Determination of the spread parameter in the Gaussian kernel for classification and regression

Wang, Wenjian; Xu, Zongben; Lu, Wen-Hsiang; Zhang, Xiaoyun

doi:10.1016/s0925-2312(02)00632-x

Cited by 347 publications

(166 citation statements)

References 13 publications

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“…Originally, SVM are developed for pattern recognition problems, such as image recognition, 30 microarray gene expression classification, 11 protein folding recognition, 31 protein structural class prediction, 32 identification of protein cleavage sites, QSAR, and other pharmaceutical data analysis, 11,33 and now, with the introduction of -insensitive loss function, SVM have been extended to solve nonlinear regression estimation and timeseries prediction and excellent performances have been obtained. 29 In SVM, the basic idea is to map the data x into a higherdimensional feature space F via a nonlinear mapping Φ and then to do linear regression in this space. Therefore, regression approximation addresses the problem of estimating a function based on a given data set G ) {( …”

Section: Methodsmentioning

confidence: 99%

Quantitative Prediction of logk of Peptides in High‐Performance Liquid Chromatography Based on Molecular Descriptors by Using the Heuristic Method and Support Vector Machine.

et al. 2005

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A new method support vector machine (SVM) and the heuristic method (HM) were used to develop the nonlinear and linear models between the capacity factor (logk) and seven molecular descriptors of 75 peptides for the first time. The molecular descriptors representing the structural features of the compounds only included the constitutional and topological descriptors, which can be obtained easily without optimizing the structure of the molecule. The seven molecular descriptors selected by the heuristic method in CODESSA were used as inputs for SVM. The results obtained by SVM were compared with those obtained by the heuristic method. The prediction result of the SVM model is better than that of heuristic method. For the test set, a predictive correlation coefficient R ) 0.9801 and root-mean-square error of 0.1523 were obtained. The prediction results are in very good agreement with the experimental values. But the linear model of the heuristic method is easier to understand and ready to use for a chemist. This paper provided a new and effective method for predicting the chromatography retention of peptides and some insight into the structural features which are related to the capacity factor of peptides.

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Section: Methodsmentioning

confidence: 99%

Quantitative Prediction of logk of Peptides in High‐Performance Liquid Chromatography Based on Molecular Descriptors by Using the Heuristic Method and Support Vector Machine.

et al. 2005

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“…The LS-SVM uses a least squares loss function instead of the ε -insensitive loss function. It is known to be easier to optimize with shorter computational time [17]. In LS-SVM, the ε -tube and slack variables are replaced by error variables, which inform on the distances from each point to the regression function.…”

Section: Least Squares Support Vector Machinementioning

confidence: 99%

Comparison of Machine Learning Regression Methods to Simulate NO<sub>3</sub> Flux in Soil Solution under Potato Crops

Fortin

Morais²,

Anctil³

et al. 2014

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Nitrate (NO3) leaching is a major issue in sandy soils intensively cropped to potato. Modelling could test the effect of management practices on nitrate leaching, particularly with regard to optimal N application rates. The NO3 concentration in the soil solution is well known for its local heterogeneity and hence represents a major challenge for modeling. The objective of this 2-yearstudy was to evaluate machine learning regression methods to simulate seasonal NO3 concentration dynamics in suction lysimeters in potato plots receiving different N application rates. Four machine learning function approximation methods were compared: multiple linear regressions, multivariate adaptive regression splines, multiple-layer perceptrons, and least squares support vector machines. Input candidates were chosen for known relationships with NO3 concentration. The best regression model was obtained with a 6-inputs least squares support vector machine combining cumulative rainfall, cumulative temperature, day of the year, N fertilisation rate, soil texture, and depth.

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“…However, their work relies almost entirely on empirical evidence and qualitative remarks. Wang et al (2003) argue that the Gaussian parameter should be chosen with respect to a Fisher-discriminantbased measure. Guo et al use mutual information theory to guide parameter selection (Guo et al, 2005a) and parameter scaling (Guo et al, 2005b).…”

Section: State-of-the-artmentioning

confidence: 99%

A signal theory approach to support vector classification: The sinc kernel

et al. 2009

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Fourier-based regularisation is considered for the support vector machine classification problem over absolutely integrable loss functions. By invoking the modest assumption that the decision function belongs to a Paley-Wiener space, it is shown that the classification problem can be developed in the context of signal theory. Furthermore, by employing the Paley-Wiener reproducing kernel, namely the sinc function, it is shown that a principled and finite kernel hyper-parameter search space can be discerned, a priori.Subsequent simulations performed on a commonly-available hyperspectral image data set reveal that the approach yields results that surpass state-of-the-art benchmarks.

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Determination of the spread parameter in the Gaussian kernel for classification and regression

Cited by 347 publications

References 13 publications

Quantitative Prediction of logk of Peptides in High‐Performance Liquid Chromatography Based on Molecular Descriptors by Using the Heuristic Method and Support Vector Machine.

Quantitative Prediction of logk of Peptides in High‐Performance Liquid Chromatography Based on Molecular Descriptors by Using the Heuristic Method and Support Vector Machine.

Comparison of Machine Learning Regression Methods to Simulate NO<sub>3</sub> Flux in Soil Solution under Potato Crops

A signal theory approach to support vector classification: The sinc kernel

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Determination of the spread parameter in the Gaussian kernel for classification and regression

Cited by 347 publications

References 13 publications

Quantitative Prediction of logk of Peptides in High‐Performance Liquid Chromatography Based on Molecular Descriptors by Using the Heuristic Method and Support Vector Machine.

Quantitative Prediction of logk of Peptides in High‐Performance Liquid Chromatography Based on Molecular Descriptors by Using the Heuristic Method and Support Vector Machine.

Comparison of Machine Learning Regression Methods to Simulate NO&lt;sub&gt;3&lt;/sub&gt; Flux in Soil Solution under Potato Crops

A signal theory approach to support vector classification: The sinc kernel

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Comparison of Machine Learning Regression Methods to Simulate NO<sub>3</sub> Flux in Soil Solution under Potato Crops