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.