Find the exactly correct separating hyperplane of SVM when the data is not perfectly linearly separable I am thinking about the following case where the data in region 1 is always positive and the data in region 2 is always negative, but the data in region 3 can be both positive and negative. Are there any existing results on finding exactly the $l_1$ and $l_2$ (or region 3)?

As far as my understanding of SVM when the data is not perfectly linearly separable, we can maximize the soft margin to find the separating hyperplane. We can control the penalty of misclassification to achieve different separating hyperplanes. But is there a method for finding the exactly correct separating plane like $l_1$ and $l_2$? I am not very familiar with SVM, and I would really appreciate it if you can provide some comments or references.
I think you can create a &quot;half-hard&quot; SVM problem. It will be like the hard SVM for positive labels (without the error term) but for negative example it will be the like the soft SVM (with the error term).
This wil guarantee you get the line that labels correctly all positive examples, but still tries to label as many of the negative examples as it can (and also create the largest margin it can)
You can do this twice to get both lines $l_1$ and $l_2$.