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How does SVM adjust for classes that cannot be linearly separated?

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While the maximum margin classifier is optimal in theory, in practice, observations cannot be perfectly separated in most classification problems. Therefore, expecting to define a hyperplane that perfectly separates between classes with no misclassifications is not realistic. Instead of using a hard margin classifier, SVM uses a soft margin that allows for some misclassifications in the training process. The extent to which the algorithm is allowed to have misclassifications is controlled by a regularization parameter C and is typically tuned during cross validation. This issue is another example of the bias/variance tradeoff that occurs throughout machine learning, as the soft margin classifier introduces some bias with the hope of reducing variance when classifying future observations. In the case of a soft margin classifier, the support vector includes observations both on and within the margins. 

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