## 3 Materials and Methods
### Feature Optimization  
The candidate features from training/test datasets are optimized over the _universal lead feature matrix_ to obtain the classification feature vector. The frame width, \(k\), of each target feature, \(h_{k}\), from \(2n\) candidate features, is optimized over \(p_{k}^{T}\), from the lead matrix. We perform a two-tiered optimization, where \(h_{k}\) and \(p_{k}^{T}\) are first compared with their respective invariant function scores (3), and similarity is calculated as Equation (7):  
\[\sum_{i=1}^{k}1-\frac{I(h_{k})_{i}}{I\big{(}p_{k}^{T}\big{)}_{i}}<\ k\times n \tag{7}\]  
where \(I(h_{k})_{i}\) = invariant feature score at index \(i\), \(I\big{(}p_{k}^{T}\big{)}_{i}\) = invariant lead feature score at index \(i\), and \(n\) = length of each n-gram linguistic pattern. In the event that the \(h_{k}\) does not match any lead feature, then a second-tier comparison is scored, as given in Equation (8):  
\[\sum_{i=1}^{k}1-\ \text{sim}\Big{(}h_{k},\ p_{k}^{T}\Big{)}_{i}<\ k\times n \tag{8}\]  
where \(\text{sim}\big{(}h_{k},\ p_{k}^{T}\big{)}_{i}\) = index-wise pos-tag feature similarity between \(h_{k}\) and \(p_{k}^{T}\). Among all optimized \(p_{k}^{T}\) values, the one with maximum invariance to \(h_{k}\) is adapted. Corresponding \(p_{k}^{T}\) lead matrix scores are substituted to develop training/test classification feature vectors, as shown in Equation (9):  
\[\theta(h_{k})=\begin{cases}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  
of Interacting Proteins (DIP) to have PPI-specific content in which the interactions were annotated manually, in addition to 25 abstracts without PPI-specific content. BioInfer has the maximum number of instances among the five corpora, with 1100 sentences, as it contains annotations not only for PPI but also for other types of events. This is achieved through retaining sentences with more than one pair of interacting entities after querying the PubMed retrieval system with extracted interacting entities in pairs from the DIP and keeping a random subset of sentences annotated for entities of protein, gene, and RNA relationships, too. IEPA comprises 486 sentences with a specific pair of co-occurring chemicals from PubMed abstracts in which the interactions were annotated, and the majority of the entities was proteins. HPRD50 contained 145 sentences with annotations and lists of positive/negative PPI and was constructed by taking 50 random abstracts referenced by the Human Protein Reference Database (HPRD) [27], in which human proteins and genes were identified by the ProMiner software, while direct physical interactions, regulatory relations, and modifications were annotated by experts. The LLL corpus was originally created for the Learning Language in Logic 2005 (LLL05) challenge, a task focusing on the extraction of protein/gene interactions from biology abstracts in the Medline bibliography database. It contains three types of _Bacillus subtilis_ gene interactions and has only 77 sentences, making it the smallest dataset among the five corpora. In addition, we also evaluated our system using Aldea, a new corpus for PPI detection tasks that was developed from a collection of PubMed abstracts.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Corpus** & **Sentences** & **\#Positive** & **\#Negative** \\ \hline HPRD50 & 145 & 163 & 270 \\ LLL & 77 & 164 & 166 \\ IEPA & 486 & 163 & 270 \\ AIMed & 1955 & 1000 & 4834 \\ BioInfer & 1100 & 2534 & 7132 \\ Aldea & 1273 & 789 & 2083 \\ \hline \end{tabular}
\end{table}
Table 2: PPI corpora statistics.  
Figure 2: Distribution of PPI corpora used for performance evaluation.