A few days ago, while sitting in the machine learning class, I was thinking about the following problem about designing a classifier:
AFAIK, In traditional SVM, the goal is maximizing the minimum gap. To cope with noise, we may add slack variables to our constrained optimization programming.
BUT, why don’t we just maximize the total gap (sum of gaps) instead of max. of the min?! This way, outliers act as negative gaps. This problem would be defined as Linear Programming, so we have efficient solution for it.
I just wonder if this approach has been used before. Or is it convertible to some other commonly-used objective functions?