Table 1 Procedure in LSVM

1)

For i=1,2,…,N, sample x _i uniformly at random from \({\mathcal {X}}\), and obtain y _i ∈{±1} according to x _i .

2)

Obtain a linear discriminant function \(\tilde {h}(\boldsymbol {x})\) such that \(\{\boldsymbol {x}\ |\ \tilde {h}(\boldsymbol {x})=\boldsymbol {0}\}\) becomes the hyperplane which is equidistant from the centers of \({\mathcal {D}}\) and of inputs with y=−1.

3)

Set \(\tilde {{\mathcal {X}}}=\{\boldsymbol {x}\in {\mathcal {X}}\ |\ \tilde {h}(\boldsymbol {x})<0\}\)

4)

For i=1,2,…,M, sample \(\tilde {\boldsymbol {x}}_{i}\) uniformly at random from \(\tilde {{\mathcal {X}}}\), and obtain \(\tilde {y}_{i}\in \{\pm 1\}\) according to \(\tilde {\boldsymbol {x}}_{i}\)

5)

Iterate 2) to 4) for K times

6)

Estimate a discriminant function \(\hat {\boldsymbol {w}}\cdot \boldsymbol {\phi }(\boldsymbol {x})\) by SVM