The Experts below are selected from a list of 41547 Experts worldwide ranked by ideXlab platform

Xiangyu Hua - One of the best experts on this subject based on the ideXlab platform.

  • robust Support Vector Regression with generic quadratic nonconvex e insensitive loss
    Applied Mathematical Modelling, 2020
    Co-Authors: Junbin Gao, Yuanhai Shao, Yan Jin, Xiangyu Hua
    Abstract:

    Abstract In this paper, we propose a robust Support Vector Regression with a novel generic nonconvex quadratic e-insensitive loss function. The proposed method is robust to outliers or noise since it can adaptively control the loss value and decrease the negative influence of outliers or noise on the decision function by adjusting the elastic interval parameter and adaptive robustification parameter. Given the nature of the nonconvexity of the optimization problem, a concave-convex programming procedure is employed to solve the proposed problem. Experimental results on two artificial data sets and three real-world data sets indicate that the proposed method outperforms Support Vector Regression, L1-norm Support Vector Regression, least squares Support Vector Regression, robust least squares Support Vector Regression, and Support Vector Regression with the Huber loss function on both robustness and generalization ability.

Deepak Gupta - One of the best experts on this subject based on the ideXlab platform.

  • on robust asymmetric lagrangian ν twin Support Vector Regression using pinball loss function
    Applied Soft Computing, 2021
    Co-Authors: Deepak Gupta, Umesh Gupta
    Abstract:

    Abstract The main objective of twin Support Vector Regression (TSVR) is to find the optimum Regression function based on the e -insensitive up- and down-bound with equal influences on the Regression function where all the data points have a different location above the up-bound points and below the down-bound points. However, the effects of all data points must be distinct based on their distribution in the Regression function. Recently, asymmetric v-twin Support Vector Regression (Asy-v-TSVR) is encouraged on the same subject but still, the present matrices in the mathematical formulation have faced the problem of semi-definite. In order to handle this problem effectively, a new regressor model named as robust asymmetric Lagrangian v-twin Support Vector Regression using pinball loss function (URALTSVR) proposes as a pair of the unconstrained minimization problem to handle not only the noise sensitivity and instability of re-sampling but also consist positive definite matrices. Here, we suggest the proposed model URALTSVR in such a way where the pinball loss function is playing a vital role to control the fitting error inside the asymmetric tube. One of the advantages is that unlike TSVR and Asy-v-TSVR, it considers the concept of structural risk minimization principle through the inclusion of regularization term as well as change the one-norm of the Vector of the slack variable by two-norm, which yields the dual problem to be strongly convex, stable and well-posed. Aforementioned, the proposed formulation has a continuous and piecewise quadratic problem that is solved by their gradients based iterative approaches. Specifically, we analyze the three implementations of URALTSVR with the baselines approaches Support Vector Regression (SVR), TSVR and Asy-v-TSVR, which discard the dependencies to solve a pair of quadratic programming problem (QPP) for obtaining the unique global solution. Overall, SRALTSVR1 based on smooth approximation function performs outstanding for artificial and real-world datasets.

  • training lagrangian twin Support Vector Regression via unconstrained convex minimization
    Knowledge Based Systems, 2014
    Co-Authors: S Balasundaram, Deepak Gupta
    Abstract:

    In this paper, a new unconstrained convex minimization problem formulation is proposed as the Lagrangian dual of the 2-norm twin Support Vector Regression (TSVR). The proposed formulation leads to two smaller sized unconstrained minimization problems having their objective functions piece-wise quadratic and differentiable. It is further proposed to apply gradient based iterative method for solving them. However, since their objective functions contain the non-smooth 'plus' function, two approaches are taken: (i) either considering their generalized Hessian or introducing a smooth function in place of the 'plus' function, and applying Newton-Armijo algorithm; (ii) obtaining their critical points by functional iterative algorithm. Computational results obtained on a number of synthetic and real-world benchmark datasets clearly illustrate the superiority of the proposed unconstrained Lagrangian twin Support Vector Regression formulation as comparable generalization performance is achieved with much faster learning speed in accordance with the classical Support Vector Regression and TSVR.

Zongxia Xie - One of the best experts on this subject based on the ideXlab platform.

  • short term wind speed or power forecasting with heteroscedastic Support Vector Regression
    IEEE Transactions on Sustainable Energy, 2016
    Co-Authors: Shiguang Zhang, Zongxia Xie
    Abstract:

    Wind speed or wind power forecasting plays an important role in large-scale wind power penetration due to their uncertainty. Support Vector Regression, widely used in wind speed or wind power forecasting, aims at discovering natural structures of wind variation hidden in historical data. Most current Regression algorithms, including least squares Support Vector Regression (SVR), assume that the noise of the data is Gaussian with zero mean and the same variance. However, it is discovered that the uncertainty of short-term wind speed satisfies Gaussian distribution with zero mean and heteroscedasticity in this work. This kind of task is called heteroscedastic Regression. In order to deal with this problem, we derive an optimal loss function for heteroscedastic Regression and develop a new framework of $\nu$ -SVR for learning tasks of Gaussian noise (GN) with heteroscedasticity. In addition, we introduce the stochastic gradient descent (SGD) method to solve the proposed model, which leads the models to be trained online. Finally, we reveal the uncertainty properties of wind speed with two real-world datasets and test the proposed algorithms on these data. The experimental results confirm the effectiveness of the proposed model.

Jinxing Che - One of the best experts on this subject based on the ideXlab platform.

  • subsampled Support Vector Regression ensemble for short term electric load forecasting
    Energy, 2018
    Co-Authors: Jinxing Che, Youlong Yang
    Abstract:

    Abstract Accurate prediction of short-term electric load is critical for power system planning and operation. However, integration of the point estimation into the power system is constrained by its uncertainty nature and low interpretability for confidence level. For this propose, this study derives and tests methods to model and forecast short term load point estimation and its confidence interval length by using Subsampled Support Vector Regression ensemble (SSVRE). To improve the computational accuracy and efficiency, a subsampling strategy is designed for the programming implementation of the Support Vector Regression (SVR) learning process. This subsampling strategy ensures that each individual SVR ensemble has enough diversity. Then, for model selection, we present a novel swarm optimization learning based on all the individual SVR ensembles. The advantage of swarm coordination learning is that we can ensure that each individual SVR ensemble has enough strength for forecasting the short term load data. Theoretically, the latest research shows that formal statistical inference procedures can be determined for small size subsamples based ensemble. In practice, a subset of small size subsamples is employed for the speeding-up of SVR learning process. Accordingly, the results indicate the better performance and lower uncertainty of SSVRE model in forecasting short term electric load.

  • Support Vector Regression based on optimal training subset and adaptive particle swarm optimization algorithm
    Applied Soft Computing, 2013
    Co-Authors: Jinxing Che
    Abstract:

    Abstract Support Vector Regression (SVR) has become very promising and popular in the field of machine learning due to its attractive features and profound empirical performance for small sample, nonlinearity and high dimensional data application. However, most existing Support Vector Regression learning algorithms are limited to the parameters selection and slow learning for large sample. This paper considers an adaptive particle swarm optimization (APSO) algorithm for the parameters selection of Support Vector Regression model. In order to accelerate its training process while keeping high accurate forecasting in each parameters selection step of APSO iteration, an optimal training subset (OTS) method is carried out to choose the representation data points of the full training data set. Furthermore, the optimal parameters setting of SVR and the optimal size of OTS are studied preliminary. Experimental results of an UCI data set and electric load forecasting in New South Wales show that the proposed model is effective and produces better generalization performance.

Xinjun Peng - One of the best experts on this subject based on the ideXlab platform.

  • efficient twin parametric insensitive Support Vector Regression model
    Neurocomputing, 2012
    Co-Authors: Xinjun Peng
    Abstract:

    In this paper, an efficient twin parametric insensitive Support Vector Regression (TPISVR) is proposed. The TPISVR determines indirectly the Regression function through a pair of nonparallel parametric-insensitive up- and down-bound functions solved by two smaller sized Support Vector machine (SVM)-type problems, which causes the TPISVR not only have the faster learning speed than the classical SVR, but also be suitable for many cases, especially when the noise is heteroscedastic, that is, the noise strongly depends on the input value. The proposed method has the advantage of using the ratio of the parameters @n and c for controlling the bounds of fractions of Support Vectors and errors. The experimental results on several artificial and benchmark datasets indicate that the TPISVR not only has fast learning speed, but also shows good generalization performance.

  • primal twin Support Vector Regression and its sparse approximation
    Neurocomputing, 2010
    Co-Authors: Xinjun Peng
    Abstract:

    Twin Support Vector Regression (TSVR) obtains faster learning speed by solving a pair of smaller sized Support Vector machine (SVM)-typed problems than classical Support Vector Regression (SVR). In this paper, a primal version for TSVR, termed primal TSVR (PTSVR), is first presented. By introducing a quadratic function to approximate its loss function, PTSVR directly optimizes the pair of quadratic programming problems (QPPs) of TSVR in the primal space based on a series of sets of linear equations. PTSVR can obviously improve the learning speed of TSVR without loss of the generalization. To improve the prediction speed, a greedy-based sparse TSVR (STSVR) in the primal space is further suggested. STSVR uses a simple back-fitting strategy to iteratively select its basis functions and update the augmented Vectors. Computational results on several synthetic as well as benchmark datasets confirm the merits of PTSVR and STSVR.