Support Vector Machines

Your goal is to learn a SVM in the traditional dual formulation for the iris-slwc.txt dataset. This is a simple 2D dataset, consisting of 2 dimensions (the sepal length and width), and the third column is the class (+1,-1). One of the class corresponds to iris-setosa, and the other class to other types of irises.

Implement the stochastic gradient ascent algorithm 21.1 in chapter 21, with three different kernels, namely, the linear kernel, the inhomogeneous quadratic kernel, and the homogeneous quadratic kernel. Use \(\epsilon=0.0001\) and \(C=10\), and hinge loss.

At the end, print all values of non-zero \(\alpha_i\), i.e., for the support vectors, in the following format:
\(i, \alpha_i\), one per line.
You should also print the number of support vectors.

Do this for both the kernels. The results on the linear kernel should approximately match the hyperplane \(h_{10}\) in example 21.7.

To check when the quadratic kernel is useful. You may try the quadratic kernel on the iris-PC.txt data. The results should match those given in Example 21.8.