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 $e_i$ and we have equality constraints here because the minimization objective will always make $e_k$ to measure the error from the correct side of hyperplane.

The Lagrangian function is

Then the conditions for optimality:

Writing this in matrix form

where

and the solution is given by

## Bibliographic data

@article{
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",
}