Rediscovering alignment relations with Graph Convolutional Networks

The authors present a thorough analysis of the application of Graph Convolutional Neural (GCN) networks for knowledge graph alignment. The technical approach and analysis appear to be sound. The application area of knowledge graph alignment is of significant practical importance. The work is original and the writing is of good quality.

I have two suggestions for improving the manuscript.

First, the main manuscript contains a large amount of very detailed result tables. It is laudable that the authors present all these details, but I also have the concern that the reader cannot see the forest for the trees: What are the main trends and practically significant findings that one can glean from the results? E.g., which models and parameters work best, and what are the general trends that can be observed, if any? I would suggest that quite a few of the detailed data tables could be moved to an appendix / supplementary material, and that a condensed table or graph given a condensed overview of these main key insights is put into the main manuscript text instead. Most readers will come to this manuscript with the question of how they can best apply the described methodology to their own problem, and the paper should make it as easy as possible to answer that question.

Second, the authors present these detailed results for their own datasets (biomedical data with a focus on pharmacogenomic information), but it is unclear to what extent the presented findings could generalize to another dataset, potentially in another knowledge domain. The authors should discuss more how much (or how little) they expect the findings in this paper to generalize to other knowledge graphs, and what their intuitive expectations are for some other kinds of knowledge graph. An even better addition would of course be to apply the algorithms to at least another, independent and different knowledge graph, and to compare if there are common trends across different knowledge graphs -- but I leave it to the authors to decide if this is worthwhile and feasible.

Minor comments:

The input layer of the GCN is a one-hot encoded vector -> I just want to remark that it is surprising that this approach scaled for such a large graph! Perhaps mention scalability issues or considerations if there were any. Did you consider trainable dense vector embeddings?

"We experimented this approach"
-> "We conducted experiments with this approach"

"somehow corresponding to"
-> "corresponding to"

"in the Resource Description Format"
-> "in the Resource Description Framework (RDF) format"

"and their predicate represent the"
-> "and their predicates represent the"

"Here, we use the results of a rule-based method [10] in a “knowledge graph as silver standard” perspective [11]."
-> I think you should elucidate what you mean by that.

"We experimented our work within the"
-> "We conducted experiments within the" (please also check the use of the word experiment in other sections of the document; I will cease highlighting it from here on)

"We propose different gold clusterings"
-> "We propose different gold clusterings (named C0 - C6)"

Figure 3: x axis labeling is so small as to be illegible, please fix.

"input layer consists in"
-> "input layer consists of"

Tables 6: There should perhaps be some separator line between G0 and G5 results to make the table more intuitive.

The paper investigates the properties of dense vector spaces with respect to their capability of representing correctly the similarities of nodes in knowledge graphs (KG).

In particular, the paper exploits graph convolutional networks in order to learn node embedding by preserving the properties of KG nodes to be related in terms of distances between their vector representation.

The related work section gives an overview of other approaches exploiting graph embedding for the task of KB alignment. The section outlines also the differences with the proposed approach. I would just suggest to try to summarize the literature contributions in a more systematic way, maybe using comparative tables or any other kind of synthetic overview of the main insights that one can take from the literature.

Section. 3.2 provides a description of the approach. It is very clear and understandable but there are three points on which some further detail would be beneficial: 1) clarify better on what the proposed solution is different from others and how the GCN model is tuned (if any fine tuning is made); 2) discuss how much this GCN architecture is specifically tailored for the knowledge graph at hand or if this can be applied successfully on any KG; 3) it is not completely clear to me how the semantics of KG relations are taken into account in this phase. Is this depending on the choice of the relations taken into account or there are some special configuration and/or hyper parameter than can be used to deal with the different semantics of the KG relations?

I also have some concerns with respect to the choice of the clustering algorithms . First I would say that the availability in sklearn of algorithms is not the better motivation for the choice (also because there are many others solutions for clustering in sklearn as well). Then, why using single linkage and ward with hierarchical clustering and not complete linkage or maybe a different algorithm? About OPTICS, what about other density based approaches like DBSCAN, spectral clustering and so on?

Then, how the number of clusters and/or the criterion for selecting the clusters is used? Is it something that should be tailored empirically of the specific KB or it is possible to generalize the method for selecting the most appropriate selection?

In the experimental section, if I understand correctly authors use gold clusters to train the GCN and then to evaluate the approach. There is a distinction between the training set and the test set? How are they defined on which proportion? How do you perform stratified sampling of nodes for training and test?

In the table of results ward seems to have poor performances on some of the clusters. Any idea of the reason? I would suggest to introduce some error analysis here, maybe a confusion matrix would be sufficient to understand better the different behavior of different clustering approaches.

The paper presents an approach to predict alignment relations within a knowledge graph. The topic is very interesting and challenging, and the use of GCNs is promising to encode the semantics of knowledge graphs. Reusing previously computed alignments for training is valid as this could potentially be given by an automatic system. The approach is also applied in a real scenario. However, although the presented work has potential, I believe it is in a premature stage.

- Novelty. The use of GCNs could still be seen as novel as more evidence is needed of their potential to encode the semantics of KGs. However, the use of inference rules is used in a standard way. Coming from the Semantic Web I am expecting to perform reasoning before any further steps. Otherwise the data in the graph is not complete. The paper refers to works like logic tensor networks, but these approaches (i.e., neuro-symbolic systems) try to have a tight integration between the machine learning model and the symbolic representations.

- Inference rules. The used inference rules are limited. They lack inference rules involving  domain and range as in the RDFS Semantics standard and many more if taking into account OWL 2 RL. Is there any motivation about this? Description Logics is mentioned in the paper, but no more details are given about the motivation of using these inference rules only. Which inference engine is used? Transformation in G1 is not standard, typically nodes are not merged but edges are propagated to equivalent nodes.

- Focus and contribution. At the beginning of the paper it seems the approach can be applied to the alignment of independent KGs as the Ontology Matching community is mentioned as motivation, but the approach focuses on the discovery of related entities within a single KG. I believe that the matching of independent KGs brings a different challenge as the embedding spaces are independent and one needs to bridge them. The work is also presented as an approach to "rediscover alignments", but in the end only clusters of related entities are proposed. Predicting the right relationships is an important challenge, especially commiting to a logical equivalence or subsumption.

- OWL vs SKOS. I miss some examples to understand the nature of the presented relationships via owl:sameAs and the SKOS ones. I understand that SKOS relationships may be useful when the logical implications are unclear and it is safer to say that something is just related or a close match.However, since owl:sameAs is used I am wondering why rdfs:subclassOf is not used instead of (or together with) skos:broadMatch. I'm also missing skos:exactMatch and owl:equivalentClass. Are there equivalence/relatedness relationships among classes? Note that, if using OWL semantics, owl:sameAs connects instances not classes.

- Limited evaluation. The evaluation is interesting as the approach is applied in a real scenario. However, it is limited to a single KG that fits the purposes of the presented approach. It would be interesting to evaluate the approach on other KGs and eventually on a matching task between independent KGs. Furthermore there should be an evaluation about the accuracy of predicting the expected equivalence relationship. It seems that the similarity of the computed embeddings goes in the right direction, but no more results are given.

Minor comments
- Table 5: The statistics do not match my intuition. I was expecting G5 to have more edges
- Introduction falls into details quite quickly but without in-depth details to understand all the steps, so it leaves you with many questions about the followed process.
- Suggested reference about SW conformant KGs: https://arxiv.org/pdf/2003.02320.pdf