Standard Standard Support Vector Machine Research Articles

Postearthquake Casualty Prediction Based on Heatmaps and Wavelet Supporting Vector Machines

The prediction of casualties in earthquakes is very important for improving the efficiency of emergency rescue measures and reducing the number of casualties. Given the time lag and poor accuracy of population density data published in statistical yearbooks, a Baidu heatmap is used in this study to accurately estimate the regional population density. Based on the standard support vector machine (SVM) prediction model, a piecewise loss function and a robust wavelet kernel function are proposed to effectively reduce the prediction error. Given a characteristic attribute set of factors related to earthquake casualties, the new prediction model is tested in 34 cases involving earthquake cases on the Chinese mainland since 2011. Compared with other prediction techniques, the proposed robust wavelet SVM can converge more quickly, and the prediction error is lower than that of the standard backpropagation neural network (BPNN) and standard SVM.

A Novel Support Vector Machine Based on Hybrid Bat Algorithm and Its Application to Identification of Low Velocity Impact Areas

The standard support vector machine (SVM) performs poorly on the identification problem of low velocity impact areas due to its lower accuracy rate. Improving SVM’s performance using the bat algorithm (BA) is feasible, but BA has the premature convergence problem. In this study, a hybrid bat algorithm with double mutation operations (DMBA), in which the Cauchy mutation operator and the extremal optimization mutation operator are integrated into BA, is proposed to enhance BA’s ability to jump out of the local optima. Then, a novel SVM based on this hybrid BA, which is called SVM_DMBA, is developed to address the identification problem. Compared with the standard SVM and twelve improved SVM methods which are combined with the standard algorithms, advanced algorithms, and bat variants, the significant performance of SVM_DMBA is validated using UCI datasets. Moreover, to identify low velocity impact areas, SVM_DMBA is applied to the low velocity impact localization system based on fiber Bragg grating (FBG) sensors. The statistical results indicate that SVM_DMBA is a significantly effective method for identifying the low velocity impact areas and generates higher identification accuracy than comparative methods. For 64 low velocity impact areas of $30\,\,\text {mm}\times 30\,\,\text {mm}$ on an aluminium plate, the average identification error obtained by SVM_DMBA is 1.615%.

A new adaptive weighted imbalanced data classifier via improved support vector machines with high-dimension nature

The standard support vector machine (SVM) models are widely used in various fields, but we show that they are not rationally defined from the perspective of geometric point, which is likely to degrade the models’ performances theoretically, especially under the high-dimensional cases. In this paper, we consider a composite penalty and propose an elastic net support vector machine (ENSVM). Unlike the doubly regularized support vector machine (DrSVM, Wang et al. (2006)), we impose the penalty to the slack variables rather than the normal vectors of the hyperplane. Then, we prove that ENSVM is more rationally defined than standard SVM and DrSVM (in section 3.2.1). Moreover, the ENSVM demonstrates a more stable and high-dimension nature inherently, while the simulation results cogently support these merits. Besides, we also combine fused weights with ENSVM and propose an adaptive weighted elastic net support vector machine (AWENSVM), to make the primal model more adaptive and robust to the imbalanced data. Compared with the other popular SVMs, the AWENSVM model proposed in this paper performs better obviously.

Infinite norm large margin classifier

Standard support vector machine (SVM) achieves good generalization by maximizing margin and the leading optimization problem can be solved by quadratic programming (QP). Geometrically, such margin description benefits from closed-formed Euclidian distance formula between the support vectors to the decision plane (point-to-plane) based on L2 norm. However, for non-L2 norm learning machines, such as L1- or infinite-norm, due to their non-differentiability, it is difficult to obtain close-formed point-to-plane distance and thus rarely seen large margin classifiers based on other norms in literatures. In this paper, we proposed an infinite-norm large margin classifier, termed as InfLMC. Firstly, for any given points and a plane, the foresaid close-formed distance and projection formula, based on infinite nom, are mathematically described, and then, similar to L2-SVM, infinite norm margin can be directly derived. Thus, the proposed InfLMC is constructed by maximizing margin and simultaneously minimizing experience error. Furthermore, the leading optimization problem can be solved by a linear programming problem (LP) rather than QP in standard SVM. Finally, the experimental results on some artificial and UCI datasets show its performance in test correctness and running time-consume.

Large-Scale Data Classification Based on Ball Vector Machine

The quadratic programming problem in the standard support vector machine (SVM) algorithm has high time complexity and space complexity in solving the large-scale problems which becomes a bottleneck in the SVM applications. Ball Vector Machine (BVM) converts the quadratic programming problem of the traditional SVM into the minimum enclosed ball problem (MEB). It can indirectly get the solution of quadratic programming through solving the MEB problem which significantly reduces the time complexity and space complexity. The experiments show that when handling five large-scale and high-dimensional data sets, the BVM and standard SVM have a considerable accuracy, but the BVM has higher speed and less requirement space than standard SVM.

Relaxing support vectors for classification

We introduce a novel modification to standard support vector machine (SVM) formulations based on a limited amount of penalty-free slack to reduce the influence of misclassified samples or outliers. We show that free slack relaxes support vectors and pushes them towards their respective classes, hence we use the name relaxed support vector machines (RSVM) for our method. We present theoretical properties of the RSVM formulation and develop its dual formulation for nonlinear classification via kernels. We show the connection between the dual RSVM and the dual of the standard SVM formulations. We provide error bounds for RSVM and show it to be stable, universally consistent and tighter than error bounds for standard SVM. We also introduce a linear programming version of RSVM, which we call RSVMLP. We apply RSVM and RSVMLP to synthetic data and benchmark binary classification problems, and compare our results with standard SVM classification results. We show that relaxed influential support vectors may lead to better classification results. We develop a two-phase method called RSVM2 for multiple instance classification (MIC) problems, where RSVM formulations are used as classifiers. We extend the two-phase method to the linear programming case and develop RSVMLP2. We demonstrate the classification characteristics of RSVM2 and RSVMLP2, and report our classification results compared to results obtained by other SVM-based MIC methods on public benchmark datasets. We show that both RSVM2 and RSVMLP2 are faster and produce more accurate classification results.

Kernel machines for epilepsy diagnosis via EEG signal classification: A comparative study

We carry out a systematic assessment on a suite of kernel-based learning machines while coping with the task of epilepsy diagnosis through automatic electroencephalogram (EEG) signal classification. The kernel machines investigated include the standard support vector machine (SVM), the least squares SVM, the Lagrangian SVM, the smooth SVM, the proximal SVM, and the relevance vector machine. An extensive series of experiments was conducted on publicly available data, whose clinical EEG recordings were obtained from five normal subjects and five epileptic patients. The performance levels delivered by the different kernel machines are contrasted in terms of the criteria of predictive accuracy, sensitivity to the kernel function/parameter value, and sensitivity to the type of features extracted from the signal. For this purpose, 26 values for the kernel parameter (radius) of two well-known kernel functions (namely, Gaussian and exponential radial basis functions) were considered as well as 21 types of features extracted from the EEG signal, including statistical values derived from the discrete wavelet transform, Lyapunov exponents, and combinations thereof. We first quantitatively assess the impact of the choice of the wavelet basis on the quality of the features extracted. Four wavelet basis functions were considered in this study. Then, we provide the average accuracy (i.e., cross-validation error) values delivered by 252 kernel machine configurations; in particular, 40%/35% of the best-calibrated models of the standard and least squares SVMs reached 100% accuracy rate for the two kernel functions considered. Moreover, we show the sensitivity profiles exhibited by a large sample of the configurations whereby one can visually inspect their levels of sensitiveness to the type of feature and to the kernel function/parameter value. Overall, the results evidence that all kernel machines are competitive in terms of accuracy, with the standard and least squares SVMs prevailing more consistently. Moreover, the choice of the kernel function and parameter value as well as the choice of the feature extractor are critical decisions to be taken, albeit the choice of the wavelet family seems not to be so relevant. Also, the statistical values calculated over the Lyapunov exponents were good sources of signal representation, but not as informative as their wavelet counterparts. Finally, a typical sensitivity profile has emerged among all types of machines, involving some regions of stability separated by zones of sharp variation, with some kernel parameter values clearly associated with better accuracy rates (zones of optimality).

Hyperellipsoidal Statistical Classifications in a Reproducing Kernel Hilbert Space

Standard support vector machines (SVMs) have kernels based on the Euclidean distance. This brief extends standard SVMs to SVMs with kernels based on the Mahalanobis distance. The extended SVMs become a special case of the Euclidean distance when the covariance matrix in a reproducing kernel Hilbert space is degenerated to an identity. The Mahalanobis distance leads to hyperellipsoidal kernels and the Euclidean distance results in hyperspherical ones. In this brief, the Mahalanobis distance-based kernel in a reproducing kernel Hilbert space is developed systematically. Extensive experiments demonstrate that the hyperellipsoidal kernels slightly outperform the hyperspherical ones, with fewer SVs.

Prediction Model of Non-Iterative Least Squares Support Vector Machines Based on Quadratic Renyi-Entropy

By comparing and analysing the model of non-iterative least squares support vector machines (LS-SVM) based on quadratic Renyi-entropy, traditional LS-SVM model and standard support vector machines (SVM) model, this paper concludes whether the number of training samples or computing time,non-iterative LS-SVM model based on quadratic Renyi-entropy are significantly better than the model of traditional LS-SVM and standard SVM model and it also proves the effectiveness of applying the concept of quadratic Renyi-entropy on financial distress prediction. At the same time, by the comparison of different point of 3 years of ST which is from 1to 2, the author concludes the forecast accuracy of 1 year ago before ST, the further distance away from the piont of ST, the lower the prediction accuracy is.

An SMO Algorithm for the Potential Support Vector Machine

We describe a fast sequential minimal optimization (SMO) procedure for solving the dual optimization problem of the recently proposed potential support vector machine (P-SVM). The new SMO consists of a sequence of iteration steps in which the Lagrangian is optimized with respect to either one (single SMO) or two (dual SMO) of the Lagrange multipliers while keeping the other variables fixed. An efficient selection procedure for Lagrange multipliers is given, and two heuristics for improving the SMO procedure are described: block optimization and annealing of the regularization parameter epsilon. A comparison of the variants shows that the dual SMO, including block optimization and annealing, performs efficiently in terms of computation time. In contrast to standard support vector machines (SVMs), the P-SVM is applicable to arbitrary dyadic data sets, but benchmarks are provided against libSVM's epsilon-SVR and C-SVC implementations for problems that are also solvable by standard SVM methods. For those problems, computation time of the P-SVM is comparable to or somewhat higher than the standard SVM. The number of support vectors found by the P-SVM is usually much smaller for the same generalization performance.

A WEIGHTED SUPPORT VECTOR MACHINE FOR DATA CLASSIFICATION

This paper presents a weighted support vector machine (WSVM) to improve the outlier sensitivity problem of standard support vector machine (SVM) for two-class data classification. The basic idea is to assign different weights to different data points such that the WSVM training algorithm learns the decision surface according to the relative importance of data points in the training data set. The weights used in WSVM are generated by a robust fuzzy clustering algorithm, kernel-based possibilistic c-means (KPCM) algorithm, whose partition generates relative high values for important data points but low values for outliers. Experimental results indicate that the proposed method reduces the effect of outliers and yields higher classification rate than standard SVM does when outliers exist in the training data set.

Robust support vector machine with bullet hole image classification

This paper proposes a robust support vector machine for pattern classification, which aims at solving the over-fitting problem when outliers exist in the training data set. During the robust training phase, the distance between each data point and the center of class is used to calculate the adaptive margin. The incorporation of the average techniques to the standard support vector machine (SVM) training makes the decision function less detoured by outliers, and controls the amount of regularization automatically. Experiments for the bullet hole classification problem show that the number of the support vectors is reduced, and the generalization performance is improved significantly compared to that of the standard SVM training.