Research Article
Efficient Model Selection for Sparse Least-Square SVMs
Algorithm 1
The Reduced Forward Least-Squares Approximation SVM.
INPUT: | (i) The data set | (ii) which is the number of support vectors desired in the expansion of the solution and | (iii) A dictionary of basis functions | INITIALIZATION: | (i) Generate a permutation of integers between 1 and . The first elements form a vector | which are the indices of randomly-sampled columns from the dictionary matrix . | (ii) Current residue vector , current dictionary which is initially a matrix of evaluations of candidate basis functions on | training data: | | (iii) The matrix and the vector b both starts as empty is appended a row and grows by one extra element | at each iteration, which in the end forms a linear system. | (iv) A variable which is the pointer to the current investigated basis functions and also a count of selected basis functions. At | the start, . | FOR AND | | | (v) The residue vector is reduced by as the target values for the next linear system of size : | | (vi) Update the dictionary matrix and prune the candidate basis functions which can be represented as a linear combinations | of the previously selected ones: | FOR AND | | | IF | | | | | | BACK SUBSTITUTION: | The positive elements of , which is represented by in ascending order, are the indices of the selected basis | functions. columns of matrix whose indices are and forms a linear system, on which the process of back substitution is | performed for the solution: | | FOR | | OUTPUT: | The solution is defined by |
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