model very easily applicable to different types of buildings with few model adjustments. The SVM regression model was built to predict a week of future energy usage based on past energy, temperature, and dew point temperature data.