Framework for Ontology Alignment and Mapping

Transcription

1 Framework for Ontology Alignment and Mapping Marc Ehrig, Steffen Staab and York Sure Abstract Semantic alignment between ontologies is a necessary precondition to establish interoperability between agents or services using different individual ontologies. This cannot be done manually beyond a certain complexity and size of ontologies. The core contribution in this article is the Framework for Ontology Alignment and Mapping (FOAM). With FOAM we address requirements from an application-based perspective such as high quality results, efficiency, high degree of automation with optional user-interaction, flexibility with respect to use cases, and easy adjusting and parameterizing. FOAM consists of a general alignment process based on the ontology-encoded semantics, different instantiations of the process focusing on various aspects of ontology alignment, and finally the concrete implementation as a powerful but easy to use Open Source tool. The evaluation results show that the different instantiations individually outperform existing approaches. However, best results can be gained when combining them. We expect that the findings suit not only the Semantic Web community, but may solve integration problems of related computer science fields as well. 1

2 1 Introduction Semantic alignment between ontologies is a necessary precondition to allow interoperability between agents or services using these different individual ontologies. The advantages of a world-wide Semantic Web lie in its machine-processability through such agents or services. For instance, in a setting where knowledge is distributed across the globe, it is automatically possible to derive new insights without human interaction.thus, ontology alignment and mapping become a core issue to resolve. Generally, there are two approaches for this. Either the alignment process is initiated before-hand, during the creation of an ontology. Ontology engineers discuss, negotiate, and vote, to come up with a shared ontology. Or alignment is performed afterwards, thus aligning ontologies and schemas which already exist. In this work we focus on the latter issue. Through these alignments we can translate requests and data between different ontologies, or we can even perform a complete merge of ontologies. As one can easily imagine, this cannot be done purely manually beyond a certain complexity, size, or number of ontologies any longer. Automatic or at least semi-automatic techniques have to be developed to reduce the burden of manual creation and maintenance of alignments. In recent years we have seen a range of research work on methods proposing such alignments [?,?,?]. When we tried to apply these methods to some of the real-world scenarios we address in other research contributions, e.g., querying a distributed peerto-peer network with many different knowledge representations (ontologies),[?,?] we found that existing alignment methods were not suitable for the tasks at hand. In particular, we need to resolve the issues of multiple use cases, such as ontology merging, ontology mapping, data integration, and query rewriting, to name a few. Existing methods focus on resolving one particular of the issues, making it difficult to reuse these approaches for already slightly different tasks. From the different use cases one can derive typical core requirements for an ontology alignment algorithm: (i) The returned alignments need to be of high quality meaning that most existing alignments need to be identified and only few wrong ones may be among them. (ii) The alignment process needs to be efficient and fast to suit on-the-fly alignment. (iii) Optional well though-out user-interaction can help to improve results. (iv) The approach needs to be flexible with respect to the different mentioned use cases. And (v) easy adjusting and parameterizing for inclusion of other approaches should be provided. Depending on the application these requirements might vary with respect to importance. In this article we consider different existing and novel approaches to fulfill these requirements. Only by this way we may reach the overall goal of having a framework for ontology alignment suiting a wide range of use cases and in specific meeting the demands of our use cases for the real world. For the end-user we provide a powerful but easy to use tool taking ontologies as input and returning alignments (with explanations) as output (Figure 1). Our framework for ontology alignment and mapping, FOAM, consists of a general alignment process, different instantiations of the process focusing on different requirements of ontology alignment, and the concrete implementation as a tool. FOAM has been applied in many real-world scenarios seamlessly and is already integrated into the ontology engineering platform OntoStudio

3 Input FOAM Framework for Ontology Alignment and Mapping Output incl. Explanation Figure 1: Ontology Alignment The remainder of this article starts with a clarification of terminology (Section 2). We then describe a canonical process for ontology alignment that subsumes the different approaches compared in this paper (Section 3). In Section 4, different approaches for proposing alignments are described and mapped to the canonical process. Besides well-known approaches, new approaches with specific foci are presented. Experimental results (Section 5) complement the comparison of the approaches across several dimensions. An investigation of related work is provided in Section 6. This paper closes with an outlook and an overall conclusion. 2 Terminology Before we start we need to clarify the underlying terminology. 2.1 Ontology In the understanding of this paper an ontology consists of both schema and instantiating data. An ontology O is therefore defined by the following tuple: O := (C, H C, R C, H R, I, R I, ι C, ι R, A) Concepts C of the schema are arranged in a subsumption hierarchy H C. Binary relations R C exist between pairs of concepts. Relations can also be arranged in a subsumption hierarchy H R. (Meta-)Data is constituted by instances I of specific concepts. Theses instances are interconnected by relational instances R I. Instances and relational instances are connected to concepts resp. relations by the instantiations ι C resp. ι R. Additionally one can define axioms A which can be used to infer knowledge from already existing knowledge. An extended definition can be found in [?]. Common languages to represent ontologies are RDF(S) or OWL, [?,?], though one should note that each language offers different modeling primitives. Ontologies are the input for the ontology alignment process. The following fragment of an automobile ontology O := ({automobile, luxury,...}, {...}, {speed(automobile, INT EGER),...}, {...}, {...}, {...}, {...}, {...}, {...}) can be represented in OWL as shown in Example 1. 3

4 <owl:class rdf:about= auto:automobile /> <owl:class rdf:about= auto:luxury /> <owl:datatypeproperty rdf:about= auto:speed > <rdfs:domain rdf:resource = auto:automobile /> <rdfs:range rdf:resource= xsd#integer /> </owl:datatypeproperty> Example 1. Fragment of Domain Ontology in OWL 2.2 Alignment and Mapping We here define our use of the term alignment similarly to [?]. Given two ontologies O 1 and O 2, aligning one ontology with another means that for each entity (concept C, relation R, or instance I) in ontology O 1, we try to find a corresponding entity, which has the same intended meaning, in ontology O 2. Formally, we define an ontology alignment function, align, based on the vocabulary, E, of all entities e E and based on the set of possible ontologies, O, as a partial function: align : E O O E, with e O 1 ( f O 2 : align(e, O 1, O 2 ) = f align(e, O 1, O 2 ) = ). A entity e interpreted in an ontology O is either a concept, a relation or an instance, i.e., e O C R I. We usually write e instead of e O when the ontology O is clear from the context of the writing. We write align O1,O 2 (e) for align(e, O 1, O 2 ). We derive a function align O1,O 2 by defining align O1,O 2 (e, f) align O1,O 2 (e) = f. We leave out O 1, O 2 when they are evident from the context and write align(e) = f and align(e, f), respectively. Once a (partial) alignment, align, between two ontologies O 1 and O 2 is established, we also say entity e is aligned with entity f iff align(e, f). An entity can be aligned to at most one other entity. A pair of entities (e, f) that is not yet in alignment and for which appropriate alignment criteria still need to be tested is called a candidate alignment. Two entities which have been aligned are also often called a mapping. They represent the output, the alignment process. The following example illustrates an alignment. Two ontologies O 1 and O 2 describing the domain of car retailing are given (Figure 2). Concepts are depicted as rectangular boxes, relations as hexagons, and instances as rounded boxes. Subsumption and instantiation relations are drawn as stretched triangles respectively. A relation has an incoming arrow from its domain and an outgoing arrow to its range. The labeled edges represent relation instances. In the example of Ontology 1 we have six concepts (Object, Vehicle,... ), two relations (hasowner and hasspeed), and three instances (Marc,... ). As one can see from the graph there is a subsumption hierarchy, e.g., between Object and Vehicle. Further each Vehicle hasowner Owner and each Car hasspeed Speed. On the instance level, the PorscheKA123 hasowner Marc and hasspeed 250km/h. Ontology 2 models the same domain slightly differently. Based on human experience a reasonable alignment between the two ontologies is given in Table 1 as well as by the dashed lines in the figure. Obviously things and objects, the two vehicles, cars and automobiles, as well as the two speeds are the same. 4

5 Further the relations hasspeed and hasproperty correspond to each other. Also the two instances Porsche KA-123 and Marc s Porsche are the assumed to be the same, which are both fast cars. Ontology 1 Ontology 2 Concept Relation Instance Alignment Figure 2: Example Ontologies and their Alignment Table 1: Alignment Table for Relation align O1,O 2 (e, f) Ontology O 1 Ontology O 2 Object Thing Car Automobile Porsche KA-123 Marc s Porsche Speed Characteristic 250 km/h fast Apart from one-to-one alignments as investigated in this article one entity often has to be aligned with a complex composite such as a concatenation of terms (first and last name) or an entity with restrictions (a sports-car is a car going faster than 250 km/h). [?,?] propose approaches for this. Our work does not deal with such issues of complex ontology alignments. As complex alignments consist of elementary alignments, our work can be seen as basis for this though. 3 Process We observed that alignment methods may be mapped onto a generic alignment process. We briefly introduce this canonical process that subsumes the heuristics-based align- 5

6 ment approaches. Figure 3 illustrates its six main steps in the most common order. Input to this process are two ontologies, which need to be aligned with one another. 1. Feature Engineering: Select small excerpts of the overall ontology definition to describe a specific entity (e.g., the label to describe the concept o1:car). 2. Search Step Selection: Choose two entities from the two ontologies to compare (e.g., o1:car and o2:automobile). 3. Similarity Computation: Indicate a similarity for a given description of two entities (e.g., simil label (o1:car,o2:automobile)=0). 4. Similarity Aggregation: Aggregate multiple similarity assessments for one pair of entities into a single measure (e.g., simil label (o1:car,o2:automobile) +simil instances (o1:car,o2:automobile)=0.5). 5. Interpretation: Use all aggregated numbers, some threshold and some interpretation strategy to propose the equality for the selected entity pairs (align(o1:car)= ). 6. Iteration: As the similarity of one entity pair influences the similarity of neighboring entity pairs, the equality is propagated through the ontologies (e.g., it may lead to a new simil(o1:car,o2:automobile)=0.85, subsequently resulting in align(o1:car)=o2:automobile. 6. Iteration Input 1. Feature Engineering 2. Search Step Selection 3. Similarity Computation 4. Similarity Aggregation 5. Interpretation Output Figure 3: General Alignment Process Eventually, the output returned is an alignment table representing the function align O1,O 2. Each of the presented steps can initialized through specific parameters. We can therefore refer to the process as a parameterizable alignment method [?], thus making FOAM a very flexible framework. In the following sections we will provide a toolbox of data structures and methods (the parameters for the process) common to many approaches that align ontologies. This gives us a least common denominator based on which concrete approaches instantiating the process depicted in Figure 3 can be compared more easily. To make the individual steps clearer the corresponding implemented activities of one specific alignment approach, namely Naïve Ontology Mapping (NOM) [?], are described with each step. 6

7 3.1 Feature Engineering To compare two entities from two different ontologies, one considers their characteristics, i.e. their features. The features may be specific for an alignment generation algorithm, in any case the features of ontological entities (of concepts, relations, instances) need to be extracted from extensional and intensional ontology definitions. See also [?] and [?] for an overview of possible features and a classification of them. Possible characteristics include: Identifiers: Strings with dedicated formats, such as unified resource identifiers (URIs) or RDF labels. RDF/S Primitives: For example, properties or subclass relations. OWL Primitives: One entity can be, e.g., declared as being the sameas another entity. Derived Features: These constrain or extend simple primitives (e.g. most-specificclass-of-instance). Aggregated Features: For them we need to aggregate more than one simple primitive, e.g. a sibling is every instance-of the parent-concept of an instance. Domain Specific Features: Often ontology alignment has to be performed in a specific application of one domain. For these scenarios domain-specific features provide additional value for the alignment process. Returning to our example, the relation speed is not a general ontology feature, but a feature which is defined in the automobile domain, e.g., in a domain ontology. Thus it will be important for correctly and only aligning representations of concrete vehicles. Ontology External Features: Any kind of information not directly encoded in the ontology, such as a bag-of-words from a document describing an instance, is subsumed by this class of features. We again refer to the example in Figure 2. The actual feature consists of a juxtaposition of relation name and entity name. The Car concept of ontology 1 is characterized through its label Car, the concept which it is linked to through subclassof, i.e., Vehicle, its concept sibling boat, and the direct property, hasspeed. Car is also described by its instances Porsche KA-123. The relation hasspeed on the other hand is described through the domain Car and the range Speed. An instance would be Porsche KA-123, which is characterized through the instantiated property instance of hasowner, Marc and the property instance hasspeed, 250 km/h. NOM Approach: For the NOM approach we rely on identifiers and RDF/S primitives only. The complete list of used features is presented in Table 2. As already mentioned FOAM however can be easily extended with other features. 3.2 Search Step Selection Before the comparison of entities can be processed it is necessary to choose which entities to compare. The most common and obvious is to compare all entities of the 7

8 first ontology with all entities of the second ontology. Any pair is treated as a candidate alignment. Nevertheless it can make sense to choose or prioritize among the candidate alignments. For the integration of databases there exists a related technique called blocking [?]. A concrete approach for ontologies will be explained in one of the more advanced ontology alignment approaches later in this article. 3.3 Similarity Computation We define a similarity measure for comparison of ontology entities as a partial function as follows (cf. [?]): sim : E E O O [0, 1] Different similarity measures sim k (e, f, O 1, O 2 ) are indexed by the variable k. Further, we leave out O 1, O 2 when they are evident from the context and write sim k (e, f). The following similarity measures are needed to compare the features of ontological entities. This list can easily be adapted and extended for additional features. For completeness we define the variable t representing the current iteration round. Object Equality: Object equality is based on existing logical assertions especially assertions from previous iterations of our process: { 1 align sim obj (a, b) := t 1 (a) = b, 0 otherwise Explicit Equality: This checks whether a logical assertion, such as given by the OWL sameas primitive, already forces two entities to be equal: { 1 iff statement(a, sameas, b), sim exp (a, b) := otherwise} 0 otherwise String Similarity: Based on Levenshtein s edit distance, ed [?], the similarity of two strings can be measured on a scale from 0 to 1 (cf. [?]). sim str (c, d) := max(0, min( c, d ) ed(c, d) ) min( c, d ) WordNet Synonyms: Similarity measures might make use of additional external resources. This one relies on the synonym sets defined in WordNet [?]. Two strings representing synonyms return 1, otherwise 0. Set Similarity: For many features we have to determine to what extent two entity sets of entities F, G E are similar. To remedy the problem we use the following heuristic. An entity is described by its distance to any other entity. We assume that if entities have very similar distances to all other entities, they must be very similar. We can now determine an average entity representing the set. Finally 8

9 we can measure the similarity of the two involved sets by applying the cosine measure: f F f sim set (F, G) = f F f g G g g G g with f = (sim(f, f 1 ), sim(f, f 2 ),..., sim(f, g 1 ), sim(f, g 2 ),...), g analogously. Dice Coefficient: Further, two sets of entities can be compared based on the overlap of the sets individuals[?]. Unfortunately this is only possible if the individuals are marked with a clear identifier: sim dice (F, G) := x (F G) x (F G) NOM Approach: The similarity computation between an entity of O 1 and an entity of O 2 is done by using a wide range of similarity functions. Each similarity function is based on a feature of both ontologies and a respective similarity measure as shown in Table 2 for NOM. In the first part of the table two concepts are compared. No. 1 represents that for each of the two concepts the labels are retrieved and these labels are compared using the (syntactic) string similarity. 3.4 Similarity Aggregation Our assumption is that a well thought-out combination of the so far presented features and similarity measures leads to better alignment results compared to using only one at a time. Clearly not all introduced similarity methods have to be used for each aggregation, especially as some methods have a high correlation. Even though a number of methods exist, no research paper especially focused on the combination and integration of these methods. Generally, similarity aggregation can be expressed through: k=1...n sim agg (e, f) = w k adj k (sim k (e, f)) k=1...n w k with w k being the weight for each individual similarity measure, and adj k being a function to transform the original similarity value (adj : [0, 1] [0, 1]), which might yield better results. Averaging: The adjustment function adj k is set to be the identity function. Further all the individual weights are equally set to 1. As result we receive a simple average over all individual similarities: adj k (x) = id(x) w k = 1 9

10 Table 2: Features and Similarity Measures for Different Entity Types in NOM. The corresponding ontology is indicated through an index. Comparing No. Feature Similarity Measure Concepts 1 (label,x 1 ) string(x 1, X 2 ) 2 (identifier,x 1 ) explicit(x 1, X 2 ) 3 (X 1,sameAs,X 2) relation object(x 1, X 2) 4 (direct relations,y 1 ) set(y 1, Y 2 ) 5 all (inherited relations,y 1) set(y 1, Y 2) 6 all (superconcepts,y 1 ) set(y 1, Y 2 ) 7 all (subconcepts,y 1 ) set(y 1, Y 2 ) 8 (subconc.,y 1) / (superconc., Y 2) set(y 1, Y 2) 9 (superconc.,y 1 ) / (subconc., Y 2 ) set(y 1, Y 2 ) 10 (concept siblings,y 1) set(y 1, Y 2) 11 (instances,y 1 ) set(y 1, Y 2 ) Relations 1 (label,x 1) string(x 1, X 2) 2 (identifier,x 1 ) explicit(x 1, X 2 ) 3 (X 1,sameAs,X 2 ) relation object(x 1, X 2 ) 4 (domain,x d1 ) and (range,x r1) object(x d1, X d2 ), (X r1, X r2) 5 all (superrelations,y 1 ) set(y 1, Y 2 ) 6 all (subrelations,y 1) set(y 1, Y 2) 7 (relation siblings,y 1 ) set(y 1, Y 2 ) 8 (relation instances,y 1) set(y 1, Y 2) Instances 1 (label,x 1 ) string(x 1, X 2 ) 2 (identifier,x 1) explicit(x 1, X 2) 3 (X 1,sameAs,X 2 ) relation object(x 1, X 2 ) 4 all (parent-concepts,y 1 ) set(y 1, Y 2 ) 5 (relation instances,y 1) set(y 1, Y 2) Relation- 1 (domain,d 1 ) and (range,r 1 ) object(d 1, D 2 ), (R 1, R 2 ) Instances 2 (parent relation,y 1) set(y 1, Y 2) 10

11 Linear Summation: For this aggregation only the weights w k have to be determined. The adj k ustment function is set to be the identity function. adj k (x) = id(x) We assume that similarities can be aggregated and are increasing strictly. The weights are assigned manually or learned, e.g., using machine learning on a training set. [?] have thoroughly investigated the effects of different weights on the alignment results. In our approach we are basically looking for similarity values supporting the hypothesis that two entities are equal. If a measure doesn t support the thesis, it still doesn t necessarily mean that it s opposing it. We respect the open world assumption in this paper. Further, this aggregation has the favorable characteristic that one can prove that eventually the alignments converge [?]. Linear Summarization with Negative Evidence: A negative value for w k needs to be applied if the individual similarity is not evidence of an alignment, but in contrary indicates that two entities should not be aligned. A typical example of such a case would be that super-concepts of the first entity have a high similarity with sub-concepts of the second entity. This is also included in Table 2 (No. 8 and 9 of the concepts). Sigmoid Function: A more sophisticated approach emphasizes high individual similarities and de-emphasizes low individual similarities. In the given case a promising function would be the sigmoid function, which has to be shifted to fit our input range of [0... 1] (see Figure 4). 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0, ,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Figure 4: Sigmoid function adj k (x) = sig k (x 0.5) with sig k (x) = 1 1+e a k x and a k being a parameter for the slope. The rational behind using a sigmoid function is explained best using an example. When comparing two labels, the chance of having the same entity if only one or 11

12 two letters differ is very high; these might just be because of type errors or different grammatical forms. Whereas, if only three or four letters match, there is no information in this similarity at all; an aggregation of several of these low values should not lead to an alignment. High values are therefore further increased; low values are further decreased. The parameters of the sigmoid function can be regarded as an extension of the similarity methods, as they have to be adjusted according to the method sim k they are applied to. Afterwards, the modified values are summed with specific weights w k attached to them. NOM Approach: NOM uses this sigmoid function for weighting its similarity measures. Further it makes use of negative evidence, as sometimes this is clearer than positive evidence. 3.5 Interpretation The approaches presented in this article are heuristics-based. An alignment is set, if the similarity indicates this. An alignment is not directly logically inferred by a reasoner as, e.g., in the work of [?]. This makes it easier to cope with limited support for or small inconsistencies in alignments which will always be the case for real world scenarios. Therefore, from the similarity values we derive the actual alignments. We assign alignments based on a threshold t applied to the aggregated similarity measures. Further, each entity may participate in either one or multiple alignments. We use the thresholds presented in [?]. Every similarity value above the cut-off indicates an alignment; every one below the cut-off is dismissed. Constant Similarity Value: For this method a fixed constant c is taken as threshold. t = c The constant threshold seems reasonable as we are collecting evidence for alignments. If too little evidence is extracted from the ontologies, it is simply not possible to reliably present alignments from this. However, it is difficult to determine this value. One possibility is an average that maximizes the quality in several test runs. Alternatively it might make sense to let experts determine the value, which only works if the similarity value can be interpreted by them. Delta Method: For this method the threshold for the similarity is defined by taking the highest similarity value of all and subtracting a fixed value c from it. t = max(sim agg (e i1 j 1, e i2 j 2 ) e i1 j 1 O i1, e i2 j 2 O i2 ) c N Percent: This method is closely related to the former one. Here we take the highest similarity value and subtract a fixed percentage p from it. t = max(sim agg (e i1 j 1, e i2 j 2 ) e i1 j 1 O i1, e i2 j 2 O i2 )(1 p) 12

13 The latter two approaches are motivated through the idea that similarity is also dependent on the domain. The calculated maximum similarity can be an indicator for this and is fed back into the algorithm. At some point during the design of an alignment process one has to decide how many alignments an entity might possibly be involved: One Alignment Link: The goal of this approach is to attain a single alignment between two entities from the best similarity values. As there can be only one best match, every other match is a potential mistake, which should be dropped. Practically we do cleansing in the alignment table by removing entries with already aligned entities. A greedy strategy starts with the largest similarity values first. Ties are broken arbitrarily by argmax (g,h), but with a deterministic strategy. align(e, f) (sim agg (e, f) > θ) ((e, f) = argmax (g,h) U V sim agg (g, h)). Multiple Alignment Links: Often it makes sense to keep multiple alignments, e.g., if a user checks the results manually after all. In this case the interpretation can be expressed through the following formula. align(e, f) sim(e, f) > t. NOM Approach: NOM interprets similarity results by two means. First, it applies a fixed threshold to discard spurious evidence of similarity. Second, NOM enforces bijectivity of the alignments by ignoring candidate mappings that would violate this constraint and by favoring candidate alignments with highest aggregated similarity scores. 3.6 Iteration For calculating the similarity of one entity pair many of the described methods rely on the similarity input of other entity pairs. The first round uses only basic comparison methods based on labels and string similarity to compute the similarity between entities. By doing the computation in several rounds one can access the already computed pairs and use more sophisticated structural similarity measures. This is related to the similarity flooding algorithm of [?], which in contrast to our approach doesn t interpret the edges through which the similarity is spread. Several possibilities when to stop the calculations have been described in the literature: Fixed Number of Rounds No More Changes to Alignments Changes Below a Certain Threshold Time Constraint 13

14 In his work [?] proved that the approach converges when certain characteristics apply to the algorithm. In specific, the weighting and aggregation function is critical in this context. Convergence can only be guaranteed if the overall similarity, i.e., the sum of all individual similarities, not just the similarities of alignments, rises monotonic and with smaller steps for each iteration. If the last change of overall similarity (increased by the sequence of estimated changes to come) is lower than the distance of any found alignment or non-alignment to the threshold, one can conclude that this gap will never be bridged, thus the alignments will not change. The iterative process can be stopped. When having more than one round of calculation the question arises if the results of each round should be converted/adjusted before they are fed back for the next round. One approach is to reuse only the similarity of the best alignments found. A possible way could be to give the best match a weight of 1, the second best of 1 2, and the third of 1 3. Potentially correct alignments are kept with a high probability but leave a path for second best alignments to replace them. The danger of having the system being diverted by low similarity values is minimized in this way. NOM Approach: For the first round NOM uses only a basic comparison method based on labels and string similarity to compute the similarity between entities. By doing the computation in several rounds one can access the already computed pairs and use more sophisticated structural similarity measures. Therefore, in the second round and thereafter NOM relies on all the similarity functions listed in Table 2. As we also include negative evidence in our considerations, we cannot guarantee the monotonic increase of similarity and thus convergence. But, in all our tests we have found that after ten rounds the approach converges in practice and hardly any further changes occur in the mapping table. This is independent from the actual size of the involved ontologies. NOM therefore restricts the number of runs to a fixed number. 4 Alignment Approaches After having presented the general ontology alignment process with possible parameters we will now describe particular instantiations thereof. We start with three wellknown tools: PROMPT: PROMPT uses labels to propose alignments between two ontologies [?]. These are then merged. Anchor-PROMPT: Anchor-PROMPT adds structural evidence to this [?]. GLUE: In their approach [?] use machine learning techniques to build instance classifiers. Further they rely on the structures. Our framework FOAM comprises four approaches: Naive Ontology Mapping (NOM): NOM has already been explained along the general process in the previous section [?]. It uses a big number of different ontology features. Further, it is our baseline approach we compare all others against. Quick Ontology Mapping (QOM): This approach lies its focus on efficiency considerations of alignment algorithms [?]. 14

15 Active Ontology Alignment (AOA): With this approach we aim at exploiting user interaction in the best possible way. Alignment Process Feature Estimation and Learning (APFEL): For the last approach we use machine learning techniques to gain an presumably optimal alignment approach [?]. We describe all approaches along the general alignment process. Each of them has two distinct ontologies as input, and shall return the corresponding alignments. 4.1 PROMPT/Label-Approach Before presenting various advanced approaches to compute ontology alignments we present a straight forward simple approach, which is only based on the labels of the compared entities. We do this along the example of the PROMPT-tool. PROMPT [?] is a tool that provides a semi-automatic approach to ontology merging and alignment. Together with ONION [?] it was one of the first tools for ontology merging. PROMPT is available as a plug-in to the Protégé 2 toolsuite. After having identified alignments by matching of labels the user is prompted to mark the alignments which should actually be merged. While merging PROMPT further presents possible inconsistencies. For this paper we concentrate on the actions performed to identify possible alignment candidates aka. the merging candidates. We do not consider the following merging steps. 1. Feature Engineering: The original PROMPT only uses labels. These could be taken e.g. from the RDFS ontology. 2. Search Step Selection: PROMPT relies on a complete comparison. Each pair of entities from ontology one and two is checked for similarity. 3. Similarity Computation: The system determines the similarities based on whether entities have similar labels. Specifically, PROMPT checks for identical labels as shown in Table 3. Table 3: PROMPT/Label: Features and Measures for Similarity Comparing No. Feature Similarity Measure Entities 1 (label,x 1) explicit(x 1, X 2) 4. Similarity Aggregation: As PROMPT uses only one similarity measure, aggregation is not necessary

16 5. Interpretation: PROMPT presents the pairs which have an identical label. For these pairs chances are high that they are actually the same. The user manually selects the ones he deems to be correct, which are then merged in PROMPT. PROMPT is therefore a semi-automatic tool for ontology alignment. 6. Iteration: The similarity computation does not rely on any previous computed entity alignments. One round is therefore sufficient. 4.2 Anchor-PROMPT Anchor-PROMPT [?] constitutes an advanced version of PROMPT which includes similarity measures based on ontology structures. Main changes occur for the similarity computation (step 3) and the iteration (step 6). 3. Similarity Computation: Anchor-PROMPT traverses paths between anchor points. The anchor points are entity pairs already identified as being equal, e.g., based on their identical labels. Along these paths new alignment candidates are suggested. Specifically, paths are traversed along hierarchies as well as along other relations. This corresponds to our similarity functions based on sub- and super-concepts no. 6 and 7 and other properties no. 4 in Table Iteration: Iteration is done in Anchor-PROMPT to allow manual refinement. After the user has acknowledged the proposition, the system recalculates the corresponding similarities and comes up with new merging suggestions. Table 4: Anchor-PROMPT: Features and Measures for Similarity Comparing No. Feature Similarity Measure Concepts 1 (label,x 1 ) explicit(x 1, X 2 4 all (direct properties,y 1) set(y 1,Y 2) 6 all (super-concepts,y 1 ) set(y 1,Y 2 ) 7 all (sub-concepts,y 1) set(y 1,Y 2) Other Entities 1 (label,x 1 ) explicit(x 1, X GLUE GLUE [?] is an approach for schema alignment. It makes extensive use of machine learning techniques. 1. Feature Engineering: In a first step the Distribution Estimator uses a multistrategy machine learning approach based on a sample alignment set. It learns concept classifiers based on instance descriptions, i.e., their naming, or the textual content of web pages. Naturally a big amount of example instances is needed for this learning step. Further the relaxation labeling step uses features such as subsumption, frequency, etc. 16

17 2. Search Step Selection: As in the previous approaches GLUE checks every candidate alignment. 3. Similarity Computation, 4. Similarity Aggregation, 5. Interpretation: In GLUE, steps 3, 4, and 5 are very tightly interconnected, which is the reason why they are presented as one step here. From this also the alignment of concepts is derived. From the Similarity Estimator (the two learned concept classifiers) GLUE derives whether concepts in two schemas correspond to each other. Concepts and relations are further compared using relaxation labeling. The intuition of relaxation labeling is that the label of a node (in our terminology: alignment assigned to an entity) is typically influenced by the features of the node s neighborhood in the graph. The authors explicitly mention subsumption, frequency, and nearby nodes. A local optimal alignment for each entity is determined using the similarity results of neighboring entity pairs from a previous round. The individual constraint similarities are summarized for the final alignment probability. The additional relaxation labeling, which takes the ontological structures into account, is again based solely on manually encoded predefined rules. Normally one would have to check all possible labeling configurations, which includes the alignments of all other entities. The developers are well aware of the problem arising in complexity, so they set up sensible partitions i.e. labeling sets with the same features are grouped and processed only once. The probabilities for the partitions are determined. One assumption is that features are independent, which the authors admit will not necessarily hold true. Through multiplication of the probabilities we finally receive the probability of a label fitting the node i.e. one entity being aligned with another one. The pair with the maximal probability is the final alignment result. 6. Iteration: To gain meaningful results only the relaxation labeling step and its interpretation have to be repeated several times. The other steps are just carried out once. The GLUE machine learning approach suits a scenario with extensive textual instance descriptions, but may not suit a scenario focused more to ontology structures. Further, relations or instances can not be directly aligned with GLUE. 4.4 Quick Ontology Mapping (QOM) When we tried to apply existing methods to some of the real-world scenarios we address in other research contributions, we found that existing alignment methods were not suitable for the ontology integration task at hand, as they all neglected efficiency. To illustrate our requirements: We have been working in realms where light-weight ontologies are applied such as the ACM Topic hierarchy with its 10 4 concepts or folder structures of individual computers, which corresponded to 10 4 to 10 5 concepts. Finally, we are working with Wordnet exploiting its 10 6 concepts (cf. [?]). When aligning between such light-weight ontologies, the trade-off that one has to face is between effectiveness and efficiency. For instance, consider the knowledge management platform built on a Semantic Web And Peer-to-peer basis in SWAP [?]. It is not sufficient 17

18 to provide its user with the best possible alignment, it is also necessary to answer his queries within a few seconds even if two peers use two different ontologies and have never encountered each other before. For this purpose, we optimize the effective, but inefficient NOM approach towards our goal. The outcome is an extended version: QOM Quick Ontology Mapping [?]. We would also like to point out that the efficiency gaining steps can be applied to other alignment approaches as well. 1. Feature Engineering: Like NOM, QOM exploits RDFS features. 2. Search Step Selection: A major ingredient of run-time complexity is the number of candidate alignment pairs which have to be compared to actually find the best alignments. Therefore, we use heuristics to lower the number of candidate alignments. Fortunately we can make use of ontological structures to classify the candidate alignments into promising and less promising pairs. In particular we use a dynamic programming approach [?]. In this approach we have two main data structures. First, we have candidate alignments which ought to be investigated. Second, an agenda orders the candidate alignments, discarding some of them entirely to gain efficiency. After the completion of the similarity analysis and their interpretation new decisions have to be taken. The system has to determine which candidate alignments to add to the agenda for the next iteration. The behavior of initiative and ordering constitutes a search strategy. We suggest the subsequent strategies to propose new candidate alignments for inspection: Random: A simple approach is to limit the number of candidate alignments by selecting either a fixed number or percentage from all possible candidate alignments. Label: This restricts candidate alignments to entity pairs whose labels are near to each other in a sorted list. Every entity is compared to its label -neighbors. Change Propagation: QOM further compares only entities for which adjacent entities were assigned new alignments in a previous iteration. This is motivated by the fact that every time a new alignment has been found, we can expect to also find similar entities adjacent to these found alignments. Further, to prevent very large numbers of comparisons, the number of pairs is restricted by an upper bound. This is necessary to exclude ontological artifacts such as ontologies with only one level of hierarchy from thwarting the efficiency efforts. Hierarchy: We start comparisons at a high level of the concept and property taxonomy. Only the top level entities are compared in the beginning. We then subsequently descend the taxonomy. Combination: The combined approach used in QOM follows different optimization strategies: it uses a label subagenda, a randomness subagenda, and a change propagation subagenda. In the first iteration the label subagenda is pursued. Afterwards we focus on alignment change propagation. Finally we shift to the 18

19 Table 5: Features and Similarity Measures for Different Entity Types Contributing to Aggregated Similarity in QOM. Features with a lower case a have been modified for efficiency considerations. Comparing No. Feature Similarity Measure Concepts 1 (label,x 1) string(x 1, X 2) 2 (identifer,x 1 ) explicit(x 1, X 2 ) 3 (X 1,sameAs,X 2 ) relation object(x 1, X 2 ) 4 (direct relations,y 1 ) set(y 1, Y 2 ) 5a (relations of direct superconc., Y 1 ) set(y 1, Y 2 ) 6a (direct superconcepts, Y 1) set(y 1, Y 2) 7a (direct subconcepts, Y 1 ) set(y 1, Y 2 ) 8a (subconc.,y 1) / (superconc., Y 2) set(y 1, Y 2) 9a (superconc.,y 1 ) / (subconc., Y 2 ) set(y 1, Y 2 ) 10 (concept siblings,y 1 ) set(y 1, Y 2 ) 11a (direct instances,y 1) set(y 1, Y 2) Relations 1 (label,x 1 ) string(x 1, X 2 ) 2 (identifier,x 1) explicit(x 1, X 2) 3 (X 1,sameAs,X 2 ) relation object(x 1, X 2 ) 4 (domain,x d1 ) and (range,x r1) object(x d1, X d2 ),(X r1, X r2) 5a (direct superrelations, Y 1 ) set(y 1, Y 2 ) 6a (direct subrelations, Y 1 ) set(y 1, Y 2 ) 7 (relation siblings,y 1) set(y 1, Y 2) 8a (direct relation instances,y 1 ) set(y 1, Y 2 ) Instances 1 (label,x 1) string(x 1, X 2) 2 (identifier,x 1 ) explicit(x 1, X 2 ) 3 (X 1,sameAs,X 2) relation object(x 1, X 2) 4a (direct parent-concepts, Y 1 ) set(y 1, Y 2 ) 5 (relation instances,y 1 ) set(y 1, Y 2 ) Relation- 1 (domain,x d1 ) and (range,x r1 ) object(x d1, X d2 ),(X r1, X r2 ) Instances 2 (parent relation,y 1 ) set(y 1, Y 2 ) randomness subagenda, if the other strategies do not identify sufficiently many correct alignment candidates. With these multiple agenda strategies we only have to check a bounded and restricted number of alignment candidates from ontology 2 for each original entity from ontology 1.Please note that the creation of the presented agendas does require processing resources itself. 3. Similarity Computation: QOM is based on a wide range of ontology feature and heuristic combinations. In order to optimize QOM, we have restricted the range of costly features as specified in Table 5. In particular, QOM avoids the complete pairwise comparison of trees in favor of a(n incomplete) top-down strategy. The accentuated comparisons in the table were changed from features which point to complete inferred sets to features only retrieving limited size direct sets. 19

20 4. Similarity Aggregation: The aggregation of single methods is only performed once per candidate alignment and is therefore not critical for the overall efficiency. Therefore, QOM uses a sigmoid function with manually assigned weights in this step. 5. Interpretation: Also the interpretation step of QOM is not critical with respect to efficiency. A threshold is determined and bijectivity of alignments is maintained. The alignments have to be checked once for this. 6. Iteration: QOM iterates to find alignments based on lexical knowledge first and based on knowledge structures later. Assuming that ontologies have a fixed percentage of entities with similar lexical labels, we will easily find their correct alignments in the first iteration. We also assume that these are evenly distributed over the two ontologies, i.e., the distance in terms of links in the ontology to the furthest not directly found alignment is constant. Through the change propagation agenda we carry on to the next adjacent alignment candidates with every iteration step. The number of required iterations remains constant; it is independent from the size of the ontologies Comparing Run-time Complexity We determine the worst-case run-time complexity of the algorithms to propose alignments as a function of the size of the two given ontologies. Thereby, we wanted to base our analysis on realistic ontologies and not on artifacts. We wanted to avoid the consideration of large ontologies with n leaf concepts but a depth of the concept hierarchy H C of n 1. [?] have examined the structure of a large number of ontologies and found, that concept hierarchies on average have a branching factor of around 2 and that the concept hierarchies are neither extremely shallow nor extremely deep. Hence, in the following we base our results on their findings. The different algorithmic steps contributing to complexity 3 are aligned to the canonical process of Section 3. For each of the algorithms, one may then determine the costs of each step. First, one determines the cost for feature engineering (feat). The second step is the search step i.e. candidate alignments selection (sele). For each of the selected candidate alignments (comp) we need to compute k different similarity functions sim k and aggregate them (agg). The number of entities involved and the complexity of the respective similarity measure affect the run-time performance. Subsequently the interpretation of the similarity values with respect to alignment requires a run-time complexity of inter. Finally we have to iterate over the previous steps multiple times (iter). Then, the worst case run-time complexity is defined for all approaches by: c = (feat + sele + comp ( k sim k + agg) + inter) iter 3 In this paper we assume that the retrieval of a statement of an ontology entity from a database can be done in constant access time, independent of the ontology size, e.g. based on sufficient memory and a hash function. 20

21 Depending on the concrete values that show up in the individual process steps the different run-time complexities may be derived. For NOM we derive the complexity as follows. Feature Engineering is done only once in the beginning O(f eat) = O(1). Setting up the complete candidate pairs results in a complexity of O(sele) = O(n 2 ), where n is the size of the ontologies. All the identified candidate pairs O(comp) = O(n 2 ) will then have to be compared using features and their similarities. For this we tie the complexity of the ontology feature with the corresponding similarity measure, e.g., to compare the subconcepts of two concepts we have to retrieve two subtrees (O(log(n)) and use the Set Similarity (O(setSize 2 )), which makes O( k sim k) = O(log 2 (n)). For each entity pair an aggregation operation is performed once with O(agg) = O(1). The interpretation is also done only once O(inter) = O(1). And finally with the number of iterations fixed this results in O(iter) = O(1). The worst case run-time behaviors of PROMPT, Anchor-PROMPT, GLUE, NOM, and QOM are given in the Table 6. Table 6: Complexity of Alignment Approaches Label/PROMPT O(n 2 1) Anchor-PROMPT O(n 2 log 2 (n)) GLUE 4 O(n 2 ) NOM O(n 2 log 2 (n)) QOM O(n log(n)) 4.5 Active Ontology Alignment Existing alignment approaches first identify the alignment fully automatically and then leave it up to the user to decide afterwards which ones are correct and may therefore be used in the respective application. Unfortunately it is extremely difficult to create a reasonable fully-automatic approach and even for the best approaches the results are often not satisfying. We therefore want to draw attention to a problem which hasn t been addressed in depth yet: the proper usage of human interaction for aligning ontologies. We aim to exploit the potential of user input already during runtime of an automatic alignment process. In our approach we want to include user input in the general process during runtime. Two core questions arise: 1. At which point of the ontology alignment process is user interaction reasonable? 2. What is the user to be asked to maximally increase the quality of the alignment results? 3. How should the input affect the process parameters, i.e., should they be adjusted? 4 This result is based on optimistic assumptions about the learner. 21

22 The second question is closely related to active learning approaches in machine learning [?]. The two ontologies represent the input and the correct alignments are the learning goal. Through exemplary alignments a background classifier is incrementally trained. The active learner focuses on processing those examples first which have the highest information value for building the classifier. We assume that optimization steps that can be done in beforehand have already been performed. 1. Feature Engineering: Active Ontology Alignment exploits RDF/OWL features. 2. Search Step Selection: The selection of data for the comparison process is kept simple. All entities of the first ontology are compared with all entities of the second ontology. Any pair is treated as a candidate alignment. 3. Similarity Computation: The best strategy for the similarity computation can be determined in beforehand. We will therefore simply keep the methods from the NOM approach as depicted in Table Similarity Aggregation: Again we use a sigmoid function with manually assigned weights in this step. 5. Interpretation: The only element dynamically changing throughout the alignment process are the automatically identified alignments themselves. We therefore want to include the user in the interpretation step during runtime. From all the calculated similarities we have received an aggregated similarity value. This value expresses the confidence that the two compared entities are the same, i.e., they can be aligned. A general threshold is set and all similarity values above the threshold automatically lead to an alignment, all below lead to a non-alignment. In this approach we further involve the user in the decision of whether an entity pair can be aligned or not. For scalability reasons it is not possible to present all the found (non-)alignments to the user for validation. However, the threshold represents a critical value, where the automatic classification has the highest doubt. Our hypothesis is that removing this uncertainty brings the biggest gains. Only alignments with this similarity value are presented to the user for validation. Further, similarities are heavily dependent on the graph structure of the ontology (see [?]): e.g., if all instances of two concepts are aligned, the concepts are most probably also to be aligned. The explicit alignment of a highly interlinked entity affects more other entities than a lowly interlinked entity. Highly interlinked entities are therefore given priority in comparison to lowly linked ones. The third question was whether to adjust the process parameters reacting to the input. This is done through changing the threshold. If the majority of answers have been positive, the threshold is set too high. For the following rounds, it is decreased according to the actual ratio of positive and negative answers. The opposite applies, if negative answers exceed their positive counterparts. The threshold is too low and 22