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Is that an assumption that in SVMs there is a separation of -1 to +1 for all the sample data points, i.e., if x_p is a positive label point then w.x_p + b >= 1 and if x_n is a negative label point then w.x_n <= -1; where w is the vector perpendicular to separating hyper-plane. I was watching this lecture https://www.youtube.com/watch?time_continue=4&v=_PwhiWxHK8o that raises my doubt. Thanks in advance.

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The version of SVM that does not allow any positive point to be on negative side of boundary and vice versa, is called hard margin SVM. The version that allows but penalizes this violation is called soft margin SVM. In practice, always soft margin is used since it is unlikely that classes would be perfectly separated, they probably overlap in some regions.

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