. 2010 Jun 8;11:309. doi: 10.1186/1471-2105-11-309

Table 1.

Acronyms

	ℝ^N	the dual variable of SVM
Q	ℝ^{N × N}	a semi-positive definite matrix
C	ℝ^N	a convex set
Ω	ℝ^{N × N}	a combination of multiple semi-positive definite matrices
j	ℕ	the index of kernel matrices
p	ℕ	the number of kernel matrices
θ	[0, 1]	coefficients of kernel matrices
t	[0, + ∞)	dummy variable in optimization problem
	ℝ^p
	ℝ^p
	ℝ^Dor ℝ^Φ	the norm vector of the separating hyperplane
ϕ(·)	ℝ^D→ ℝ^Φ	the feature map
i	ℕ	the index of training samples
	ℝ^D	the vector of the i-th training sample
ρ	ℝ	bias term in 1-SVM
ν	ℝ⁺	regularization term of 1-SVM
ξ_i	ℝ	slack variable for the i-th training sample
K	ℝ^{N × N}	kernel matrix
	ℝ^D× ℝ^D→ ℝ	kernel function,
	ℝ^D	the vector of a test data sample
y_i	-1 or +1	the class label of the i-th training sample
Y	ℝ^{N × N}	the diagonal matrix of class labels Y = diag(y₁, ..., y_N)
C	ℝ⁺	the box constraint on dual variables of SVM
b	ℝ⁺	the bias term in SVM and LSSVM
	ℝ^p
k	ℕ	the number of classes
	ℝ^p
	ℝ^p	variable vector in SIP problem
u	ℝ	dummy variable in SIP problem
q	ℕ	the index of class number in classification problem, q = 1, ..., k
A	ℝ^{N × N}
λ	ℝ⁺	the regularization parameter in LSSVM
e_i	ℝ	the error term of the i-th sample in LSSVM
	ℝ^N	the dual variable of LSSVM,
ϵ	ℝ⁺	precision value as the stopping criterion of SIP iteration
τ	ℕ	index parameter of SIP iterations
	ℝ^p