A short paper reviews the prior work on SVM with kernel functions and then move on the introduce a SVM classifier formulated by optimizing for least square error. Refer to previous post for notations.

The classification problem is:

The error is modelled by and we have equality constraints here because the minimization objective will always make to measure the error from the correct side of hyperplane.

The Lagrangian function is

Then the conditions for optimality:

Writing this in matrix form


and the solution is given by

Bibliographic data

   author = "J. A. K. Suykens and J. Vandewalle",
   title = "Least Squares Support Vector Machine Classifiers",
   journal = "Neural Processing Letters",
   volume = "9",
   number = "3",
   pages = "293--300",
   year = "1999",