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HYPERPLAN VECTORIEL EQUATION SOFTWARE
Of course, for a large number of points you would use an optimization software to solve this. To help you understand the above concepts, here is a simple arbitrarily solved example. Such a point is called a support vector.įor $w_0$, we can select any support vector $x_s$ and solve
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The beauty of SVM is that if the data is linearly separable, there is a unique global minimum value. We find w and b by solving the following objective function using Quadratic Programming.Ĭoming to your first question, the value of b will not scalar as it will be decided by the above equation. To define an optimal hyperplane we need to maximize the width of the margin ( w ).
![hyperplan vectoriel equation hyperplan vectoriel equation](https://i.ytimg.com/vi/IygO0NCVShw/maxresdefault.jpg)
The hyperplane that defines the cases is known as the support vectors.ĭefine an optimal hyperplane: maximize the marginĮxtend the above definition for non-linearly separable problems: have a penalty term for misclassifications.ĭo the mapping of the data to the top space so that it is easier to classify with linear decision levels: reformulate the problem so that data is mapped completely to this space. SVM performs classification by finding the hyperplane(a subspace whose dimension is one less than that of its surrounding space) that maximizes the margin between the two classes.