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Twin support vector regression (TSVR) aims at finding 휖-insensitive up- and down-bound functions for the training points by solving a pair of smaller-sized quadratic programming problems (QPPs) rather than a single large one as in the conventional SVR. So TSVR works faster than SVR in theory. However, TSVR gives equal emphasis to the points above the up-bound and below the down-bound, which leads to the same influences on the regression function. In fact, points in different positions have different effects on the regressor. Inspired by it, we propose an asymmetric ν-twin support vector regression based on pinball loss function (Asy- ν-TSVR). The new algorithm can effectively control the fitting error by tuning the parameters ν and p. Therefore, it enhances the generalization ability. Moreover, we study the distribution of samples and give the upper bounds for the samples locating in different positions. Numerical experiments on one artificial dataset, eleven benchmark datasets and a real wheat dataset demonstrate the validity of our proposed algorithm. [ABSTRACT FROM AUTHOR]

Support vector regression (SVR) and neural network (NN) models were used to predict average daily gain (ADG), feed efficiency (FE), and feed intake (FI) of broiler chickens during the starter period. Input variables for construction of the models were levels of dietary protein and branched-chain amino acids (BCAA; valine, isoleucine, and leucine). Starting with 241 lines, the SVR and NN models were trained using 120 data lines and the remainder (n = 121) was used as the testing set. The SVR models were developed using different kernel functions including: linear, polynomial (second and third order), radial basis function (RBF), and sigmoidal. In order to evaluate the SVR models, their performance was compared to that of multilayer perceptron (MLP)- and RBF-type NN models. Results indicated that MLP-type NN models were the most accurate in predicting the investigated output variables (R2 for ADG in training and testing = 0.81 and 0.81; FE = 0.87 and 0.87; FI = 0.68 and 0.62). Among the different SVR kernels, best performance was achieved with the RBF (R2 for ADG in training and testing = 0.76 and 0.76; FE = 0.85 and 0.87; FI = 0.46 and 0.48) and polynomial (third order) function (R2 for ADG in training and testing = 0.77 and 0.77; FE = 0.85 and 0.87; FI = 0.46 and 0.39), whose prediction ability was better than that of the RBF-type NN (R2 for ADG in training and testing = 0.75 and 0.75; FE = 0.82 and 0.82; FI = 0.41 and 0.39) models. Sigmoidal SVR models provided the poorest prediction. The work demonstrates that, through proper selection of kernel functions and corresponding parameters, SVR models can be considered as an alternative to NN models in predicting the response of broiler chickens to protein and BCAA. This type of model should also be applicable in poultry and other areas of animal nutrition. [ABSTRACT FROM AUTHOR]

In this paper, a simplification of the necessary and sufficient Karush-Kuhn-Tucker (KKT) optimality conditions for the Lagrangian support vector regression in 2-norm resulting a naïve root finding problem of a system of equations in m variables is proposed, where m is the number of training examples. However, since the resulting system of equations contains terms having the nonsmooth “plus” function, two approaches are considered: (i) the problem is reformulated into an equivalent absolute value equation problem and solved by functional iterative and generalized Newton methods and (ii) solve the original root finding problem by generalized Newton method. The proofs of convergence and pseudo-codes of the iterative methods are given. Numerical experiments performed on a number of synthetic and real-world benchmark datasets showing similar generalization performance with much faster learning speed in comparison with support vector regression (SVR) and as good as performance in comparison with the least squares SVR, unconstrained Lagrangian SVR proposed in Balasundaram et al. (Neural Netw 51:67-79, 2014), twin SVR and extreme learning machine clearly indicate the effectiveness and suitability of the proposed problem formulation solved by functional iterative and generalized Newton methods. [ABSTRACT FROM AUTHOR]

Accurately, forecasting of the flatness plays a highly significant role in the flatness theory and flatness control system, but it is quite difficult and complicated due to the nonlinear characteristics of flatness pattern recognition and lack of available observed data set. Recently, support vector regression (SVR) is being proved an effective machine learning technique for solving nonlinear regression problem with small sample set, because of its nonlinear mapping capabilities. However, it has also been proved that the prediction precision of SVR is highly dependent of SVR parameters, which are hardly choosing for the SVR. As in many excellent algorithms, gravitational search algorithm (GSA) not only has strong global searching capability, but also is very easy to implement. In the paper, an improved gravitational search algorithm (IGSA) is presented to further enhance optimal performance of GSA, and it is employed to serve as a method for pre-selecting SVR parameters. Based on SVR and IGSA algorithms, a forecasting model of flatness pattern recognition is proposed. Where, the IGSA is employed to optimize the parameters of SVR model to determine the parameters as fast and accurate as possible. Afterward, a procedure of forecasting flatness was put forward to evaluate the efficiency of the proposed IGSA-SVR model, which was compared with normal SVR model, IGSA-BP model and extreme learning machine model. The results affirm that the proposed algorithm outperforms other technique. [ABSTRACT FROM AUTHOR]

One of the major activities of financial firms and private investors is to predict future prices of stocks. However, stock index prediction is regarded as a challenging task of the prediction problem since the stock market is a complex, chaotic and nonlinear dynamic system. As stock markets are highly dynamic and exhibit wide variation, it may be more realistic and practical that assumed the stock index data are a nonlinear mixture data. In this study, a hybrid stock index prediction model by utilizing nonlinear independent component analysis (NLICA), support vector regression (SVR) and particle swarm optimization (PSO) is proposed. In the proposed model, first, the NLICA is used to deal with the nonlinearity property of the stock index data. The proposed model utilizes NLICA to extract features from the observed stock index data. The features which can be used to represent underlying/hidden information of the data are then served as the inputs of SVR to build the stock index prediction model. Finally, PSO is applied to optimize the parameters of the SVR prediction model since the parameters of SVR must be carefully selected in establishing an effective and efficient SVR model. In order to evaluate the performance of the proposed approach, the closing indexes of the Taiwan stock exchange capitalization weighted stock index, Shanghai stock exchange composite index and Bombay stock exchange index are used as illustrative examples. Experimental results showed that the proposed hybrid stock index prediction method significantly outperforms the other six comparison models. It is an efficient and effective alternative for stock index forecasting. [ABSTRACT FROM AUTHOR]

Stock index forecasting is one of the most difficult tasks that financial organizations, firms and private investors have to face. Support vector regression (SVR) has become a popular alternative in stock index forecasting tasks due to its generalization capability in obtaining a unique solution. However, the major limitation of SVR is that it cannot capture the relative importance of independent variables to the dependent variable when many potential independent variables are considered. This study incorporates feature selection method and SVR for building stock index forecasting model. The proposed model uses multivariate adaptive regression splines (MARS), an effective nonlinear and nonparametric regression methodology, to identify important forecasting variables. The obtained significant predictor variables are then served as the inputs for the SVR model. Experimental results reveal that the obtained important variables from MARS can improve the forecasting performance of the SVR models. Moreover, the MARS results provide useful information about the relationship between the selected predictor variables and stock index through the obtained basis functions, important predictor variables and the MARS prediction function. Hence, the proposed stock index forecasting model can generate good forecasting performance and exhibits the capability of identifying significant predictor variables, which provide valuable information for further investment decisions/strategies. [ABSTRACT FROM AUTHOR]

In this paper, a simple and linearly convergent Lagrangian support vector machine algorithm for the dual of the twin support vector regression (TSVR) is proposed. Though at the outset the algorithm requires inverse of matrices, it has been shown that they would be obtained by performing matrix subtraction of the identity matrix by a scalar multiple of inverse of a positive semi-definite matrix that arises in the original formulation of TSVR. The algorithm can be easily implemented and does not need any optimization packages. To demonstrate its effectiveness, experiments were performed on well-known synthetic and real-world datasets. Similar or better generalization performance of the proposed method in less training time in comparison with the standard and twin support vector regression methods clearly exhibits its suitability and applicability. [ABSTRACT FROM AUTHOR]

In this paper, extreme learning machine (ELM) for ε-insensitive error loss function-based regression problem formulated in 2-norm as an unconstrained optimization problem in primal variables is proposed. Since the objective function of this unconstrained optimization problem is not twice differentiable, the popular generalized Hessian matrix and smoothing approaches are considered which lead to optimization problems whose solutions are determined using fast Newton-Armijo algorithm. The main advantage of the algorithm is that at each iteration, a system of linear equations is solved. By performing numerical experiments on a number of interesting synthetic and real-world datasets, the results of the proposed method are compared with that of ELM using additive and radial basis function hidden nodes and of support vector regression (SVR) using Gaussian kernel. Similar or better generalization performance of the proposed method on the test data in comparable computational time over ELM and SVR clearly illustrates its efficiency and applicability. [ABSTRACT FROM AUTHOR]

Twin support vector regression (TSVR) was proposed recently as a novel regressor that tries to find a pair of nonparallel planes, i.e., ε-insensitive up- and down-bounds, by solving two related SVM-type problems. However, it may incur suboptimal solution since its objective function is positive semi-definite and the lack of complexity control. In order to address this shortcoming, we develop a novel SVR algorithm termed as smooth twin SVR (STSVR). The idea is to reformulate TSVR as a strongly convex problem, which results in unique global optimal solution for each subproblem. To solve the proposed optimization problem, we first adopt a smoothing technique to convert the original constrained quadratic programming problems into unconstrained minimization problems, and then use the well-known Newton-Armijo algorithm to solve the smooth TSVR. The effectiveness of the proposed method is demonstrated via experiments on synthetic and real-world benchmark datasets. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to predict NO and NO2 concentrations 4 days in advance by comparing two artificial intelligence learning methods, namely, multi-layer perceptron and support vector machines, on two kinds of spatial embedding of the temporal time series. Hourly values of NO and NO2 concentrations, as well as meteorological variables were recorded in a cross-road monitoring station with heavy traffic in Szeged, in order to build a model for predicting NO and NO2 concentrations several hours in advance. The prediction of NO and NO2 concentrations was performed partly on the basis of their past values, and partly on the basis of temperature, humidity and wind speed data. Since NO can be predicted more accurately, its values were considered primarily when forecasting NO2. Time series prediction can be interpreted in a way that is suitable for artificial intelligence learning. Two effective learning methods, namely, multi-layer perceptron and support vector regression are used to provide efficient non-linear models for NO and NO2 time series predictions. Multi-layer perceptron is widely used to predict these time series, but support vector regression has not yet been applied for predicting NO and NO2 concentrations. Three commonly used linear algorithms were considered as references: 1-day persistence, average of several day persistence and linear regression. Based on the good results of the average of several day persistence, a prediction scheme was introduced, which forms weighted averages instead of simple ones. The optimization of these weights was performed with linear regression in linear case and with the learning methods mentioned in non-linear case. Concerning the NO predictions, the non-linear learning methods give significantly better predictions than the reference linear methods. In the case of NO2, the improvement of the prediction is considerable, however, it is less notable than for NO. [ABSTRACT FROM AUTHOR]