# A Special Structural Based Weighted Network Approach for the Analysis of Protein Complexes
## 4 Datasets and Evaluation Criteria
### Evaluation Criteria
#### 4.2.1 Computation of Recall, Precision and F-Measure  
To calculate evaluation metrics, we must first compute the similarity between detected and reference complexes based on neighborhood affinity in order to measure their closeness [53; 76; 77]. Hence, let \(P=\{p_{1},p_{2},\ldots,p_{k}\}\) be detected protein complexes \(\mathsf{C}_{P}(v)\) and \(R=\{r_{1},r_{2},\ldots,r_{l}\}\) be the reference protein complexes. Here, we denote the detected and reference proteins complexes by \(p_{i}\) and \(r_{j}\) respectively. Thus, neighborhood affinity between the detected and reference protein complexes is calculated like so:  
\[NA(p_{i},r_{j})=\frac{\left|N(p_{i})\cap N(r_{j})\right|^{2}}{\left|N(p_{i}) \right|\left|N(r_{i})\right|}, \tag{28}\]  
where \(NA(p_{i},r_{j})\) is the neighborhood affinity in the range of \([0,1)\), \(\left|N(p_{i})\right|\) represents the size of detected complex, \(\left|N(r_{j})\right|\) represents the size of the reference complex, and \(\left|N(p_{i})\cap N(r_{j})\right|\) denotes the number of common proteins from the detected and reference complexes. Here, the larger the \(NA(p_{i},r_{j})\), the closer the two complexes are. Given a threshold \(\kappa,ifNA(p_{i},r_{j})\geq\kappa\), then \(p_{i}\) is similarly matched with \(r_{j}\) so we set \(\kappa=0.2\) according to [22; 53; 78]. From Equation (28) we can calculate recall, precision and F-measure. Let \(\mathcal{N}_{\mathcal{P}}=\left|\{p|p\in P,\exists r\in R,NA(p,r)\geq\kappa\}\right.\) and \(\mathcal{N}_{\mathcal{R}}=\left|\{r|r\in R,\exists p\in P,NA(r,p)\geq\kappa\}\right.\) be the number of the corrected detected and reference complexes that match at least one real protein and detected complex, respectively. Now, we define recall and precision using the formula  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Datasets** & **Number of Protein** & **Number of Edges** & **Network Density** \\ \hline BioGRID & 5640 & 59,748 & \(3.16\times 10^{-6}\) \\ DIP & 4930 & 17,202 & \(1.42\times 10^{-3}\) \\ Human & 15,459 & 144,687 & \(1.21\times 10^{-3}\) \\ Yeast & 6194 & 74,826 & \(3.90\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: The general details of PPI networks used for the simulation.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Complex** & **Number of** & **Overlapping** & **Non-Overlapping** & **Protein** & **Average** \\
**Datasets** & **Protein Complexes** & **Complexes** & **Complexes** & **Coverage** & **Size** \\ \hline NewMIPS & 328 & 283 & 45 & 1171 & 14.93 \\ CYC2008 & 236 & 108 & 128 & 1628 & 4.71 \\ Human complexes & 2289 & - & - & 6206 & 8.57 \\ Yeast complexes & 1045 & - & - & 2773 & 8.92 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The details of the benchmark protein complexes.  
\[Recall=\frac{|\{r|r\in R,\exists p\in P,NA(r,p)\geq\kappa\}|}{|R|}=\frac{\mathcal{N }_{\mathcal{R}}}{|R|}, \tag{29}\]  
and  
\[Precision=\frac{|\{p|p\in P,\exists r\in R,NA(p,r)\geq\kappa\}|}{|P|}=\frac{ \mathcal{N}_{\mathcal{P}}}{|P|}, \tag{30}\]  
In general, a smaller protein complex has a higher precision, and a larger protein complex has a higher recall hence the two metrics often have an inverse relationship. Since the F-measure is the harmonic mean of recall and precision using Equations (29) and (30), we can define the F1-measure by  
\[F1-measure=\frac{2\times Precision\times Recall}{|Precision+Recall|}, \tag{31}\]