Smooth Support Vector Regression Research Articles

Development of ε-insensitive smooth support vector regression for predicting minimum miscibility pressure in CO2 flooding

Development of ε-insensitive smooth support vector regression for predicting minimum miscibility pressure in CO2 flooding

One norm linear programming support vector regression

In this paper, a new linear programming formulation of a 1-norm support vector regression (SVR) is proposed whose solution is obtained by solving an exterior penalty problem in the dual space as an unconstrained minimization problem using Newton method. The solution of modified unconstrained minimization problem reduces to solving just system of linear equations as opposed to solving quadratic programming problem in SVR, which leads to extremely simple and fast algorithm. The algorithm converges from any starting point and can be easily implemented in MATLAB without using any optimization packages. The main advantage of the proposed approach is that it leads to a robust and sparse model representation meaning that many components of the optimal solution vector will become zero and therefore the decision function can be determined using much less number of support vectors in comparison to SVR, smooth SVR (SSVR) and weighted SVR (WSVR). To demonstrate its effectiveness, experiments were performed on well-known synthetic and real-world benchmark datasets. Similar or better generalization performance of the proposed method in less training time in comparison with SVR, SSVR and WSVR clearly exhibits its suitability and applicability.

Modeling Method Based on Smooth Support Vector Regression with Independent Component Analysis Feature Extraction

Smooth Support Vector Regression (SSVR) is new modified edition of traditional support vector regression for better performance. To further improve the modeling capability of SSVR, it is necessary to take into account the feature extraction based on Independent Component Analysis (ICA) before SSVR. Simulation on the example of function approximation shows that the result of SSVR based on ICA feature extraction is better than that of SSVR without ICA preprocess.

Slump Flow Modeling of Self-Compacting Concrete Using Smooth Support Vector Regression (SSVR)

A new method of prediction based on smooth support vector regression (SSVR) is introduced to resolve the slump flow modelling of self-compacting concrete (SCC). The slump flow is a function of the content of all concrete ingredients, including cement, silica fume, water, superplasticizer, coarse and fine aggregate. In this paper, the basic ideas underlying SSVR are reviewed, and the potential of the SSVR for multiple regression (modelling) problems is demonstrated by applying the method to model of slump flow from experimental data. The results of experimentation indicate that SSVR has excellent performance on slump flow prediction. Compared with traditional prediction method such as second order regression, SSVR has much more accurate and effective to prediction of slump flow and it is very promising result.

Trend analysis of rotor-to-stator impact-rub based on smooth support vector regression

Traditional methods of mathematical modelling usually get complicated non-linear models for rub-impact fault. Besides, time-frequency domain analysis is very difficult to solve the problem because of its own limitation. Based on analysis need of degree and trend of rub-impact fault, support vector regression (SVR) arithmetic is imported, which adopts method of time series analysis. Smooth support vector regression (SSVR) using smoothing method in SVR suggests a best tradeoff between complexity of model and learning ability to establish linear model which is able to reflect the implicit mechanism of series data. Model of Jeffcott rotor was established to simulate actual rotor rub-impact fault, and SSVR was applied to analyse trend of time series data of rub-impact fault. The results indicate that SSVR is obviously superior to neural network, and is effective to analyse trend of rotor-to-stator impact-rub fault, which has guiding significance for using and maintenance of rotating machine.

Incremental smooth support vector regression for Takagi–Sugeno fuzzy modeling

We propose an architecture for Takagi–Sugeno (TS) fuzzy system and develop an incremental smooth support vector regression (ISSVR) algorithm to build the TS fuzzy system. ISSVR is based on the ε-insensitive smooth support vector regression (ε-SSVR), a smoothing strategy for solving ε-SVR, and incremental reduced support vector machine (RSVM). The ISSVR incrementally selects representative samples from the given dataset as support vectors. We show that TS fuzzy modeling is equivalent to the ISSVR problem under certain assumptions. A TS fuzzy system can be generated from the given training data based on the ISSVR learning with each fuzzy rule given by a support vector. Compared with other fuzzy modeling methods, more forms of membership functions can be used in our model, and the number of fuzzy rules of our model is much smaller. The performance of our model is illustrated by extensive experiments and comparisons.

Study of E-Smooth Support Vector Regression and Comparison with E- Support Vector Regression and Potential Support Vector Machines for Prediction for the Antitubercular Activity of Oxazolines and Oxazoles Derivatives

A new smoothing method for solving ? -support vector regression (?-SVR), tolerating a small error in fitting a given data sets nonlinearly is proposed in this study. Which is a smooth unconstrained optimization reformulation of the traditional linear programming associated with a ?-insensitive support vector regression. We term this redeveloped problem as ?-smooth support vector regression (?-SSVR). The performance and predictive ability of ?-SSVR are investigated and compared with other methods such as LIBSVM (?-SVR) and P-SVM methods. In the present study, two Oxazolines and Oxazoles molecular descriptor data sets were evaluated. We demonstrate the merits of our algorithm in a series of experiments. Primary experimental results illustrate that our proposed approach improves the regression performance and the learning efficiency. In both studied cases, the predictive ability of the ?- SSVR model is comparable or superior to those obtained by LIBSVM and P-SVM. The results indicate that ?-SSVR can be used as an alternative powerful modeling method for regression studies. The experimental results show that the presented algorithm ?-SSVR, plays better precisely and effectively than LIBSVMand P-SVM in predicting antitubercular activity.

An Incremental Approach to TS Fuzzy Modeling

This paper proposes an incremental smooth support vector regression (ISSVR) method for TS fuzzy modeling. Under certain assumptions on membership functions, we propose an optimization problem for TS fuzzy modeling based on the structural risk minimization principle. We show that this problem is an SVR problem with non-positive definite kernels. It cannot be solved using conventional SVR. Then we establish a connection between this TS fuzzy modeling problem and smooth support vector regression (SSVR), which is a smoothing strategy for solving SVR. The problem is always solvable using SSVR because SSVR puts no restrictions on the kernel. Then we apply an incremental approach to the SSVR by selecting informative samples from the training dataset. Taking advantage of SSVR, more forms of membership functions can be used in our model compared with conventional methods. Experiments show that the proposed ISSVR-based TS fuzzy model has good generalization ability with small number of fuzzy rules.

TS-fuzzy modeling based on ε-insensitive smooth support vector regression

This paper establishes a connection between Takagi-Sugeno TS fuzzy systems and e-insensitive smooth support vector regression e-SSVR, a smooth strategy for solving e-SVR. In previous e-SVR-based fuzzy models, the form of membership functions is restricted by the Mercer condition. The e-SSVR formulation puts no restrictions on the kernel. Therefore, the proposed e-SSVR-based TS-fuzzy modeling method relaxes the restriction on membership functions. By applying the reduced kernel technique, the number of fuzzy rules is reduced without scarifying the generalization ability. The computational complexity is also reduced by the reduced kernel technique. The performance of our method is illustrated by extensive experiments and comparisons.

A Smooth Support Vector Regression Based on Maclaurin Series Expansion

A Smooth Support Vector Regression Based on Maclaurin Series Expansion

The Asymptotic Study of Smooth Entropy Support Vector Regression

In this paper, a novel formulation, smooth entropy support vector regression (SESVR), is proposed, which is a smooth unconstrained optimization reformulation of the traditional linear programming associated with an e-insensitive support vector regression. An entropy penalty function is substituted for the plus function to make the objective function con- tinuous ,and a new algorithm involving the Newton-Armijo algorithm proposed to solve the SESVR converge globally to the solution. Theoretically, we give a brief convergence proof to our algorithm. The advantages of our presented algorithm are that we only need to solve a system of linear equations iteratively instead of solving a convex quadratic program, as is the case with a conventional SVR, and lessen the influence of the penalty parameter C in our model. In order to show the efficiency of our algorithm, we employ it to forecast an actual electricity power short-term load. The experimental results show that the presented algorithm, SESVR, plays better precisely and effectively than SVMlight and LIBSVR in stochastic time series forecasting.

Research on Smooth Support Vector Regression Based on Hermite

Polynomial smooth techniques are applied to Support Vector Regression model by an accurate smooth approximation which is offered by Hermite Interpolation polynomial. We use Hermite Interpolation to generate a new polynomial smooth function which is proposed for thefunction in ε-insensitive support vector regression of interpolation functions. Their important property is discussed. It can be shown that the approximation accuracy and smoothing rank of polynomial functions can be as high as required.

A Sliding‐window Smooth Support Vector Regression Model for Nonlinear Blast Furnace System

AbstractBlast furnace is one of the most complex industrial reactors and remains some unsolved puzzles, such as blast furnace automation, prediction of the inner thermal state, etc. In this work, a sliding‐window smooth support vector regression model is presented to address the issue of predicting the blast furnace inner thermal state, represented by the silicon content in blast furnace hot metal in the context. Different from the traditional numerical prediction models of silicon, the constructed SW‐SSVR model is devoted to predicting the changing trend of silicon and exhibits good performance with high percentage of successful trend prediction, competitive computational speed and timely online service. Additionally, some sharp fluctuation trend in the silicon test data can also be followed well by the SW‐SSVR model, which is always difficult for traditional data–driven based silicon prediction models. All of these indicate that the SW‐SSVR model is a good candidate to predict the change of blast furnace inner thermal state, and may provide a guide for operators to take proper action on operating blast furnace in advance.

A Novel Smooth Support Vector Regression Based on CHKS Function

This paper presents a new smooth approach to solve support vector regression (SVR). Based on Karush-Kuhn-Tucker complementary condition in optimization theory, a smooth unconstrained optimization model for SVR is built. Since the objective function of the unconstrained SVR model is non-smooth, we apply the smooth techniques and replace the ε-insensitive loss function by CHKS function. Newton-Armijo algorithm is used to solve the smooth CHKS-SSVR model. Primary numerical results illustrate that our proposed approach improves the regression performance and the learning efficiency.

On finite Newton method for support vector regression

In this paper, we propose a Newton iterative method of solution for solving an e-insensitive support vector regression formulated as an unconstrained optimization problem. The proposed method has the advantage that the solution is obtained by solving a system of linear equations at a finite number of times rather than solving a quadratic optimization problem. For the case of linear or kernel support vector regression, the finite termination of the Newton method has been proved. Experiments were performed on IBM, Google, Citigroup and Sunspot time series. The proposed method converges in at most six iterations. The results are compared with that of the standard, least squares and smooth support vector regression methods and of the exact solutions clearly demonstrate the effectiveness of the proposed method.

/spl epsi/-SSVR: a smooth support vector machine for /spl epsi/-insensitive regression

A new smoothing strategy for solving /spl epsi/-support vector regression (/spl epsi/-SVR), tolerating a small error in fitting a given data set linearly or nonlinearly, is proposed in this paper. Conventionally, /spl epsi/-SVR is formulated as a constrained minimization problem, namely, a convex quadratic programming problem. We apply the smoothing techniques that have been used for solving the support vector machine for classification, to replace the /spl epsi/-insensitive loss function by an accurate smooth approximation. This will allow us to solve /spl epsi/-SVR as an unconstrained minimization problem directly. We term this reformulated problem as /spl epsi/-smooth support vector regression (/spl epsi/-SSVR). We also prescribe a Newton-Armijo algorithm that has been shown to be convergent globally and quadratically to solve our /spl epsi/-SSVR. In order to handle the case of nonlinear regression with a massive data set, we also introduce the reduced kernel technique in this paper to avoid the computational difficulties in dealing with a huge and fully dense kernel matrix. Numerical results and comparisons are given to demonstrate the effectiveness and speed of the algorithm.