This paper explores the problem of selecting good terms as seed signature for abstraction of OWL ontologies. Existing methods generate seed signatures based on geographic connections, which is far from su cient to produce a satisfactory abstract. This restricts the reusability of OWL ontologies from the aspect of knowledge management. In this paper, we propose a signature extension approach to generate seed signatures for modularization and uniform interpolation of OWL ontologies, both of which are ontology abstraction techniques. The approach establishes the semantic relevance of terms by taking into account as much as possible metadata information of an OWL ontology, and computes a numerical value to measure the relevance of terms using their embedding transformed based on a so-called OWL2Vec* framework. An empirical evaluation of the approach shows that the proposed method signi cantly outperforms other term selection baselines in making accurate selections. Besides, a case study on ontology abstraction tasks shows that modularization tools can make more complete and precise abstractions using the signature extended by our method.
Because of the heterogeneous nature of web resources, ontologies developed for the semantic web are typically large, sometimes monolithic, and knowledge modelled therein is rich and covers multiple topics. This may however restrict the reusability and interoperability of ontologies in real-world application scenarios, since large ontologies can be di cult to manage, unwieldy to manipulate, and moreover costly to reason about.
Consider an ontology reuse use case where an ontologist wants to import a football ontology into a growing sports knowledge base. Currently the only wellestablished ontology concerning football is the BBC Sports Ontology3, which, however, publishes data about all types of competitive physical activities, pertaining not only to the topic of football. Importing the whole ontology into the Copyright © 2021 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). 3 https://www.bbc.co.uk/ontologies/sport knowledge base is not di cult from an engineering perspective, but as one can expect, many web services upon the knowledge base such as search, querying, retrieval, which typically involve extensive reasoning, may become problematic, as too much irrelevant information has been, automatically yet unnecessarily, introduced. Such information makes no contribution to the formalization of the information about football but increases the computational cost.
A straightforward way to tackle these challenges of reusability and interoperability is to extract a fragment of an ontology that can behave in the same way as the original ontology in a speci c context, but is signi cantly smaller. In the above case, this means to extract from the BBC Sports Ontology a fragment that contains su ciently many logical statements to summarize all knowledge about football. Ideally, this fragment should be as small as possible.
Two logic-based approaches have been developed for computing fragments of
ontologies. One is based on modularization [
As one could expect, the quality of extracted fragments depends largely on
the seed signature fed to modularization and uniform interpolation procedures.
We may say that a fragment is complete if it covers all essential information
about the topic of interest, and a fragment is precise if it is complete and in
addition, it does not include too much irrelevant information about the topic
of interest. More speci cally, if we selected as seed signature too few terms to
summarize all materials of the topic, we would lose important information that
a user may be interested in, and if we selected as seed signature too many terms
with some of them not strongly relevant to the topic, we would include too
much additional information. Importing more information can also change the
de nitions of the terms in the original ontology, and destroy the coherence and
consistency of the original ontology [
Nevertheless, very little attention has been paid to the problem of term
selection for ontology extraction. Chen et al. [
Evidently, following this signature extension strategy one must obtain a larger seed signature with which, a more informative fragment will be produced, but we may argue that the seed signature obtained in this way, i.e., using a signature extension algorithm based merely on geographic connections, could hardly yield a complete fragment. Our argument is that: the relevance between a term and the expanding seed signature should be evaluated based on a consideration of all metadata of the participating terms in the context of the host ontology, rather than based merely on their geographic connections.
Consider a scenario where an ontologist wants to extract from a multi-domain ontology a fragment that describes football and closely related information; see Figure 1. With the central term \Football" being selected as a single seed in the primitive signature, an extension = fFootball; BallGame; Sports; Player; FootballPlayerg is obtained using the above signature extension algorithm. Terms in other domains such as MentholSpray will not be collected in , because it is geographically isolated from the domain of Sports. However, the annotated information of MentholSpray explains that \MentholSpray can be used as pain reliever for sports players". In this sense the term MentholSpray is supposed to be strongly relevant to the topic. Collecting MentholSpray in the extended signature may enable the expanded knowledge base to answer queries regarding the treatment of an injury in a football match. This is a good example showing that the relevance between a term and the expanding seed signature in the context of the host ontology could be established based on important metadata of the participating terms, for example, based on their lexical information.
In this paper, we propose a novel term selection approach to discovering
semantic relationships between two isolated groups of terms. The idea is to
measure the relevance of non- terms with terms based on their D-dimensional
vector representation computed from important metadata of the ontology using
OWL2Vec* [
For space reasons, we have to assume readers' familiarity with the notions of
ontology modularization [
Arguably, most topics can satisfactorily be summarized or de ned by a set of concept names, but do not depend too much on role names. Hence, in this paper, we only consider the seed signature to be a set of concept names.
The signature sig(O) of an ontology O is the set of all concept names in O. Given an ontology O and a seed signature sig(O) containing a single or a few concept names suggested by domain experts or simply selected by users, which are believed to be the central term or terms that can best summarize the topic of interest, our approach computes an extension 0 of in three steps, namely concept representation learning, computing relevance value, and signature extension based on relevance value. 0 is the seed signature to be fed to modularization and uniform interpolation procedures. 2.1
The rst step is to transform all concept names A in O into D-dimensional vectors in a vector space where the relevance of each concept name (to ) is computed based on important metadata of O.
Our concept representation learning model is based on OWL2Vec* [
A set of concept embedding feAD : A 2 NC g,
A distance function d : RD R ! [0; 1].
Output: A relevance function f : NC ! [0; 1], triples) converted from the OWL ontology by OWL2Vec*, the so-called lexical information about the ontology, i.e., annotations, and the so-called logical information about the concepts and roles in the ontology, i.e, subsumption, equivalence, disjointness, etc.
We note that OWL2Vec* was not meant for term selection tasks, so we make modi cationstothe original OWL2Vec* model to maximize the performance of the downstream term selection models. In particular,we designed a ne-tuning process to further improve ontology embedding, which was task-speci c and further discussed in section 3. In the end, every concept name A is represented as a D-dimensional vector eA. The second step is to compute the relevance value of every (non- ) concept name A in O w.r.t. . The computation is based on the relative distance of e A to its nearest seed neighbour (the nearest seed name) in the vector space. The range of the relevance value is [0; 1] with 1 standing for the strongest relevance and 0 for the weakest relevance. The relevance value is computed by a newly developed algorithm called Nearest Neighbor Ranking algorithm (NN-RANK), shown in Algorithm 1.
NN-RANK rst computes the distance from each concept name to each seed name in the vector space. In principle, many distance functions d : RD RD ! [0; 1] can be used to achieve this, but the Consine distance, formulated as d(eA; eB) = 1
eA eB keAk2 keBk2 has made the best measure of relevance in our experiments. j j distance values are computed in this way for each concept name A, while the smallest distance value, which denotes the shortest distance, is identi ed as a valid distance value of A to . NN-RANK then sorts all concepts names in O by their valid distance value. Concept names with smaller valid distance values are considered to be semantically more relevant to the seed signature, and thus to the central topic. These valid distance values (and the corresponding concept names) are then uniformly distributed between 0 and 1. The result is the relevance value of each A w.r.t. . 2.3
A natural question arises: how to use the computed relevance values to guide the selection of terms for ontology abstraction? Upon di erent application demands, the strategies may vary. Without a well-acknowledged gold standard, a feasible solution could be to measure the \degree" of relevance and de ne to what degree the relevance is a concept name can be thought of as \relevant" to the seeds in . For example, one could set a numerical threshold on the relevance value at 0.9 if she wants to gain a more cohesive abstraction of ontology and at 0.5 if she wants to have a looser one. We leave this exibility to users. Given a threshold at the scale of 0 to 1, our approach extends the primitive seed signature by adding to the concept names with relevance value no less than . The result is 0 = [ fA j A 2 sig(O) ^ f (A; ) g.
Computing j sig(O)j j j distances requires linear time to j sig(O)j, and the subsequent sorting requires linear time to j sig(O)j. Hence, we have the following lemma regarding the time complexity of NN-RANK.
Lemma 1. Given any OWL ontology O in SROIQ and a primitive seed signature sig(O) with n = j sig(O)j and k = j j, our term selection approach always computes an extended seed signature 0 such that 0 in O(n log n+kn) time. 3
In this experiment, we used NN-RANK to predict SNOMED CT Refset components. The aim was to show that the algorithm could enrich a given primitive seed signature with concept names highly relevant to the initial seeds (in a vector space). The experiment was conducted on a work station with an Intel Xeon CPU @ 2.60GHz and 32 GB memory.
SNOMED CT5 is currently the most comprehensive, multilingual clinical healthcare ontology in the world. A SNOMED CT Refset6 is a collection of SNOMED CT components sharing speci c characteristics (e.g., a speci c domain). An example of SNOMED CT Refset is the Malaria refset released by the 5 https://www.snomed.org/ 6 https://con uence.ihtsdotools.org/display/DOCGLOSS/refset National Resource Centre for EHR Standards in India, which includes ndings, disorders, and organisms related to Malaria. Arguably, the refset published o cially by a group of ontology engineers and domain experts, can be considered as a complete and precise standard of an Malaria abstract of SNOMED CT.
Our task was to predict concepts in SNOMED CT Refsets based on a seed signature (randomly or manually) selected from the refsets. This task was designed to t with realistic scenarios where we needed to develop a new refset with least intervention from domain experts. We assumed that refsets developed by the domain experts were complete and precise fragments, containing concepts that were highly interconnected on the semantic level (e.g., in the same clinical domain). Therefore, the task of predicting SNOMED CT Refset components could be used to evaluate the performance of term selection models.
To better position our algorithm, we compared NN-RANK with two other
term selection strategies, namely, a strategy adapted from locality-based
modularization [
We considered the International Edition of SNOMED CT (version July 2020), which contains 354,256 concepts, 355,214 logical axioms, and 1,506,185 description axioms. We used two sets of publicly accessible and in-use term collections, NHS refsets 7 and NRC refsets 8, as the target refsets.
The NHS refsets, issued by the National Health Service (NHS) in the UK, o ered from the full Edition of SNOMED CT a set of components de ned by a particular requirement. The NRC refsets were released by the National Resource Centre for EHR Standards (NRCeS) in India, which contained 30 standalone refsets covering concepts related to common diseases.
We adopted two metrics widely used in classi cation and ranking tasks, namely the Normalized Discounted Cumulative Gain (NDCG) and the Area under the ROC Curve (AUC), to evaluate the performance of term selection models. Both measures returned high values if a model made accurate predictions, i.e. they measured the similarity between the approximations and the refset components.
Ontology embedding generated by OWL2Vec* on SNOMED CT was used for the concept embedding, where each concept was represented by a 200-dimensional vector. Di erent from the original OWL2Vec* model, we used a ne-tuning pro7 https://dd4c.digital.nhs.uk/dd4c/ 8 https://www.nrces.in/resources#snomedct releases cess specially designed for this task, to further improve the ontology embedding. Speci cally, refsets in this process were transformed to documents containing (concept uri, refset identi er, concept uri) triples, then a Word2Vec model was used to ne-tune the pre-computed concept embedding on these documents. The ne-tuning process was done in a 10-fold cross validation manner, which meant that evaluations on any refset is based on a concept embedding ne-tuned on 90% refsets other than itself.
For NRC refsets, two seed signatures r and s consisted of K concepts respectively were used throughout the experiment. r was randomly selected among all the refset concepts, while s was manually selected with the aim that the K concepts it contained could describe the topic from di erent aspects. For NHS refsets, we only used a di erent set of r generated in the same way. It was crucial to be able to set the size of the primitive seed signature K accordingly to the application. In realistic use cases, the seed signature may be manually selected, where smaller K means less manual cost, so K = 5 is used in the experiments.
We used the OWL API syntactic locality module extraction tool9 as the
implementation of the locality-based module, and the o cial implementation
of Sig-Ext. For Meta-SVDD, our implementation was based on the source code
provided by [
Besides, NN-RANK slightly outperformed Meta-SVDD, particularly when using s. We will conduct a case study on the aforementioned Malaria refset to explain the mechanism and e ectiveness of NN-RANK in this task.
Figure 2 shows the distribution of the Malaria refset components and other SNOMED CT concepts in a 2-dimensional vector space. As illustrated in the gure, refset components tended to form a number of minor clusters, with each containing some highly semantically relevant concepts. The whole refset was composed of several concept clusters instead of a giant cluster. This meant that when two seed concepts A1 and A2 were given, any concept A that was similar to A1 or A2, i.e. d(eA; eA1 ) < or d(eA; eA2 ) < with being a small value greater than 0, were more likely to be a refset component compared to another A which was similar to the average of eA1 and eA2 , i.e., d (eA; (eA1 + eA2 )=2) < . NN-RANK was designed to t in this multi-clusters pattern, and achieved better performance compared to other models utilizing concept embedding.
The performance of NN-RANK could be signi cantly enhanced when seed signatures described the topic from di erent aspects. For a high quality primitive seed signature like s, an increased seed signature size would generally led to more accurate selection results. 3.2
For the current setting of N = 354; 256; K = 5; D = 200 and using Cosine distance as the distance function, NN-RANK generated 0 within 5 seconds. For comparison, it usually takes minutes to hours for other approaches (e.g., Starmodularization and Sig-Ext) to compute on a large-scale ontology like SNOMED CT, and ve minutes for the Meta-SVDD model to converge in the same setting.
It is true that our approach takes around 2 hours to build embedding vectors on SNOMED CT, but this cost is acceptable in real-life scenarios since the training is conducted only once but can be meaningfully used many times and forever. Also, the training time can be adjusted. When the ontology contains less than 100K logical and annotation axioms, it is typically less than one hour. 4
In this part, we explored how input signature extended by NN-RANK benets di erently between modularization and uniform interpolation in the OWL ontology abstraction task.
We considered HeLiS10, an ALCHIQ(D) ontology integrating knowledge about food and activity from a nutritional point of view. The experiment was based on HeLiS v1.10 which has 172,213 axioms, 277 concepts, and 50 roles. First, we randomly generated 10 concept subsets from sig(OHeLiS ) with the size of subsets ranged from 1 to 5. These randomly generated concept sets, denoted as r, could be the approximations of seed signatures around random topics. Then NN-RANK returned the ordered sets 0.
As the abstractions in real-life are usually small in size, we chose the top 10%
of 0 (i.e., set the threshold as 0.9) to be the input signature for modularization
and uniform interpolation. We used UI-FAME [
We compared 0+UI-FAME and 0+Star-modularization to see the e ectiveness of NN-RANK to di erent abstraction methods. From table 3, we can see that UI-FAME generated more compact abstractions. Besides, UI-FAME was sensitive to the input signature. These results make sense because locality-based modularization introduced other terms which were not in 0 but uniform interpolation stuck to 0. Experiments with thresholds setting as 0.3, 0.5, and 0.7 show that the size of 0 did not a ect the compactness of the locality-based module abstraction.
Term selection allowed users to extend the seed signature in an adjustable way. For uniform interpolation, it is a key step to select suitable terms for the speci ed topic, because the semantics of the topic is mainly captured by the input terms. We observe that once if the input terms were not su cient enough for uniform interpolation, the module could be very small, containing many meaningless axioms like A v > or concept assertion axioms. NN-RANK+UI-FAME generated knowledge highly relative to the topic. For instance, in Table 4, the topic was \SpecialBread". The related axioms in OHeLiS were contained in Ofragment. Clearly, \SpecialBread" had ve individuals. Besides, these individuals had no other super-classes except \SpecialBread'. As commonsense knowledge, \OliveBread" can be \OlivesAndOliveProducts", \SoyBread" can be \SoyProducts", \MilkBread" can be \MilkAndDairyProducts", which were missing in OHeLiS. So without the extension of NN-RANK, these related concepts could not be preserved in r + Star-modularization or r + UI-FAME. While NN-RANK could preserve them according to that \OlivesAndOliveProducts", \SoyProducts", and \MilkAndDairyProducts" were lexically close to the individuals of the topic concept \SpecialBread".
To sum up, with NN-RANK modules and uniform interpolants produced more complete fragments. In addition, 0+uniform interpolation produced more precise fragments than 0+modularization. 5
This paper makes a preliminary attempt to address the problem of extending the given seed signature with new terms selected sophisticatedly through embeddingbased computation of important metadata of an OWL ontology. An evaluation of the approach on a predication task of a SNOMED CT refset shows that our approach makes accurate selections compared with other term selection baselines. A case study shows that high-quality modules and uniform interpolants of OWL ontologies can be produced using our term selection approach.
The absence of standardized benchmarks remains the main bottleneck in evaluating the performance of term selection methods. Hence, a number of prede ned question answering instances that are generated based on the input ontology might be helpful in deciding the completeness and precision of the generated abstracts of OWL ontologies. For a problem Q that can be answered by querying an ontology O, a satisfactory abstract M of O regarding a input signature should be able to answer Q if Q is relevant to , and should not be able to answer Q if Q is not relevant to .
The authors would like to thank the reviewers for their insightful comments and good suggestions. This work was supported by National Natural Science Foundation of China (grant 62006114) and Open Research Projects of Zhejiang Lab (grant 2021KE0AB08).