The nature of statistical learning theory
The nature of statistical learning theory
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Handbook of massive data sets
K-T.R.A.C.E: A kernel k-means procedure for classification
Computers and Operations Research
Support vector machines for spam categorization
IEEE Transactions on Neural Networks
Support vector machines for histogram-based image classification
IEEE Transactions on Neural Networks
Support vector machine with adaptive parameters in financial time series forecasting
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
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A new quadratic kernel-free non-linear support vector machine (which is called QSVM) is introduced. The SVM optimization problem can be stated as follows: Maximize the geometrical margin subject to all the training data with a functional margin greater than a constant. The functional margin is equal to W T X + b which is the equation of the hyper-plane used for linear separation. The geometrical margin is equal to $$\frac{1}{||W||}$$ . And the constant in this case is equal to one. To separate the data non-linearly, a dual optimization form and the Kernel trick must be used. In this paper, a quadratic decision function that is capable of separating non-linearly the data is used. The geometrical margin is proved to be equal to the inverse of the norm of the gradient of the decision function. The functional margin is the equation of the quadratic function. QSVM is proved to be put in a quadratic optimization setting. This setting does not require the use of a dual form or the use of the Kernel trick. Comparisons between the QSVM and the SVM using the Gaussian and the polynomial kernels on databases from the UCI repository are shown.