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Calculating Dual Form of SVM Equation

  1. Dec 15, 2013 #1
    I am trying to calculate the dual form of an SVM optimisation problem:

    ELWm1.png
    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?
     
  2. jcsd
  3. Dec 18, 2013 #2

    jhae2.718

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    Gold Member

    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##.
     
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