the first phase. There are two main reasons for this decision. First, although ENSVM can be reformulated as a QP, the size of the problem is larger than the classical SVM due to the additional linear constraints introduced by the $L_1$-norm. Second, since we have already identified (approximately) the feature support in the first phase of the algorithm, enforcing sparsity in the reduced feature space becomes less critical. The two-phase algorithm is summarized in Algorithm \[alg:hipad\].

\[alg:hipad\] Given ${\textbf{w}}^0, b^0, {\textbf{a}}^0, {\textbf{c}}^0, {\textbf{u}}^0,$ and ${\textbf{v}}^0$. **PHASE 1: ADMM for ENSVM** $({\textbf{w}}^{\textrm{ADMM}},b^{\textrm{ADMM}}) \gets \textrm{ADMM-ENSVM}({\textbf{w}}^0, b^0, {\textbf{a}}^0, {\textbf{c}}^0, {\textbf{u}}^0,{\textbf{v}}^0)$ **PHASE 2: IPM for SVM** $\widetilde{{\textbf{w}}} \gets $ non-zero components of ${\textbf{w}}^{\textrm{ADMM}}$ $(\widetilde{X}, \widetilde{Y}) \gets $ sub-matrices of $(X, Y)$ corresponding to the support of ${\textbf{w}}^{\textrm{ADMM}}$ $({\textbf{w}},b) \gets \textrm{SVM-IPM}(\widetilde{X}, \widetilde{Y}, \widetilde{{\textbf{w}}}$), through (SVM-D). $({\textbf{w}},b)$

Domain Knowledge Incorporation {#sec:enk-svm}
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Very often, we have prior domain knowledge for specific classification tasks. Domain knowledge is most helpful when the training data does not form a comprehensive representation of the underlying unknown population, resulting in poor generalization performance of SVM on the unseen data from the same population. This often arises in situations where labeled training samples are scarce, while there is an abundance of unlabeled 