Solver

Full name Microsoft.VisualBasic.MachineLearning.SVM.Solver Assembly Microsoft.VisualBasic.MachineLearning Members 4

An SMO algorithm in Fan et al., JMLR 6(2005), p. 1889--1918 Solves:

	min 0.5(\alpha^T Q \alpha) + p^T \alpha

		y^T \alpha = \delta
		y_i = +1 or -1
		0 <= alpha_i <= Cp for y_i = 1
		0 <= alpha_i <= Cn for y_i = -1

Given:

Q, p, y, Cp, Cn, and an initial feasible point \alpha l is the size of vectors and matrices eps is the stopping tolerance

solution will be put in \alpha, objective value will be put in obj

01 Syntax

Microsoft.VisualBasic.MachineLearning.SVM.Solver

02 Methods

Name	Overloads	Summary
reconstruct_gradient	1	reconstruct inactive elements of G from G_bar and free variables
Solve	1	Solve the quadratic programming sub-problem of the support vector machine.
select_working_set	1	return 1 if already optimal, return 0 otherwise

03 Fields

Name	Overloads	Summary
G	1	gradient of objective function

04 Members

method reconstruct_gradient #

reconstruct_gradient

reconstruct inactive elements of G from G_bar and free variables

method Solve #

Solve(Int32, IQMatrix, Double(), SByte(), Double(), Double, Double, Double, SolutionInfo, Boolean)

Solve the quadratic programming sub-problem of the support vector machine.

Parameters

Name	Type	Description
`l`	`Int32`	The number of the variables (the training samples).
`Q`	`IQMatrix`	The kernel matrix of the current svm formulation.
`p_`	`Double()`	The linear term of the objective function.
`y_`	`SByte()`	The signed label (+1/-1) of each variable.
`alpha_`	`Double()`	The lagrange multiplier of each variable, the solution will be written into this array.
`Cp`	`Double`	The upper bound of the lagrange multiplier of the positive side variables.
`Cn`	`Double`	The upper bound of the lagrange multiplier of the negative side variables.
`eps`	`Double`	The stopping tolerance of the iteration.
`si`	SolutionInfo	The SolutionInfo object which will be filled with the solution information.
`shrinking`	`Boolean`	Whether the shrinking heuristic should be applied during the iteration?

method select_working_set #

select_working_set(Int32())

return 1 if already optimal, return 0 otherwise

Parameters

Name	Type	Description
`working_set`	`Int32()`	The output array which will receive the indices of the two selected variables, its length should be 2 or more.

Returns

1 when the current solution is already optimal, otherwise 0.

field G #

gradient of objective function