Support Vector Machine (SVM) [6] is one of the most popular and efficient algorithms for classification, which aims to find a separating hyperplane that optimally separates sets of different class labels. In most cases, it might be impossible to separate the classes using a merely linear function. However, the non-separable data might be linearly separable in a high-dimensional space, and an optimal separating hyperplane can be determined. Thus, with the help of some non-linear mapping (or kernel) functions, the input data is first transformed into a high-dimensional feature space, and
  
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Despite SVMs falling into irrelevancy this is one of the clearest explanations of how they work I’ve seen

