# Capturing Protein Domain Structure and Function Using Self-Supervision on Domain Architectures
## 4 Results
### Quantitative Intrinsic Evaluation
For ease of presentation, we show only the results for non-redundant InterPro annotations at Table 1a, and we provide the complete results in the Appendix A. From Tables A1 and 1a (Appendix A), we observed that SKIP performed better overall, and the embeddings learned from non-redundant InterPro annotations always had better average recall values compared to the non-overlapping ones. The best-performing \(V^{i}_{emb}\) achieved average \(Recall_{hiter}\) of 0.538. We compared this moderate performance of \(V_{emb}\) with the performance of the randomized spaces, which was equal to 0. We concluded that our embedding spaces greatly outperformed each randomized space for domain hierarchy relation. Therefore, we admitted that the _majority_ of domains of the same hierarchy were placed in close proximity in the embedding space. 3.2. \(Rq_{Scope}\): Did Vectors of Domains with the Same Secondary Structure Class Form Clusters in the \(V_{emb}\)? We extracted the SCOPe class for each InterPro domain. This resulted in 25,196 domains with an unknown secondary structure class, 9411 with a single secondary structure class, and 2265 domains with more than one assigned class (multi-label). For clarity, we removed all multi-label and unknown instances, resulting in 9411 single-labeled instances. The class distribution of the resulting data set is shown in Appendix B. We measured the performance of the \(C^{d}_{nearest}\) classifier in each \(V^{i}_{emb}\) to examine the homogeneity of the space with respect to the SCOPe class. We split the 9411 domains in 5-fold stratified cross-validation sets. To test the change in prediction accuracy for an increasing number of neighbors, we used different sets of neighbors, namely, \(k=\{2,5,20,40\}\). We summarized the results for the best-performing \(C^{d}_{nearest}\), which was \(k=2\) for non-redundant InterPro annotations in Table 1b. We show the respective table for non-overlapping InterPro annotations in Appendix B. We compared these accuracy measurements to the respective ones of the random spaces, and we found that the lowest accuracy values, achieved for (non-overlapping, CBOW, \(w=5\), \(dim=200\), \(ep=15\)), as shown in Appendix Table A2, are twice as high as the accuracy values of the random spaces for all possible dimensions. Consequently, we concluded that domain embeddings of the same secondary structure class formed distinct clusters in the learned embedding space. 3.3. \(Rq_{ec}\): Did Vectors of Domains, with the Same Enzymatic Primary Class, Form Clusters in the \(V_{emb}\)? We processed the EC primary class, resulting in 29,354 domains with unknown EC, 7248 domains with only one EC, and 721 with more than one EC. As before, we removed all  
Figure 3. Histograms of number of InterPro annotations per protein. (**a**) Non-overlapping and (**b**) non-redundant annotations. multi-label and unknown instances, leaving 7428 domains with known EC. We augmented a domain instance with its vector representation for each \(V^{i}_{emb}\), and then we used \(C^{d}_{nearest}\)to predict the EC label. See Appendix C for the class distribution of the EC task. We reported the average \(Accuracy_{EC}\) obtained in embedding spaces learned using non-redundant InterPro annotations in Table 1c. We show the respective table for non-overlapping in Appendix C. We compared these accuracy measurements to the respective ones of the random spaces. We found that the minimum average \(Accuracy_{EC}\) value was equal to 60.51 and was achieved using (non-overlapping, CBOW, \(w=5\), \(dim=200\), \(ep=15\)), presented in Appendix Table A3. That value was approximately twice as large as the accuracy values of the random spaces for all possible dimensions; the maximum average \(Accuracy_{EC}\) for random space with \(dim=100\) was 32.64. Hence, we were able to accept that domain embeddings of the same EC primary class formed distinct clusters in a learned embedding space.