|
ℝN
|
the dual variable of SVM |
Q |
ℝN × N
|
a semi-positive definite matrix |
C |
ℝN
|
a convex set |
Ω |
ℝN × 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 |
|
ℝp
|
|
|
ℝp
|
|
|
ℝD or ℝΦ
|
the norm vector of the separating hyperplane |
ϕ(·) |
ℝD → ℝΦ
|
the feature map |
i |
ℕ |
the index of training samples |
|
ℝD
|
the vector of the i-th training sample |
ρ |
ℝ |
bias term in 1-SVM |
ν |
ℝ+
|
regularization term of 1-SVM |
ξi
|
ℝ |
slack variable for the i-th training sample |
K |
ℝN × N
|
kernel matrix |
|
ℝD × ℝD → ℝ |
kernel function,
|
|
ℝD
|
the vector of a test data sample |
yi
|
-1 or +1 |
the class label of the i-th training sample |
Y |
ℝN × N
|
the diagonal matrix of class labels Y = diag(y1, ..., yN) |
C |
ℝ+
|
the box constraint on dual variables of SVM |
b |
ℝ+
|
the bias term in SVM and LSSVM |
|
ℝp
|
|
k |
ℕ |
the number of classes |
|
ℝp
|
|
|
ℝp
|
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 |
ℝN × N
|
|
λ |
ℝ+
|
the regularization parameter in LSSVM |
ei
|
ℝ |
the error term of the i-th sample in LSSVM |
|
ℝN
|
the dual variable of LSSVM,
|
ϵ |
ℝ+
|
precision value as the stopping criterion of SIP iteration |
τ |
ℕ |
index parameter of SIP iterations |
|
ℝp
|
|