data.

For high dimensional data, ENSVM performs feature selection along with training to produce a simpler model and to achieve better prediction accuracy. However, the quality of the feature selection depends entirely on the training data. In pathological cases, it is very likely that the feature support identified by ENSVM does not form a good representation of the population. Hence, when domain knowledge about certain features is available, we should take it into consideration during the training phase and include the relevant features in the feature support should them be deemed important for classification.

In this section, we explore and propose a new approach to achieve this objective. We consider domain knowledge in the form of class-membership information associated with features. We can incorporate such information (or enforce such rules) in SVM by adding equivalent linear constraints to the SVM QP problem (KSVM) [@fung2003knowledge; @lauer2008incorporating]. To be specific, we can model the above information with the linear implication $$\label{eq:linear_implication}
    B{\textbf{x}}\leq \textbf{d} \quad \Rightarrow \quad {\textbf{w}}^T{\textbf{x}}+ b \geq 1,$$ where $B \in \mathbb{R}^{k_1\times m}$ and ${\textbf{d}}\in \mathbb{R}^{k_1}$. It is shown in [@fung2003knowledge] that by utilizing the non-homogeneous Farkas theorem of the alternative, (\[eq:linear\_implication\]) can be transformed into the following equivalent system 