Calculating Dual Form of SVM Equation

[Lavace]

I am trying to calculate the dual form of an SVM optimisation problem:

Dual Form Optimsation Problem

In my algorithm, I have a vector of alphas, vector of target outputs, and a Kernel matrix computing upfront.

However, I am stuck as to what indices alpha and j should be taking here. If i and j are equal, then everything is just squared. Is this for i =/= j?

If so, could I just duplicate each vector and flip it?

 

[jhae2.718]

I'm going to suspect that the $\sum_{i,j}$ in your equation is being used as a shorthand for $\sum_i\sum_j$, in which case $\sum_i\sum_j\alpha_i\alpha_j = \alpha_1\alpha_1 + \alpha_1\alpha_2 + \cdots + \alpha_1\alpha_m + \alpha_2\alpha_1 + \cdots + \alpha_2\alpha_m + \cdots + \alpha_n\alpha_1 + \cdots \alpha_n\alpha_m$ if $i = 1 \ldots n$ and $j = 1 \ldots m$.