Support vector machine (SVM) is a kernel based novel pattern classification method that is significant in many areas like data mining and machine learning. A unique strength is the use of kernel function to map the data into a higher dimensional feature space. In training SVM, kernels and its parameters have very vital role for classification accuracy. Therefore, a suitable kernel design and its parameters should be used for SVM training. In this paper, we present certain kernel functions for multiclass support vector machines and propose the appropriate and optimal kernel for one-versus-one (OAO) and one-versus-all (OAA) multiclass support vector machines. The performance of the one-versus-one and one-versus-all multiclass SVM are illustrated by empirical results and it is evaluated by the parameters like support vectors, support vector percentage, classification error, training error and CPU time. The experimental results demonstrate the ability to use more generalized kernel function and it goes to prove that the polynomial kernel's efficiency in terms of high classification accuracy for several datasets.

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Support Vector Machine (SVM) is a powerful classification technique based on the idea of Structural Risk Minimization. The main idea behind the Support Vector Machine is to separate the classes with a surface that maximizes the margin between them. Key Property of SVM is Kernels. However, a proper Kernel Function for a certain problem is dependent on the specific dataset and as such there is no good method on how to choose a Kernel Function. In this paper, the choice of the Kernel Function is studied empirically and optimal results are achieved. The performance of the SVM is illustrated by extensive experimental results, which indicate that with suitable Kernel and its parameters, better classification rate, Error Rate, Support Vectors and Support Vector percentage can be obtained. The experimental results of the three datasets show that opting a kernel in random is not always the best choice to achieve high generalization of classifier although it is often the default choice.

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