# Capturing Protein Domain Structure and Function Using Self-Supervision on Domain Architectures
## 4 Results
### Quantitative Intrinsic Evaluation  
In the following, we evaluated each instance of learned embedding space \(V_{emb}\) for both non-overlapping and non-redundant representations of domain architectures. An instance of \(V_{emb}\) space is the embedding space learned for a combination of the product \(annotation\_type\cdot w\cdot dim\cdot ep\). Consequently, the total number of embedding space instances is \(|annotation\_type|\cdot|w|\cdot|dim|\cdot|ep|=2\cdot 2\cdot 3\cdot 10=120\). Let \(V^{i}_{emb}\) denote such an embedding space instance. In the following subsection, we evaluated each \(V^{i}_{emb}\) for domain hierarchy, secondary structure, enzymatic primary class, and GO molecular function. Finally, all reported performances are shown _for the best-performing epoch value (\(ep\))_. Results are shown in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{(**a) Domains hierarchy**} \\ \hline
**Model\textbackslash{} Dimension** & \(dim\) = 50 & \(dim\) = 100 & \(dim\) = 200 \\ \hline CBOW, \(w\) = 2 & 0.406 (\(ep\) = 10) & 0.412 (\(ep\) = 10) & 0.414 (\(ep\) = 5) \\ CBOW, \(w\) = 5 & 0.405 (\(ep\) = 30) & 0.402 (\(ep\) = 35) & 0.382 (\(ep\) = 10) \\ SKIP, \(w\) = 2 & 0.512 (\(ep\) = 5) & 0.53 (\(ep\) = 5) & **0.538 (\(ep\) = 5)** \\ SKIP, \(w\) = 5 & 0.507 (\(ep\) = 5) & 0.525 (\(ep\) = 5) & 0.524 (\(ep\) = 5) \\ random & 0 & 0 & 0 \\ \hline \multicolumn{4}{c}{(**b) SCOPe Secondary structure**} \\ \hline
**Model\textbackslash{} Dimension** & \(dim\) = 50 & \(dim\) = 100 & \(dim\) = 200 \\ \hline CBOW, \(w\) = 2 & 77.09 (\(ep\) = 5) & 76.35 (\(ep\) = 5) & 75.77 (\(ep\) = 5) \\ CBOW, \(w\) = 5 & 78.15 (\(ep\) = 5) & 76.94 (\(ep\) = 5) & 76.84 (\(ep\) = 5) \\ SKIP, \(w\) = 2 & 84.42 (\(ep\) = 45) & 84.42 (\(ep\) = 40) & 84.08 (\(ep\) = 30) \\ SKIP, \(w\) = 5 & **84.56** (\(ep\) = 25) & 84.06 (\(ep\) = 45) & 83.72 (\(ep\) = 10) \\ random & 23.39 (\(k\) = 40) & 23.49 (\(k\) = 40) & 22.76 (\(k\) = 20) \\ \hline \multicolumn{4}{c}{(**c) EC primary class**} \\ \hline
**Model\textbackslash{} Dimension** & \(dim\) = 50 & \(dim\) = 100 & \(dim\) = 200 \\ \hline CBOW, \(w\) = 2 & 76.88 (\(ep\) = 5) & 75.85 (\(ep\) = 5) & 75.39 (\(ep\) = 5) \\ CBOW, \(w\) = 5 & 80.89 (\(ep\) = 5) & 79.89 (\(ep\) = 5) & 77.16 (\(ep\) = 5) \\ SKIP, \(w\) = 2 & 89.47 (\(ep\) = 35) & 89.06 (\(ep\) = 40) & 88.86 (\(ep\) = 5) \\ SKIP, \(w\) = 5 & **90.85** (\(ep\) = 30) & 90.41 (\(ep\) = 15) & 90.2 (\(ep\) = 5) \\ random & 33.62 (\(k\) = 40) & 32.06 (\(k\) = 40) & 32.28 (\(k\) = 40) \\ \hline \multicolumn{4}{c}{(**d) GO molecular function (_Human_)**} \\ \hline
**Model\textbackslash{} Dimension** & \(dim\) = 50 & \(dim\) = 100 & \(dim\) = 200 \\ \hline CBOW, \(w\) = 2 & 66.94 (\(ep\) = 5) & 66.32 (\(ep\) = 5) & 66.32 (\(ep\) = 5) \\ CBOW, \(w\) = 5 & 67.77 (\(ep\) = 5) & 65.87 (\(ep\) = 5) & 65.77 (\(ep\) = 5) \\ SKIP, \(w\) = 2 & 74.77 (\(ep\) = 40) & 74.18 (\(ep\) = 5) & 73.14 (\(ep\) = 5) \\ SKIP, \(w\) = 5 & **75.96** (\(ep\) = 40) & 75.53 (\(ep\) = 10) & 74.98 (\(ep\) = 5) \\ random & 37.05 (\(k\) = 40) & 37.03 (\(k\) = 20) & 37.05 (\(k\) = 40) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Intrinsic evaluation performance. (**a**) \(Recall_{hier}\) for non-redundant InterPro annotations. (**b**–**d**): \(C^{d}_{nearest}\) average accuracy over all folds: (**b**) \(Accuracy_{SCOPe}\), (**c**) \(Accuracy_{EC}\) and (**d**) \(Accuracy_{GO}\) for non-redundant InterPro annotations. For all tables, results are shown for the best-performing \(ep\) value; if \(k\) is not shown, then \(k\) = 2. Best performance of an evaluation task shown in bold. 3.1. \(Rq_{hierarchy}\): Did Vectors of Hierarchically Close Domains Form Clusters in the \(V_{emb}\)? For the first research question, we loaded the parent-child tree \(T_{hiter}\), provided by InterPro, consisting of 2430 parent domains. Then, for each \(V^{i}_{emb}\), we compared the actual and predicted children of each parent, and we averaged out the recall for all parents.