Property-based Entity Type Graph Matching

Abstract

We are interested in dealing with the heterogeneity of Knowledge bases (KBs), e.g., ontologies and schemas, modeled as sets of entity types (etypes), e.g., person, where each etype is associated with a set of properties, e.g., age or height, via an inheritance hierarchy. A huge literature exists on this topic. A common approach is to model KBs as graphs decorated with labels and reduce the problem of KB matching to that of matching these two elements, viz., labels and structure of the graph. However, labels of etypes are often misplaced, e.g., they are more general or speci c than the correct etype, as de ned by its properties. Structurebased matching may also lead to wrong conclusions as the properties assigned to an etype in an inheritance hierarchy do not depend on the order by which they are assigned and, therefore, on the speci c structure of the graph. In this paper, we propose a novel etype graph matching approach, dealing with the two problems highlighted above, based on two key ideas. The rst is to implement matching as a classi cation task where etypes are characterized by the associated properties. The second is we propose two property-based etype similarity metrics, which model the roles that properties have in the de nition of an etype. The experimental results show the e ectiveness of the algorithm, in particular for those etype graphs with a high number of properties. 1

Keywords

• Etype graph matching
• Machine learning
• Entity type similarity
• Knowledge reuse

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We are interested in dealing with the heterogeneity of Knowledge bases (KBs), e.g., ontologies and schemas, modeled as sets of entity types (etypes), e.g., person, where each etype is associated with a set of properties, e.g., age or height, via an inheritance hierarchy. A huge literature exists on this topic, e.g., [ 23, 24, 33 ]. Most etype graph matching approaches exploit label-based methods [ 6, 36 ], such as character similarity metrics and synonym analysis, and structure-based methods [ 18 ], implementing various forms of graph matching. However, labels of etypes may suggest a wrong etype [ 19, 34 ]. For example, an eagle can be labelled 1 Copyright © 2021 for this paper by its authors. Use permitted under Creative

Commons License Attribution 4.0 International (CC BY 4.0). as Bird in a general-purpose ontology and Eagle in a domain-speci c ontology. Structure-based matching may also lead to wrong conclusions as the properties assigned to an etype in an inheritance hierarchy are cumulative and depend only on the nodes in the path from the root and, therefore, do not depend on the order by which they are assigned. For example, the super-class of etype Eagle can be Animal in one etype graph and Bird in another etype graph.

As a solution to the above problems, the main intuition underlying the work described in this paper is to match etypes on the basis of the properties which are used to de ne them. It is, in fact, the properties that are used to intensionally de ne an etype which de ne it independently of its speci c name and also independently of its hierarchy [ 17 ]. Furthermore, it is fact that in most relevant ontologies, etypes are associated with su cient properties, like DBpedia [ 1 ] and OpenCyc [ 13 ]. And the reason for this is quite obvious, being the purpose of any data or knowledge integration task exactly that of extending the number of properties associated to an etype.

In this paper, we implement the above intuition based on main contributions: { We introduce two property-based etype similarity metrics, namely the horizontal similarity ESh and the vertical similarity ESv which characterise the role that properties have in the de nition of given etypes. These similarity metrics capture the main idea that for any two etypes, the properties which distinguish one etype from the other should not occur in the other etype. Since di erent properties contribute di erently for matching etypes, we introduce ESh which focuses on measuring the properties with di erent shareability, and ESv measures properties based on their speci city. { We implement the etype graph matching as a classi cation task where the matching of etypes is based on their associated properties. In this paper, we propose and evaluate a machine learning (ML)-based etype graph matching approach.

The paper is organized as follows. Section 2 introduces our own speci c formalization for etype graphs and relevant terminology. Section 3 presents two property-based etype similarity metrics. Section 4 introduces the overall etype graph matching algorithm. The evaluation details and results in Section 5, where the experiments are based on a selected test cases from the Ontology Alignment Evaluation Initiative (OAEI) [ 11 ]. Finally, we present the related work in Section 6 and the conclusions in Section 7. 2

Etype Graphs as FCA contexts

We formalize etype graphs as formal concept analysis [ 17 ] (FCA) contexts. Speci cally, we de ne an etype graph ET G as ET G = hE; P; T i, with E = fe1: : : eng being the set of etypes from the etype graph, P = fp1: : : png being the set of properties, T = fe 2 Ejhe; T (e)ig being the set of correspondences between etypes and properties, where function T (e) returns properties of e. We consider the property p is used to describe an etype e when the property belongs to set T (e). Two observations: 1. E is a set of etypes but not a set of entities. Similar to what happens in general FCA, which assumes that an entity is described by a set of property values, an etype is considered to be described by a set of properties T (e). Since in our method we focus on the correlations between etypes and properties, we organize an etype graph as etype-property correlation map as an FCA context without containing additional information. 2. Etype characterization exploits not only the properties associated with it but also the others, namely those which are not used in its de nition. Thus, we introduce the non-associated properties into our FCA context and distinguish two more di erent cases for better presenting the FCA context. As an example, Figure 1 presents the hierarchy of an etype graph, extracted from DBpedia [ 1 ]. In each box, etypes are presented in yellow and their properties in green. We formalize the etype graph in Figure 1, into an FCA context as from below. In Figure 2 we adopt the following conventions. The value box with a circle represents the fact the property is associated with the etype, e.g., citizenship is associated with Person. The value box with a cross means the property is not associated with the etype, e.g., date is not used to describe etype Person. The value \UN" represents the fact that the property is not associated with the etype but associated with at least one of its subclasses, namely unde ned. The intuition is that the property might or might not be used to describe the current etype, e.g., academy award is used to describe Artist and it might be used to describe Person since Artist is a subclass of Person. We encode these three correlations as the parameter wp. Since the correlation of \associated with" is positive for a property describing an etype, the correlation of \not associated with" is negative and the correlation of \unde ned" is neutral, we take wp to be de ned as wp 2 f1; 0; 1g. (1) 8 1, if p 2 prop(E) wp = < 0, if p 2= prop(E)&p 2 prop(E:subclass)

: -1, if p 2= prop(E)&p 2= prop(E:subclass) In the above equation, we take p as the target property and prop(E) as the properties associated with E. Thus, the circles, UNs and crosses in Figure 2 are set to 1, 0 and -1, respectively. 3

Property-based similarity

The similarity metrics are inspired to the work in [ 16, 19 ] in considering properties as one of the most important features to describe an etype and to the formalization of the \get-speci c" heuristic provided in [ 20 ]. These provide us the intuition that a more speci c property provides more information to identify an etype. Let us introduce our two etype similarity metrics in detail. 3.1

Horizontal Similarity

When measuring the speci city of a property, a possible idea is to horizontally compare the number of etypes that are described by a speci c property, namely the shareability of the property [ 19 ]. If a property is used for describing diverse etypes, it means that the property is not highly characterizing. Thus, for instance, in gure 2, the property name is used to describe Person, Place, Athlete. Dually, if a property is used for describing a few etypes or the property is associated with only one etype, this means this property can be regarded as highly characterizing, e.g., in Figure 2, property settlement is speci c for etype Place. Based on this intuition, we consider the speci city of a property is related to its shareability. Therefore, we propose SP as the metric for measuring property speci city. More precisely, SP aims to minimize the number of etypes that are associated with the target property in a speci c etype graph. We model the metric SP as:

SPET G(p) = wp e (1 n(p)) 2 [ 1; 1] (2) where p is the input property and n(p) is the number of etypes that are described by the input property in a speci c entity graph ET G, thus n(p) 0; e refers to the natural mathematical constant [ 15 ]; is a constraint factor whose aim is to produce a gentle curve. Assume that A and B are two etype graphs. Then we model ESh as follows: ESh(Ea; Eb) = 1 Xk

SPA(pi) + SPB(pi) jprop(Ea)j jprop(Eb)j 2 i=1 where we take Ea, Eb as the candidate etypes from A and B respectively. Thus Ea 2 A and Eb 2 B; prop(E) refers to the properties associated with the speci c etype and jprop(E)j refers to the number of prop(E). k is the number of matched properties which are associated with both etype Ea and Eb. SPA(pi) and SPB(pi) refer to the speci city of the aligned property pi in A and B, respectively. Notice that we have ESh(Ea; Eb) = ESh(Eb; Ea). Notice also that we apply z-score normalization [ 29 ] to ESh at the end of calculation, and that the range of ESh is between 0 to 1. (3) 3.2

Vertical Similarity

Etype graphs are organized as classi cation hierarchies such that upper-layer etypes represent more abstract or more general concepts, whereas lower-layer etypes represent more concrete or more speci c concepts [ 20, 31 ]. Correspondingly, properties of upper-layer etypes are more general since they are used to describe general concepts, vice versa, properties of lower-layer etypes are more speci c since they are used to describe speci c concepts. We assume that speci c properties will contribute more to the identi cation of an etype. For instance, in Figure 2, as a lower-layer etype, Artist can be identi ed by the property academy award but not by the property name. Based on this intuition, we propose L(p) as a metric for measuring property speci city. We model L(p) as follows: LET G(p) = wp min layer(E) 2 [ 1; 1] (4)

E2etype(p) where: is a constraint factor which normalized the range of the function; etype(p) outputs all the etypes that are described by the property p; and layer(E) refers to the layer of the inheritance hierarchy where an etype E is de ned. We de ne the vertical etype similarity metric ESv as from below.

ESv(Ea; Eb) = 1 Xk

LA(pi) 2 i=1 jprop(Ea)j +

LB(pi) jprop(Eb)j Similar to the de nition of ESh, we have candidate etypes Ea 2 A and Eb 2 B and the properties prop(E) associated with the etype E. The key di erence is that ESv exploits the property speci city based on the layer information L(p). LA(pi) and LB(pi) refer to the highest layer of the aligned property pi in A and B, respectively. Notice that ESv is symmetric as well. ESv is also normalized by z-score normalization, in the same way as ESh. Finally the range of ESv is between 0 to 1. 4

Etype Graph Matching

Figure 3 presents the Processing chart of our etype graph matching approach. It mainly consists of two matchers, the property matcher and the etype matcher. After parsing the input etype graph pair, properties are rst sent into the NLPbased property matcher, where string-based and language-based similarity metrics are exploited to match two property labels [ 3, 4 ]. Then we generate the FCA contexts according to the etypes and correlated property pairs. In this phase, we will also generate our property-based etype similarity metrics ESh and ESv and then send them all to the etype matcher. We develop a ML-based matcher which considers etype matching as a binary classi cation task. Thus, our etype matcher will predict two incoming etypes as match or unmatch and output the matched etypes as the nal results.

Algorithm 1 below presents the step-by-step process for calculating propertybased etype similarity metrics ESh and ESv. After formalizing etype graphs into FCA contexts, we assume that the two candidate FCA contexts fa and fb are generated. P M refers to the property pairs which are aligned by the property matcher, EM refers to the candidate etype pairs which are waiting for matching. For every etype pair in EM , we check their correlated properties and update the speci city values to ESh or ESv if the property pair is aligned. After traversing all the candidate etype pairs, we obtain completed etype similarities which will be used for training the ML model, or predicting if two etypes are matching. Table 1 provides some representative examples to show the etype similarity ESv and ESh between etypes from cmt-confof and cmt-conference in conference track. Algorithm 1 Etype similarity generation. ESh; ESv = etypesim(fa; fb) Input:

Candidate FCA contexts fa and fb; Output:

Property-based etype similarity ESh; ESv; 1: P M = (pa; pb) = P ropertyM atcher(fa; fb); falign pa and pb as property pairs by property matcher, where pa 2 fa and pb 2 fb.g 2: EM = (Ea; Eb) = EtypeSelector(fa; fb); fselect etypes Ea; Eb from fa; fb and assemble them as candidate etype pairs EM .g 3: for all EMi 2 EM do 4: for all pa 2 fa; pb 2 fb do 5: if (pa; pb) 2 P M then 6: ESh(EMi):add(SP (pa); SP (pb)); fadd the horizonal speci city to etype similarity ESh(EMi), refers to equation 3g 7: ESv(EMi):add(L(pa); L(pb)); fadd the vertical speci city to etype similarity ESv(EMi), refers to equation 5g 8: end if 9: end for 10: end for 11: return ESh; ESv 5

Evaluation

We rst describe the evaluation set-up and then provide the results from the experiments. 5.1

Evaluation Set-up

The main decision for the evaluation was to take OAEI as the main reference for the selection of the matching problems. As of today, this in fact the major source of ontology matching problems.

Our approach focuses on ontologies that contain etypes associated with a fair number of properties. As a result, we have selected the following cases: the bibliographic ontology dataset [ 10 ] and conference track [ 38 ] (ra1 version). From the bibliographic ontology dataset, we select series #101 and series #301304, which present real-life ontologies for bibliographic references from the web. We set these bibliographic ontologies as the training set for training our MLbased etype matcher. The conference track contains 16 ontologies, dealing with conference organizations, and 21 reference alignments. We set the 21 reference alignments from the conference track as the testing set to validate our etype matcher. We select the training and testing set from di erent cases since we aim to prove the adaptation of our approach, which also prevents our approach from over tting. Notice that there is an unbalanced positive and negative sample issue when we match two candidate ontologies, which means negative samples will be produced much more than positive samples. To address this issue, we propose a model training strategy that decreases the negative samples and duplicates a part of positive samples to achieve a balanced training set and to alleviate over tting.

In this paper, our matching approach applies a general binary classi cation strategy, which is independent of the speci c ML model. Thus, the data label is 1 or 0, which means two etypes are matching or unmatching respectively. The data consists of three kinds of attributes, which are string-based similarity metrics (N-garm [ 12 ], Longest common subsequence [ 12 ], Levenshtein distance [ 37 ]), language-based similarity metrics (Wu and Palmer similarity [ 28 ], Word2vec [ 8 ]) and property-based similarity metrics (ESh and ESv). These etype similarities aim to measure di erent aspects of the relatedness between two etypes. Here we select some of the most common string-based and language-based similarity metrics as additional metrics working with our property-based similarity metrics for achieving better etype matching results. 5.2

Experimental Results

For better evaluating the validity of our approach, we apply 4 di erent ML models, which are: random forest [ 27 ], stochastic gradient descent (SGD) classi er [ 22 ], decision tree [ 32 ] and logistic regression [ 26 ]. We have compared our work with state-of-the-art matching methods, as they came out of previous OAEI evaluation campaigns. The involved state of the art systems are: FCAMap [ 7 ], AML [ 14 ], LogMap and LogMapLt [ 21 ]. We calculate precision, recall, F1-measure, and also F0:5-measure and F2-measure [ 30 ]. Table 2 shows the results of our approach with the di erent models mentioned above, compared with the results of state-of-the-art methods. Firstly, we can nd our approach with di erent models produce slightly di erent results, the SGD classi er performs the best in general, which leads the precision, F0:5-measure and F1-measure. And, random forest advances in recall and F2-measure. Decision tree and logistic regression classi ers are marginally powerless than the other two in conference track ontologies. Secondly, extend to the overall comparison, we can nd that AML has the best overall results. Leading the precision, F0:5-measure and F1-measure. Our approach with random forest leads the results on recall and F2-measure. Considering that the average results of our approach with di erent models are performing close to the state-of-the-art on F1-measure, we can say that our approach leads to similar results as state-of-the-art competitors, while advances in di erent aspects2.

The comparison to state-of-the-art methods shows the validity of our etype matcher. Moreover, we design a second experiment which is an ablation test to evaluate if our designed property-based etype similarity metrics are e ective. In this experiment, we test on the backbone model (B) which was trained only by string-based and language-based similarity metrics. We also test on the model with ESh, ESv, and both ESh and ESv (ours), respectively. Note that the backbone model refers to Ours-SGDClassi er in table 2.

Table 3 shows the results of the ablation test, it is easy to nd by using our designed metrics, the results signi cantly improved comparing with the results of the backbone model. Moreover, although B+ESh achieve the best recall measure, B+ESv+ESh leads in precision and F1-measure, which means the best overall performance. This observation shows both our designed metrics are effective on the etype matching task. At the same time, the etype matcher achieves the best performance by simultaneously using ESv and ESh. Based on the idea originally introduced in [ 19 ] and di erent from all the previous work, our approach is based on the idea of exploiting properties as the main means for matching etypes. We provide below a short summary of the four main techniques that we exploit in the implementation of property-based etype similarity, namely, label matching, graph matching, and the use of ML and FCA.

In the early stages of ontology matching, etype matching methods mostly focused on string-based methods. The work in [ 36 ] reviews a wide range of string similarity metrics and propose an ontology alignment method by selecting different powerful similarity metrics. Later, ensemble metrics strategies were introduced in some studies [ 25 ], which apply multiple matchers based on di erent 2 All approaches do not have signi cant di erences in running times since the conference track contains no large ontology. string-based metrics. The principle of these works is that the combined matchers are more powerful than an individual matcher.

The structure of an etype graph has also been considered as important information for identifying etypes, like [ 2,18 ]. The LogMap system [ 21 ] uses a two-step matching strategy, that is, matches two etypes Ea and Eb by a lexical matcher, and then considers the etypes that are semantically close to Ea are more likely to be semantically close to Eb. AML [ 14 ] introduces an ontology matching system that consists of a string-based matcher and a structure-based matcher, building internal correspondences by exploiting is-a and part-of relationships.

Some work on matching etypes is based on the use of ML. This work models the etype matching task as a binary classi cation task, trying to encode the information like string similarities and structure information as attributes. For instance, the work in [ 5 ] achieves promising results by encoding the lexical similarity of the superclass and subclass as structural similarity.

Finally, FCA lattices have been applied in etype matching methods in the work described in [ 7, 35 ]. To re ne health records searching outputs, the work in [ 9 ] introduced a matching method based on FCA which assists the end-user in de ning their queries. In turn, in [ 35 ] a bottom-up ontology merging approach was proposed where FCA lattices were used to keep track of the ontology hierarchy. 7

Conclusions

In this paper, we have introduced a novel etype graph matching approach via property-based similarity measurement. Firstly, we discussed a novel formalization method for etype graphs, which encodes etypes and properties into FCA contexts. Then we proposed two novel metrics for measuring the contextual similarity between two etypes, namely horizontal similarity and vertical similarity. Based on our proposed metrics, we have developed a ML-based framework for etype graph matching. The experimental results show the validity of our approach.

Acknowledgements

The research conducted by Fausto Giunchiglia has received funding from the InteropEHRate project, co-funded by the European Union (EU) Horizon 2020 programme under grant number 826106, and the research conducted by Daqian Shi has received funding from the program of China Scholarships Council (No. 202007820024).

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