Hard intervalIt is the basis for selecting the segmentation hyperplane in the support vector machine. It refers to the situation where the classification is completely accurate and there is no loss function, that is, the loss value is 0. It is only necessary to find the plane exactly in the middle of two heterogeneous classes. The opposite of hard interval is soft interval.

Soft intervalIt means that a certain amount of sample classification errors are allowed. The optimization function consists of two parts, namely the interval distance from the point to the plane and the number of misclassification losses; C is the penalty coefficient, and the number of misclassifications is the weight value in the optimization function. The larger the weight value, the greater the penalty for misclassification losses.

Misclassification loss functions can be divided into Hinge loss, exponential loss, and logarithm loss, but the loss function that is often used or used by default is the soft margin function of Hinge loss.

References

【1】SVM Hard Margin and Soft Margin (CSDN Blog)