(nonlinear) to map the data into a different space where a hyperplane SVM handles this by using a kernel function However, there are situations where a nonlinear region can Line (1 dimension), flat plane (2 dimensions) or an N-dimensional
The simplest way to separate two groups of data is with a straight Of misclassifications (NP-complete problem) but the sum of distances from The algorithm tries to maintain the slack variable In this situation SVM finds the hyperplane that maximizes the margin and minimizes the However, perfect separation may not be possible, or it may result in a model with so manyĬases that the model does not classify correctly. (cases) into two non-overlapping classes. An ideal SVM analysis should produce a hyperplane that completely separates the vectors
Separable, there is a unique global minimum value. The beauty of SVM is that if the data is linearly To define an optimal hyperplane we need to maximizeīy solving the following objective function using Quadratic Programming. Map data to high dimensional space where it is easier to classify with linear decision surfaces: reformulate problem so that data is mapped implicitly to this space.Extend the above definition for non-linearly separable problems: have a penalty term for misclassifications.Define an optimal hyperplane: maximize margin.(cases) that define the hyperplane are the support vectors. A Support Vector Machine (SVM) performs classification byįinding the hyperplane that maximizes the margin between the two classes.
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