Ontology Based Data Access (OBDA) enables access to relational data with a complex structure through ontologies as conceptual domain models. A key component of an OBDA system are mappings between the schematic elements in the ontology and their correspondences in the relational schema. Today, in existing OBDA systems these mappings typically need to be compiled by hand. In this paper we present IncMap, a system that supports a semi-automatic approach for matching relational schemata and ontologies. Our approach is based on a novel matching technique that represents the schematic elements of an ontology and a relational schema in a uni ed way. Finally, IncMap can extend user-veri ed mapping suggestions in a pay-as-you-go fashion.
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val) hasTitle) leverage existing mappings. Finally, Section 4 presents an experimental evaluation using di erent (real-world) relational schemata and ontologies. Experiments show that the basic version of IncMap reduces the e ort for creating a mapping up to 20% compared to applying SF in a naive way. The incremental version of IncMap can reduce the total e ort by another 50% 70%. 2
The IncGraph model used by IncMap represents schema elements of an OWL ontology O and a relational schema R in a uni ed way. An IncGraph model is de ned as directed labeled graph (V; LblV ; E; LblE ). V represents a set of vertices, E a set of directed edges, LblV a set of labels for vertices and LblE a set of labels for edges. A label lV 2 LblV represents a name of a schema element whereas a label lE 2 LblE is either \ref" representing a so called ref-edge or \value" representing a so called val-edge. Figure 1 shows a cinematography related ontology O and relational schema R, as well as the result of constructing graphs IncGraph(O) and IncGraph(R) according to the IncGraph model. While O and R describe the same entities Directors and Movies and their relationship in a di erent way, the IncGraph O and R is designed to represent both in a structurally similar fashion.
However, after constructing the IncGraph models, structural di erences between IncGraph(O) and IncGraph(R) might still exist due to the mismatch between the high level view of the domain in ontologies and the low level view of data in relational databases. IncMap therefore adds annotations in IncGraph to bridge these structural gaps. Annotations are added as inactive ref-edges which can be activated during the schema matching process. For instance, additional ref-edges are added to IncGraph (R) as shortcuts for join-paths to better match the IncGraph (O). Moreover, another idea is to add inverse ref-edges to unify the structure resulting from modeling relationships in di erent directions (e.g., the directs-predicate in O vs. the directorFK -relationship in R in Figure 1. Finally, results from reasoning over an ontology O can also be integrated into IncGraph (O). Analyzing these annotations in detail is a future work.
Random LS SimilarityInverse LS Dist.
Random LS SimilarityInverse LS Dist. IncMap takes the IncGraphs produced for a relational schema R and for an ontology O as input. In its basic version, IncMap applies the original SF algorithm and thus creates initial mapping suggestions for the IncGraph of O and R. Additionally, IncMap can activate ref-edges (i.e., annotations) before executing the SF algorithm to achieve better results.
One important extension is the incremental version of IncMap. In this version the initial suggestions are re-ranked by IncMap by including user feedback. The idea of user feedback is that the user con rms those mapping suggestions of the previous iteration, which are required to answer a given user query over O.
We support three methods for incorporating user feedback into the matching
process: First, the naive Initializer method changes the score of con rmed or
rejected mappings to initialize the next run to 1:0 and 0:0, respectively. Second,
Self-Con dence Nodes work similar but the initialization is repeated during the
x-point computation of the SF algorithm which results in a stronger in uence
of the user feedback. Finally, In uence Nodes include additional nodes in the
graph structure to locally in uence the score of a con rmed or rejected mappings.
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IncMap is designed as a framework and provides di erent knobs to control which extensions and variations to use. A major avenue of future work is to apply optimization algorithms to nd the best con gurations automatically. 4
We evaluate IncMap using to two real-world scenarios that provided hand crafted mappings as gold standard. As a rst scenario, we evaluate a mapping from movie database IMDB to the Movie Ontology (http://www.movieontology.org) The second scenario is a mapping from the MusicBrainz database to the Music Ontology (www.musicontology.com) We evaluate IncMap w.r.t. reducing work time (i.e., e ort) needed to correct the correspondences suggested by IncMap to match the gold standard. The e ort is de ned as the sum of steps that users need to validate the suggested mappings for each node in the IncGraph (O). For validating one mapping the user needs to reject all suggested correspondences in the decreasing order of their nal ranking score until reaching the correct mapping whereas each rejection is counted as one step. Experiment 1 { Naive vs. IncGraph. In our rst experiment we compare the work time required to correct the mapping suggestions when the schema and ontology are represented naively as schema graphs, or using IncGraphs. Additionally, we vary the lexical matcher using three alternatives: randomly assigned scores (base line), Levenshtein similarity and inverse Levenshtein distance. Figure 2 shows that IncGraph works better in all cases than the naive approach. Experiment 2 { Incremental Mapping Generation. In the second experiment we evaluate the incremental schema matching in IncMap. Figure 3 show the resulting work time for the three incremental methods. Most signi cantly, incremental evaluation reduces the overall e ort (work time) by up to 50% 70% compared to the naive non-incremantal version. For both scenarios Self-Con dence Nodes and In uence Nodes work much better than the naive Initializer approach. 5
We presented IncMap, a novel semi-automatic matching approach for matching relational schemata to ontologies. Our approach is based on a novel uni ed graph model called IncGraph for ontologies and relational schemata. Based on the IncGraph model, IncMap implements a novel semi-automatic matching approach inspired by the Similarity Flooding algorithm to derive mappings using both lexical and structural similarities of ontologies and relational schemata. Our experiments with IncMap on real-world relational schemata and ontologies showed that the e ort for creating a mapping with IncMap is up to 30% less than using the Similarity Flooding algorithm in a naive way. The incremental version of IncMap reduces the total e ort of mapping creation by another 50% 70%.