I have been going through the Aster_Analytics_Foundation_Guide_0511 document to understand how exactly Aster SparseSVMTrainer pegasos algorithm works. I have been trying to rewrite the SparseSVMTrainer's Pegasos algorithm in R, but haven't yet been successful.

Could anyone, interprit

1)the definition of loss function used in here?  

2)Is w1 chosen as a null vector to start with? (Was thinking this couldn't be a random vector, since a random vector could create a random output result in Aster, which is not the case in reality. i.e. Aster SparseSVMTrainer produces the same result for Sparse input)

3)How the w_t+1 is updated in each iteration? (I've been trying different methods disucussed under Pegasos so far)

4)the dimentionality of w? (Is this  arow vector having the dimentionality equal to the number of attributes?)

5)the dimentionality of x vector? (is this matrix of dimentionality (number of samples x number of attributes)?) Or is this a Sparse input, like the one that Aster SparseSVMTrainer considers as INPUT_TABLE?

6) Does the iteration stop, if a convergence is met? If so what is the equation to check this convergence?

Thanks in advance!