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Algorithm 2

Pegasos algorithm for structured SVM.

Input: Training data set , the number of iterations , the number of samples for each iteration;

Output: The normal vector of the classification hyperplane is .

Main procedure:

1. Calculate the covariance matrix of the sample;

2. Initialize vector Arbitrarily select a vector and ask for ;

3. For

  3.1 Select the subset of the samples, , from the training set and replace with the original objective function;

  3.2 Determine the learning efficiency of the gradient descent method ;

  3.3 will use to determine the current loss of nonzero samples into a new subset

      The sub-gradient direction of the objective function can be expressed as:

  2.4 Update:

  2.5 Projection steps:

4. Get the final result