Gradient-Based Adaptation of General Gaussian Kernels

2005 ◽  
Vol 17 (10) ◽  
pp. 2099-2105 ◽  
Author(s):  
Tobias Glasmachers ◽  
Christian Igel
Keyword(s):  
Kernel Functions ◽  
Gaussian Kernel ◽  
Support Vector ◽  
Exponential Map ◽  
Linear Transformations ◽  
Kernel Size ◽  
Gaussian Kernels ◽  
Kernel Parameter ◽  
Vector Machines ◽  
Gradient Based

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.

Kernel Parameter Selection for SVM Classification

2011 ◽  
pp. 44-55
Author(s):  
Manju Bala ◽  
R. K. Agrawal
Keyword(s):  
Support Vector Machine ◽  
Kernel Function ◽  
Classification Accuracy ◽  
Parameter Selection ◽  
Kernel Functions ◽  
Gaussian Kernel ◽  
Support Vector ◽  
Svm Classification ◽  
Kernel Parameter ◽  
Benchmark Datasets

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.

scholarly journals The Impact of Different Kernel Functions on the Performance of Scintillation Detection Based on Support Vector Machines

Sensors ◽  
2019 ◽  
Vol 19 (23) ◽  
pp. 5219 ◽  
Author(s):  
Caner Savas ◽  
Fabio Dovis
Keyword(s):  
Support Vector Machines ◽  
Kernel Functions ◽  
Gaussian Kernel ◽  
Polynomial Kernel ◽  
Ionospheric Scintillation ◽  
Support Vector ◽  
Running Time ◽  
Scintillation Detection ◽  
Vector Machines ◽  
The Impact

Scintillation caused by the electron density irregularities in the ionospheric plasma leads to rapid fluctuations in the amplitude and phase of the Global Navigation Satellite Systems (GNSS) signals. Ionospheric scintillation severely degrades the performance of the GNSS receiver in the signal acquisition, tracking, and positioning. By utilizing the GNSS signals, detecting and monitoring the scintillation effects to decrease the effect of the disturbing signals have gained importance, and machine learning-based algorithms have been started to be applied for the detection. In this paper, the performance of Support Vector Machines (SVM) for scintillation detection is discussed. The effect of the different kernel functions, namely, linear, Gaussian, and polynomial, on the performance of the SVM algorithm is analyzed. Performance is statistically assessed in terms of probabilities of detection and false alarm of the scintillation event. Real GNSS signals that are affected by significant phase and amplitude scintillation effect, collected at the South African Antarctic research base SANAE IV and Hanoi, Vietnam have been used in this study. This paper questions how to select a suitable kernel function by analyzing the data preparation, cross-validation, and experimental test stages of the SVM-based process for scintillation detection. It has been observed that the overall accuracy of fine Gaussian SVM outperforms the linear, which has the lowest complexity and running time. Moreover, the third-order polynomial kernel provides improved performance compared to linear, coarse, and medium Gaussian kernel SVMs, but it comes with a cost of increased complexity and running time.

Kernel Functions Derived from Fuzzy Clustering and Their Application to Kernel Fuzzyc-Means

2011 ◽  
Vol 15 (1) ◽  
pp. 90-94 ◽  
Author(s):  
Jeongsik Hwang ◽  
◽  
Sadaaki Miyamoto
Keyword(s):  
Data Analysis ◽  
Support Vector Machines ◽  
Fuzzy Clustering ◽  
Kernel Functions ◽  
Gaussian Kernel ◽  
Support Vector ◽  
Monotone Functions ◽  
Completely Monotone Functions ◽  
Completely Monotone ◽  
Vector Machines

Among widely used kernel functions, such as support vector machines, in data analysis, the Gaussian kernel is most often used. This kernel arises in entropy-based fuzzyc-means clustering. There is reason, however, to check whether other types of functions used in fuzzyc-means are also kernels. Using completely monotone functions, we show they can be kernels if a regularization constant proposed by Ichihashi is introduced. We also show how these kernel functions are applied to kernel-based fuzzyc-means clustering, which outperform the Gaussian kernel in a typical example.

scholarly journals A Multiple Kernel Learning Model Based on p-Norm

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Jinshan Qi ◽  
Xun Liang ◽  
Rui Xu
Keyword(s):  
Multiple Kernel Learning ◽  
Research Society ◽  
Kernel Functions ◽  
Support Vector ◽  
Kernel Weights ◽  
Multiple Kernel ◽  
Vector Machines ◽  
Norm Constraint ◽  
Special Case ◽  
Elastic Constraint

By utilizing kernel functions, support vector machines (SVMs) successfully solve the linearly inseparable problems. Subsequently, its applicable areas have been greatly extended. Using multiple kernels (MKs) to improve the SVM classification accuracy has been a hot topic in the SVM research society for several years. However, most MK learning (MKL) methods employ L1-norm constraint on the kernel combination weights, which forms a sparse yet nonsmooth solution for the kernel weights. Alternatively, the Lp-norm constraint on the kernel weights keeps all information in the base kernels. Nonetheless, the solution of Lp-norm constraint MKL is nonsparse and sensitive to the noise. Recently, some scholars presented an efficient sparse generalized MKL (L1- and L2-norms based GMKL) method, in which L1  L2 established an elastic constraint on the kernel weights. In this paper, we further extend the GMKL to a more generalized MKL method based on the p-norm, by joining L1- and Lp-norms. Consequently, the L1- and L2-norms based GMKL is a special case in our method when p=2. Experiments demonstrated that our L1- and Lp-norms based MKL offers a higher accuracy than the L1- and L2-norms based GMKL in the classification, while keeping the properties of the L1- and L2-norms based on GMKL.

scholarly journals Efficient Technique for Facial Image Recognition With Support Vector Machines in 2D Images With Cross-validation in Matlab

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Support Vector Machines ◽  
Cross Validation ◽  
Facial Recognition ◽  
Kernel Functions ◽  
Efficient Technique ◽  
Support Vector ◽  
Facial Image ◽  
Vector Machines ◽  
Validation Technique ◽  
2D Images

This article presented in the context of 2D global facial recognition, using Gabor Wavelet's feature extraction algorithms, and facial recognition Support Vector Machines (SVM), the latter incorporating the kernel functions: linear, cubic and Gaussian. The models generated by these kernels were validated by the cross validation technique through the Matlab application. The objective is to observe the results of facial recognition in each case. An efficient technique is proposed that includes the mentioned algorithms for a database of 2D images. The technique has been processed in its training and testing phases, for the facial image databases FERET [1] and MUCT [2], and the models generated by the technique allowed to perform the tests, whose results achieved a facial recognition of individuals over 96%.

Support Vector Machine for Recognition of White Blood Cells of Leukaemia

2011 ◽  
pp. 93-122 ◽  
Author(s):  
Stanislaw Osowski ◽  
Tomasz Markiewicz
Keyword(s):  
Support Vector Machines ◽  
Blood Cells ◽  
White Blood Cells ◽  
Myelogenous Leukaemia ◽  
Image Feature ◽  
Gaussian Kernel ◽  
Support Vector ◽  
Vector Machines ◽  
Kernel Support Vector Machines ◽  
The Individual

This chapter presents an automatic system for white blood cell recognition in myelogenous leukaemia on the basis of the image of a bone-marrow smear. It addresses the following fundamental problems of this task: the extraction of the individual cell image of the smear, generation of different features of the cell, selection of the best features, and final recognition using an efficient classifier network based on support vector machines. The chapter proposes the complete system solving all these problems, beginning from cell extraction using the watershed algorithm; the generation of different features based on texture, geometry, morphology, and the statistical description of the intensity of the image; feature selection using linear support vector machines; and finally classification by applying Gaussian kernel support vector machines. The results of numerical experiments on the recognition of up to 17 classes of blood cells of myelogenous leukaemia have shown that the proposed system is quite accurate and may find practical application in hospitals in the diagnosis of patients suffering from leukaemia.

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