In this thesis we focus on derivation of the support vector machines. We begin with a mathematical derivation for linearly separable data, where we can easily find the optimal separable hyperplane that always separates the data into two classes. We then extend our model to linearly inseparable data, where the problem occurs since it is not possible to find a hyperplane that optimally separates the data into two classes. For this reason we introduce penalty variables and a cost parameter by which we control wrongly clustered data, thus allowing some data to fall into the wrong class. The method can also be used on nonlinear data, where we define new functions, called kernels, to calculate the optimal separation hyperplane. The support vector machines is further used in the practical example. We use historical stock's values of 34 technology companies, on which we apply the support vector machine method to predict the stock's values at a certain point in the future. In our case, we can only predict whether the stock's value will rise or fall. Using the presented method, we can then calculate probabilities of correct forecasts.
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