The Web of Linked Data is characterized by linking structured data from different sources using equivalence statements, such as owl:sameAs, as well as other types of linked properties. However, the ontologies behind these sources are not linked. The work described in this paper aims at providing alignments between these ontologies by using an extensional approach. We look at geospatial data sources on the Web of Linked Data and provide equivalence and subsumption relationships between the classes from these ontologies after building hypotheses that are supported by owl:sameAs links. We are able to model one geospatial source in terms of the other by aligning the two ontologies and thus understand the semantic relationships between the two sources.
The last few years have witnessed the beginnings of a paradigm shift from publishing isolated data from various organizations and companies to publishing data that is linked to related data from other sources, using the structured model of the Semantic Web. As the data being published on the Web of Linked Data starts to grow, the availability of related data can be used to supplement one's own knowledge base. This provides a huge potential in various domains, like the geospatial domain, where it is used in the integration of data from different sources. Apart from generating structured data, a necessary step to publish data in the Web of Linked Data is to provide links from the generated instances to other data 'out there,' based on background knowledge (e.g. linking DBpedia to Wikipedia), common identifiers (e.g. ISBN numbers), or pattern matching (e.g. names, latitude, longitude and other information used to link Geonames to DBpedia). These links are often expressed by using owl:sameAs. A common occurrence when such links between instances are asserted is the missing link between their corresponding concepts. Such a link would ideally be able to help a consumer of the information (agent/human) to model data from the other source in terms of their own knowledge. This is widely known as ontology alignment, a special form of schema alignment. Schema alignment has been extensively studied in domains like schema integration, data warehouses, E-commerce, semantic query processing, etc. [1]. There is also a considerable amount of work in ontology matching which is summarized in Euzenat et al. [2]. The advent of the Web of Linked Data warrants a renewed inspection of these methods. Our approach provides alignments between classes from two ontologies in the Web of Linked Data by looking at the instances which are linked as the same. We believe that providing an alignment between the ontologies of the two sources on the Web of Linked Data provides valuable knowledge in understanding and modeling the semantic relationships among sources.
The paper is organized as follows. We first provide background on geospatial Linked Data and describe the sources that are the subject of this paper. We then describe our approach to ontology alignment, where alignments are conjunctions of restriction classes. We follow with an empirical evaluation on three large geospatial Linked Data sources, namely GEONAMES, DBPEDIA, and LINKEDGEODATA. Finally, we briefly describe related and future work and discuss the contributions of this paper.
In this section, we provide a brief introduction to the popular use of Linked Data and the data sources from the geospatial domain that we consider.
The Linked Data movement, as proposed by Berners-Lee [3], aims to provide machinereadable connections between data in the Web. Bizer et al. [4] describes several approaches to publishing such Linked Data. Most of the Linked Data is generated automatically by converting existing structured data sources (typically relational databases) into RDF, using an ontology that closely matches the original data source. For example, GEONAMES gathers its data from around 40 different sources and it primarily exposes its data in the form of a flat-file structure, 1 which is described with a simple ontology [5]. Such an ontology might have been different if designed at the same time as the collection of the actual data. For example, all instances of GEONAMES have the same rdf:type of geonames:Feature, however they could have been more effectively typed based on the featureClass & featureCode properties.
The links in the Linked Data on the Web make the Semantic Web browsable and, moreover, increases the amount of knowledge by complementing data already presented by a resource. A popular way of linking data on the Web is the use of owl:sameAs links to represent identity links [6]. Instead of reusing existing URIs, new URIs are automatically generated while publishing linked data and an owl:sameAs link is used to say that two URI references refer to the same thing. Both Ding et al. [7] and Halpin et al. [6] discuss the popular usage of the owl:sameAs property. Halpin et al. [6] summarizes its usages as belonging to one of the four types i) same thing as but different context ii) same thing as but referentially opaque iii) represents and iv) very similar to. We however refrain ourselves from going into the specifics and use the term as asserting same thing. For example, GEONAMES uses the owl:sameAs link to represent an alias or a co-reference.
We consider three linked data sources GEONAMES2 , DBPEDIA3 and LINKEDGEODATA 4 .
GEONAMES is a geographical database that contains over 8 million geographical names consisting of 7 million unique features including 2.6 million populated places and 2.8 million alternate names. This database is downloadable free of charge and accessible in various forms like a flat table, web services, etc. We use the Linked Data representation of the database available as an RDF dump containing 6,520,110 features and 93,896,732 triples. The structure behind the data is the Geonames ontology [5], which closely resembles the flat-file structure. A typical individual in the database is an instance of type Feature and has a Feature Class associated with it. These Feature Classes can be administrative divisions, populated places, structures, mountains, water bodies, etc. Though the Feature Class is subcategorized into 645 different Feature Codes, the Feature Code is associated with a Feature instance and not as a specialization of the property feature-Class (this is probably due to automatically exporting of existing relational data into RDF rather than building data conforming to an ontology). A Feature also has several other properties, such latitude, longitude, and an owl:sameAs property linking it to an instance from DBPEDIA.
DBPEDIA is a source of structured information extracted from WIKIPEDIA containing about 1.5 million objects that are classified with a consistent ontology. Because of the vastness and diversity of the data in DBPEDIA, it presents itself as a hub for links in the Web of Linked Data from other sources [8]. The dataset includes individuals not limited to geospatial data such as 312,000 persons, 94,000 music albums, etc. We are interested in a subset of this data which GEONAMES links itself with (e.g. places, mountains, etc.). As DBPEDIA contains a large variety of data (e.g. abstracts, links to other articles, images, etc.) we limit our approach to RDF containing the rdf:type assertion and info boxes, which provide factual information.
LINKEDGEODATA is a geospatial source with its data imported from the Open Street Map (OSM) [9] project containing about 2 billion triples comprising approximately 350 million nodes and 30 million ways. In order to generate the RDF, the data extracted from the OSM project was linked to DBPEDIA instances using the user created links on OSM to WIKIPEDIA articles. These links were then used as the training set on which machine learning algorithms were applied with a heuristic on a combination of the LINKEDGEO-DATA type information, spatial distance, and name similarity [10]. As a result the set of owl:sameAs links was then expanded to include more instance matchings based on the model learnt. This data is provided by LINKEDGEODATA as an RDF dump.
We loaded these three RDF datasets into a local database. In this paper we only consider instances from DBPEDIA and GEONAMES that are linked using the owl:sameAs property. Similarly, we focus on instances from LINKEDGEODATA linked by owl:sameAs to DBPEDIA instances. In order to reduce the number of self joins required on a source table in the database, the values related to each individual were converted into a single row identified with its URI. This forms a table where the columns represent all of the properties (predicates) that occur in the triples of that source. For example, the table for GEONAMES subset contains 11 columns not including the identifier. The values for the properties (object part of a triple) go into the value of the column for the row identified by URI of the individual (subject part of a triple). We call this a vector. In cases of multivalued properties, the row is replicated in such a way that each cell contains a single value but the number of rows equals the number of multiple values. Each new row however, is still identified with the same URI, thus retaining the number of distinct individuals. In general, the total number of rows for each individual is the product of cardinalities of the value sets for each of its properties. Throughout this paper we describe our methodology using the GEONAMES-DBPEDIA dataset, but we include the findings of the LINKEDGEODATA-DBPEDIA source in the results section.
3 Ontology Alignment Using Linked Data
An Ontology Alignment is "a set of correspondences between two or more ontologies" where a correspondence is "the relation holding, or supposed to hold according to a particular matching algorithm or individual, between entities of different ontologies." [2] Entities here, can be classes, individuals, properties or formulas. Our algorithm relies on data analysis and statistical techniques for matching the two ontologies, which Euzenat et al. [2] classify as a common extension comparison approach for aligning the structure. This approach considers two sets A and B of instances belonging to the two ontologies out of which some instances are common. Set containment relationships between the set of instances A and B suggest the alignment between the two as follows: [2] also argues that using a Hamming distance is more robust than using simple set containment as it tolerates misclassified individuals and still produces acceptable results. We identify common instances between the two ontologies required for this technique using the owl:sameAs links, where the instance identifier in each ontology gets replaced with a combination of the URIs from both ontologies. Instead of limiting ourselves to existing classes, we extend the scope of our alignments by using restriction classes as explained in the following section. In its stricter sense, an alignment between classes would also consider structural conformity like cardinality constraints on properties, class hierarchies, domain and ranges of properties, etc. We however do not consider this in order to provide simpler alignments as most of these ontologies are rudimentary and based on pre-existing relational structures.
In the alignment process, instead of focusing only on classes defined by rdf:type, we also consider classes defined by conjunctions of property value restrictions (i.e, has-Value constraints in the Web Ontology Language), which we will call restriction classes in the rest of the paper. For example, each instance from GEONAMES has its rdf:type as Feature. Traditional alignments would then only be between the class Feature from GEONAMES and another class from DBPEDIA, for example Place. As mentioned before, instances in GEONAMES are also categorized by the featureCode and featureClass properties. A restriction on values of such properties gives us classes that we can effectively align with classes from DBPEDIA. For example, the restriction class formed from the concept Feature with its value of featureCode property constrained to the instance 'geonames:A.PCLI' (Independent political entity) aligns with the Country concept from DBPEDIA. Our algorithm defines restriction classes from the source ontologies and generates alignments between such restrictions clases using subset or equivalence relationships.
Defining the Space of Restriction Classes for a Vector The space of restriction classes to which an instace belongs is simply the powerset of the property-value pairs of the vector representing the instance. For example assume that the GEONAMES source has only three properties: rdf:type, featureCode and featureClass; and that the vector for the instance Saudi Arabia is (geonames:Feature, geonames:A.PCLI, geonames:A). Then this instance belongs to the restriction class defined by (rdf:type=geonames:Feature & featureClass=geonames:A). The other sets from the powerset also form such restriction classes as shown in Figure 1. We employ a bottom-up approach to determining the restriction classes to which an instance belongs. For example, the instance vector for Saudi Arabia directly supports the restriction class (rdf:type=geonames:Feature & featureCode=geonames:A.PCLI & featureClass=geonames:A). This restriction in turn supports the three restrictions shown in Figure 1. These subsequently support restrictions formed by eliminating a constraint on one of the properties in it. In general, if for the n number of properties for the vector at the current level we select m properties to constrain our restrictions, then that level would contain n m restrictions that represent elements from the combinatorial set C (n,m) from the set S (see Section 3.2). These n m restrictions would in turn support restriction sets formed by choosing (m-1) properties from S (i.e. C (n,m-1)). For a restriction at level l we call all the restrictions at level (l-1) that it supports as its parent restrictions. We can see that, if a restriction is supported by some individuals, then those individuals also support any of its parent restrictions. Using this hierarchical approach for any vector, we can build a set of restriction classes that it supports (denoted by R), in a bottum-up fashion, starting with a restriction class corresponding to the vector. It is evident that in order to consider all restriction classes, the algorithm would be exponential. We thus need some preprocessing that eliminates those columns that are not useful.
In order to reduce the search space of alignment hypotheses, we identify properties that do not contribute to the alignment. Inverse functional properties resemble secondary keys in databases and identify an instance uniquely. Thus, if a restriction class is constrained on the value of an inverse functional property, it would only have a single element in it. As an example, consider the wikipediaArticle property in GEONAMES. An instance in GEONAMES has links to multiple pages in Wikipedia, each in a different language. For example, the instance for the country Saudi Arabia5 has links to 237 different articles. Each of these in turn, however, could be used to identify only Saudi Arabia. On the other hand, each of the seven million unique features is also classified into nine different Feature Classes. Thus, featureCode and featureClass properties are not inverse functional properties and instances can be grouped by restrictions with constraints on these properties. We remove a column from the table of vectors if its corresponding property is inverse functional. In some of the cases (like the alternateName and wikipediaArticle) the multivalued properties get eliminated and thus the number of rows in the flat table gets reduced.
From these individual vectors, we then perform a join on the owl:sameAs property from GEONAMES such that we get a combination of properties from both ontologies. We call this concatenation of two vectors an instance pair. In case of multiple vectors for the same URI (as a result of multivalued properties), we get instance pairs whose count is equal to the product of the number of vectors from each of the ontologies.
We build our alignment hypothesis in a bottom-up fashion by examining each instance pair and the restriction classes that its corresponding vector supports. Each alignment hypothesis is a two part conjunction of a restriction class from the first ontology (GEONAMES) and a restriction class from the second one (DBPEDIA). In order to come up with these hypotheses we look at vectors that compose each of the instance pairs. If we build a set of restrictions R 1 from the first vector and R 2 from the second vector, then the set of hypotheses that this instance pair supports is the Cartesian product of R 1 and R 2 . We then would aggregate such hypotheses over all instance pairs and eliminate the hypotheses that contain only a singleton set of instance pairs supporting it. As a result we would be left with alignments supported by multiple instances between the two sources. In practice however this brute force method is very inefficient in space and time considerations. Hence we use an algorithm that capitalizes on the set containment property of the restrictions and thus finds alignments inspired from the bottum-up method described in Section 3.2.
For building hypotheses of alignments, we begin with each instance pair. We assert a seed hypothesis such that if vector 1 is the first part (from GEONAMES) of this pair and vector 2 is the second part (from DBPEDIA), then the restriction class corresponding to vector 1 (built of constraints on each of its property-value pairs) has an alignment with the restriction class corresponding to vector 2 . Let r 1 & r 2 be the restriction classes constituting this hypothesis. We compute P 1 & P 2 as the set of parent restrictions of . We now build a set of parent hypotheses from the seed source that contains an alignment from each restriction p 1 from P 1 to r 2 and vice versa. We keep a track of all our hypotheses and all the instances pairs that support them. If an instance pair supports one hypothesis, then it also supports all of its parent hypotheses. We can say this, because the restrictions constituting our hypothesis support their own parent restrictions, which in turn constitute our parent hypotheses. This process is illustrated in Figure 2.
After building the hypotheses, we score each hypothesis to ascertain the degree of confidence with which we hold this alignment to be true. For each hypothesis, we refer to the restriction classes constituting it. We then find all instances belonging to the restriction class r 1 from the first source and r 2 from the second source. Figure 3 shows the sets of such instances. We then compute the image of r 1 (denoted by I(r 1 )), which is the set of instances from the second source that form instance pairs with instances in r 1 , by following the owl:sameAs links. The dashed lines in the figure represent these instance pairs. All the pairs that match both restrictions r 1 and r 2 also support our hypothesis and thus is equivalent to the instance pairs corresponding to instances belonging to the intersection of the sets r 2 and I(r 1 ). This set of instance pairs that support our hypothesis is depicted as the shaded region. We can now capture subset and equivalence relations between the restriction classes by set-containment relations from the figure. For example, if the set of instance pairs identified by r 2 are a subset of I(r 1 ), then the set r 2 and the shaded region would be entirely contained in the I(r 1 ). We use two metrics P and R to quantify these set-containment relations. Figure 4 summarizes these metrics and also the different cases of intersection. In order to allow a certain margin of error induced by the dataset, we are lenient on the constraints and use the relaxed versions P' and R' as part of our scoring mechanism. Instance pairs where r 1 holds While calculating results, we find equivalences and subsets as follows. Consider a hypothesis from the restriction class 'featureClass=geonames:H' from GEONAMES to restriction class 'rdf:type=dbpedia:BodyOfWater' from DBPEDIA. Based on the support for the hypothesis we have |I(r 1 )| = 2132, |r 2 | = 1989 and |I(r 1 ) ∩ r 2 | = 1959. Thus, P' = 0.98 & R' = 0.92 and we say that it is an equivalence alignment as both P' and R' are greater than a threshold of 0.9 as explained in Figure 4. Similarly, we also identify alignments like the restriction class 'featureCode=geonames:P.PPL' ⊂ restriction class 'rdf:type=geonames:Place' and others as shown in Table 1
We generated alignments using the above described method on a subset of GEONAMES and DBPEDIA that contains only instances that are linked together. After having generated alignments on a subset of the data, we found that most of the properties left after preprocessing and removing the inverse-functional properties in DBPEDIA did not have enough support in the database. Moreover, as the classes in the DBPEDIA ontology are well-defined and highly specialized, we focused only on the rdf:type property on the DBPEDIA side for the results. Our approach generates 20116 hypotheses that cannot be specialized further and have a support of more than one instance pair. From this we get 8 equivalences, 2937 r 1 ⊂ r 2 relations and 60 r 2 ⊂ r 1 relations. Table 1 shows some examples of the equivalence classes that our algorithm finds. Note that as we consider only the subset of GEONAMES and DBPEDIA consisting of instances linked via owl:sameAs links, our algorithm classifies as equivalence alignments like the one between 'rdf:type=geonames:Feature' and 'rdf:type=dbpedia:Place', which with more linked data would probably not hold.
We also ran our algorithm on the LINKEDGEODATA-DBPEDIA subset. As these ontologies contain classes that are highly specialized, we chose to restrict the alignments only between the rdf:types of the sources. We generate 176 hypotheses that cannot be specialized further and have a support of more than one instance pair. From this we get 9 equivalences, 66 r 1 ⊂ r 2 relations and 14 r 2 ⊂ r 1 relations. These results are summarized in Table 1.
It should be noted that these alignments closely follow the semantics behind the sources. For example, looking at the results we would assume that the alignment of 'geonames:featureCode=T.MT' (Mountain) with 'rdf:type=dbpedia:Mountain' would be equivalent. Closer inspection of the GEONAMES dataset shows, however, that there are some places with Feature Codes like 'T.PK' (Peak), 'T.HLL' (Hill), etc. from GEON-AMES whose corresponding instances in DBPEDIA are all typed 'dbpedia:Mountain'. This implies that the interpretation of the concept 'Mountain' is different in both the sources and only a subsumption relation holds.
There is large previous literature on ontology matching [2]. Ontology matching has been based on terminological (e.g. linguistic and information retrieval techniques [11]), structural (e.g. graph matching [12]) and semantic (e.g. model based) approaches or their combination. The FCA-merge algorithm [13] uses extension techniques over common instances between two ontologies to generate a concept lattice in order to merge them, and thus align them indirectly. This algorithm, however, relies on a domain expert (users) to generate the merged ontology and is based on a single corpus of documents instead of two different sources, unlike our approach. Perhaps a strong parallel to our work is found in Duckham et al. [14] which also uses an extensional approach for fusion and alignment of ontologies in geospatial domain. The difference in our approach in comparison to their work (apart from the fact that it predates Linked Data) is that while their method fuses ontologies and aligns only existing classes, our approach is able to generate alignments between classes that are derived from the existing ontology by imposing restrictions on values of any or all of the properties not limited to the class type. Most of the work in information integration within the Web of Linked Data is in instance matching as explained in Bizer et al. [4]. Raimond et al. [15] use string and graph matching techniques to interlink artists, records, and tracks in two online music datasets (Jamendo and MusicBrainz) and also between personal music collections and the MusicBrainz dataset. Our approach solves a complimentary piece of the information integration problem on the Web of Linked Data by aligning ontologies of linked data sources.
Linked Data on the Web contains linked instances from multiple sources without the ontologies of the sources being themselves linked. However, it is useful to the consumers of the data to define the alignments between such ontologies. Our algorithm generates alignments, consisting of conjunctions of restriction classes, that define subsumption and equivalence relations between the ontologies. This paper focused on automatically finding alignments between the ontologies of geospatial data sources. However, the technique is general and can be applied to other Web of Linked Data data sources.
In our future work, we plan to improve the scalability of our approach, specifically, improve the performance of the algorithm that generates alignment hypotheses by using a more heuristic exploration of the space of alignments. We also plan to apply our alignment techniques to other sources in the Web of Linked Data beyond the geospatial domain, such as the richly interlinked genetic data published by Bio2RDF [16].