An Estimation of the Optimal Gaussian Kernel Parameter for Support Vector Classification

Author(s):  
Wenjian Wang ◽  
Liang Ma
Author(s):  
Manju Bala ◽  
R. K. Agrawal

The choice of kernel function and its parameter is very important for better performance of support vector machine. In this chapter, the authors proposed few new kernel functions which satisfy the Mercer’s conditions and a robust algorithm to automatically determine the suitable kernel function and its parameters based on AdaBoost to improve the performance of support vector machine. The performance of proposed algorithm is evaluated on several benchmark datasets from UCI repository. The experimental results for different datasets show that the Gaussian kernel is not always the best choice to achieve high generalization of support vector machine classifier. However, with the proper choice of kernel function and its parameters using proposed algorithm, it is possible to achieve maximum classification accuracy for all datasets.


2005 ◽  
Vol 17 (10) ◽  
pp. 2099-2105 ◽  
Author(s):  
Tobias Glasmachers ◽  
Christian Igel

Gradient-based optimizing of gaussian kernel functions is considered. The gradient for the adaptation of scaling and rotation of the input space is computed to achieve invariance against linear transformations. This is done by using the exponential map as a parameterization of the kernel parameter manifold. By restricting the optimization to a constant trace subspace, the kernel size can be controlled. This is, for example, useful to prevent overfitting when minimizing radius-margin generalization performance measures. The concepts are demonstrated by training hard margin support vector machines on toy data.


2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
Dalian Yang ◽  
Jingjing Miao ◽  
Fanyu Zhang ◽  
Jie Tao ◽  
Guangbin Wang ◽  
...  

Bearing is an important mechanical component that easily fails in a bad working environment. Support vector machines can be used to diagnose bearing faults; however, the recognition ability of the model is greatly affected by the kernel function and its parameters. Unfortunately, optimal parameters are difficult to select. To address these limitations, an escape mechanism and adaptive convergence conditions were introduced to the ALO algorithm. As a result, the EALO method was proposed and has been applied to the more accurate selection of SVM model parameters. To assess the model, the vibration acceleration signals of normal, inner ring fault, outer ring fault, and ball fault bearings were collected at different rotation speeds (1500 r/min, 1800 r/min, 2100 r/min, and 2400 r/min). The vibration signals were decomposed using the variational mode decomposition (VMD) method. The features were extracted through the kernel function to fuse the energy value of each VMD component. In these experiments, the two most important parameters for the support vector machine—the Gaussian kernel parameter σ and the penalty factor C—were optimized using the EALO algorithm, ALO algorithm, genetic algorithm (GA), and particle swarm optimization (PSO) algorithm. The performance of these four methods to optimize the two parameters was then compared and analyzed, with the EALO method having the best performance. The recognition rates for bearing faults under different tested rotation speeds were improved when the SVM model parameters optimized by the EALO were used.


2013 ◽  
Vol 798-799 ◽  
pp. 842-845
Author(s):  
Li Zhe Ma

In order to improve the prediction accuracy of stock index, eliminate of the blindness of parameters selection for support vector machine, a stock index prediction method combined the genetic simulated annealing algorithm (GASA) which integrated the parallel search of genetic algorithm with the probabilistic sudden jumping characteristics of simulated annealing algorithm, with support vector machine (SVM) is proposed. Using daily data of Shanghai stock index opening quotation which is normalization processed, the stock index prediction model based on GASA-SVM is established. Optimal parameter error penalty parameter c=1 and Gaussian kernel parameter g=1.625 are obtained. Compared the result with GA-SVM prediction model, the comparative analysis shows that GASA-SVM(MSE= 0.000191111) model prediction capabilities are superior to GA-SVM(MSE=0.000018825) prediction model. It can provide valuable references for the investors.


Author(s):  
Y N Pan ◽  
J Chen ◽  
G M Dong

Bearing performance degradation assessment is more effective than fault diagnosis to realize condition-based maintenance. In this article, a hybrid model is proposed for it based on a support vector data description (SVDD) and fuzzy c-means (FCM). SVDD, which holds excellent robustness to outliers, is used to obtain the clustering centre of normal state. The subjection of tested data to normal state is defined as a degradation indicator, which is computed by a FCM algorithm with final failure data. The results of applying this hybrid model to an accelerated bearing life test show that it can effectively assess bearing performance degradation. Furthermore, it is robust to the outliers in the training set and is not influenced by the Gaussian kernel parameter.


2020 ◽  
Vol 64 (1-4) ◽  
pp. 137-145
Author(s):  
Yubin Xia ◽  
Dakai Liang ◽  
Guo Zheng ◽  
Jingling Wang ◽  
Jie Zeng

Aiming at the irregularity of the fault characteristics of the helicopter main reducer planetary gear, a fault diagnosis method based on support vector data description (SVDD) is proposed. The working condition of the helicopter is complex and changeable, and the fault characteristics of the planetary gear also show irregularity with the change of working conditions. It is impossible to diagnose the fault by the regularity of a single fault feature; so a method of SVDD based on Gaussian kernel function is used. By connecting the energy characteristics and fault characteristics of the helicopter main reducer running state signal and performing vector quantization, the planetary gear of the helicopter main reducer is characterized, and simultaneously couple the multi-channel information, which can accurately characterize the operational state of the planetary gear’s state.


Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 208
Author(s):  
Javier Brugés Martelo ◽  
Jan Lundgren ◽  
Mattias Andersson

The manufacturing of high-quality extruded low-density polyethylene (PE) paperboard intended for the food packaging industry relies on manual, intrusive, and destructive off-line inspection by the process operators to assess the overall quality and functionality of the product. Defects such as cracks, pinholes, and local thickness variations in the coating can occur at any location in the reel, affecting the sealable property of the product. To detect these defects locally, imaging systems must discriminate between the substrate and the coating. We propose an active full-Stokes imaging polarimetry for the classification of the PE-coated paperboard and its substrate (before applying the PE coating) from industrially manufactured samples. The optical system is based on vertically polarized illumination and a novel full-Stokes imaging polarimetry camera system. From the various parameters obtained by polarimetry measurements, we propose implementing feature selection based on the distance correlation statistical method and, subsequently, the implementation of a support vector machine algorithm that uses a nonlinear Gaussian kernel function. Our implementation achieves 99.74% classification accuracy. An imaging polarimetry system with high spatial resolution and pixel-wise metrological characteristics to provide polarization information, capable of material classification, can be used for in-process control of manufacturing coated paperboard.


Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 1105 ◽  
Author(s):  
Davide Astolfi ◽  
Francesco Castellani ◽  
Andrea Lombardi ◽  
Ludovico Terzi

Due to the stochastic nature of the source, wind turbines operate under non-stationary conditions and the extracted power depends non-trivially on ambient conditions and working parameters. It is therefore difficult to establish a normal behavior model for monitoring the performance of a wind turbine and the most employed approach is to be driven by data. The power curve of a wind turbine is the relation between the wind intensity and the extracted power and is widely employed for monitoring wind turbine performance. On the grounds of the above considerations, a recent trend regarding wind turbine power curve analysis consists of the incorporation of the main working parameters (as, for example, the rotor speed or the blade pitch) as input variables of a multivariate regression whose target is the power. In this study, a method for multivariate wind turbine power curve analysis is proposed: it is based on sequential features selection, which employs Support Vector Regression with Gaussian Kernel. One of the most innovative aspects of this study is that the set of possible covariates includes also minimum, maximum and standard deviation of the most important environmental and operational variables. Three test cases of practical interest are contemplated: a Senvion MM92, a Vestas V90 and a Vestas V117 wind turbines owned by the ENGIE Italia company. It is shown that the selection of the covariates depends remarkably on the wind turbine model and this aspect should therefore be taken in consideration in order to customize the data-driven monitoring of the power curve. The obtained error metrics are competitive and in general lower with respect to the state of the art in the literature. Furthermore, minimum, maximum and standard deviation of the main environmental and operation variables are abundantly selected by the feature selection algorithm: this result indicates that the richness of the measurement channels contained in wind turbine Supervisory Control And Data Acquisition (SCADA) data sets should be exploited for monitoring the performance as reliably as possible.


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