of linear inequalities with a solution ${\textbf{u}}$ $$\label{eq:equiv_lin_constr}
    B^T{\textbf{u}}+ {\textbf{w}}= \textbf{0}, \quad \textbf{d}^T{\textbf{u}}- b + 1 \leq 0, \quad \textbf{u} \geq \textbf{0}.$$ Similarly, for the linear implication for the negative class membership we have: $$\label{eq:lin_imp_neg}
    D{\textbf{x}}\leq {\textbf{g}}\Rightarrow  {\textbf{w}}^T{\textbf{x}}+ b \leq -1, \quad D \in \mathbb{R}^{k_2\times m}, g\in\mathbb{R}^{k_2},$$ which can be represented by the set of linear constraints in ${\textbf{v}}$ $$\label{eq:equiv_lin_constr_neg}
    D^T{\textbf{v}}- {\textbf{w}}= {\textbf{0}}, \quad {\textbf{g}}^T{\textbf{v}}+ b + 1 \leq 0, \quad {\textbf{v}}\geq {\textbf{0}}.$$ Hence, to incorporate the domain knowledge represented by (\[eq:linear\_implication\]) and (\[eq:lin\_imp\_neg\]) into SVM, Fung [*et al*]{} [@fung2003knowledge] simply add the linear constraints (\[eq:equiv\_lin\_constr\]) and (\[eq:equiv\_lin\_constr\_neg\]) to (SVM-P). Their formulation, however, increases both the variable dimension and the number of linear constraints by at least $2m$, where $m$ is the number of features in the classification problem we want to solve. This is clearly undesirable when $m$ is large, which is the scenario that we consider in this paper.

In order to avoid the above increase in the size of the optimization probelm, we choose to penalize the quadratics $\|B^T{\textbf{u}}+{\textbf{w}}\|_2^2$ and $\|D^T{\textbf{v}}-{\textbf{w}}\|_2^2$ instead of their $L_1$ counterparts considered in [@fung2003knowledge]. By doing so the resulting problem is still a convex QP but with a much smaller size. Hence, 