Find maximum hyperplane separating two classes by optimizing the Langrangian function.

85 Views Asked by At

I am trying to solve the following problem:

enter image description here

I am having difficulty starting. I know this is a constrained optimization problem for support vector machines. I am wondering how the training data is applied to find w, b, and a. I am having trouble finding an example in which real values are used. I am currently using this resource:

CS Utah Support Vector Machines

It provides all the relevant equations, but I am unsure of which should be applied to this particular problem. How is the training data used as constraints for this problem? If someone could guide me in the correct direction or provide a link to a similar problem with actual values it would be really helpful. Thanks!

Edit:

I believe step 1 is to solve for the 'a' values using the Dual Langranian:

enter image description here

I am unsure of how I can get the 'a' values using these these function. If I plug in my d values (shown as y in the above picture) to the bottom summation, I get the equation a1-a2-a3=0. How do I use this to solve for the values of a and eventually the values of w and b?