Radon results for OAEI 2017 Kevin Dreßler2 , Mohamed Ahmed Sherif1 , and Axel-Cyrille Ngonga Ngomo1 1 Paderborn University, Data Science Group, Pohlweg 51, D-33098 Paderborn, Germany E-mail: {firstname.lastname}@upb.de 2 Department of Computer Science, University of Leipzig, 04109 Leipzig, Germany E-mail: {lastname}@informatik.uni-leipzig.de Abstract. Datasets containing billions of geospatial resources are increasingly being represented according to the Linked Data principles. Radon is an efficient solution for the discovery of topological relations between such geospatial re- sources according to the DE9-IM standard. Radon uses a sparse space tiling index in combination with minimum bounding boxes to reduce the computation time of topological relations. In this paper, we present the participation of Radon in the OAEI 2017 campaign. The OAEI results show that Radon outperforms the other state of the art significantly in most of the cases. 1 Presentation of the system Radon is a time-efficient link discovery algorithm for topological relations between geospatial resources, implemented within Limes [3]. Given two sets of RDF resources S and T and a relation R, the goal of link discovery is to find the mapping M = {(s, t) ∈ S × T : R(s, t)}. Radon enables the time-efficient discovery of all topological relations that can be defined in terms of the DE-9IM stan- dard [1]. In order to achieve time-efficiency, two optimization techniques are utilized: optimized sparse space tiling on the dataset level and Minimum Bounding Box (MBB)- based filtering on the resource level. In the following, we introduce the basic concepts needed to understand Radon be- fore we outline the aforementioned optimization techniques. More detailed explana- tions can be found in [5]. The Minimum Bounding Box (MBB) of a geometry g in n dimensions is the rectangular box with the smallest measure (area, volume, or hypervolume in higher dimensions) within which all points of g lie. Another term for MBB is envelope. Space tiling is a technique for indexing spatial data, where n-dimensional affine spaces are split into any number of hyperrectangles with edge lengths `i and granularity factors ∆i = (`i )−1 where i ∈ {1, . . . , n}. These hyperrectangles can then be addressed using vectors from Nn , which allows for various optimizations. 1.1 Optimized Sparse Space Tiling The goal of the optimized sparse space tiling is to generate an index I for mapping all geometries s ∈ S , t ∈ T to sets of hyperrectangles. For the sake of clarity, the following description focuses on the two-dimensional case. As a first step, we use a heuristic to get good granularity factors for both latitude and longitude dimensions (∆ϕ , ∆λ ). Then, we apply space tiling, in which we map a geometry g to the set of hyperrectangles over which its MBB spans. To implement this idea, we insert a reference to g into all those hyperrectangles, that are realized as entries of a HashMap. To optimize (i.e. sparsify) the generated index, we start by computing estimated total hypervolumes (eth) of the datasets S and T . We first index the dataset with the smaller eth for each resource of the other dataset. We then add only to I the subset of resources from the second dataset which shares the same hyperrectangles from the first dataset resources contained in I. Using this technique together with the HashMap implementation of the hyperrectangle index significantly reduces the size of the generated data structure and consequently also the time to traverse it. 1.2 MBB-based Filtering After the optimized sparse space tiling step described above, we traverse the gener- ated index, visiting one hyperrectangle at a time. As a consequence of our approach, each generated hyperrectangle contains references to at least one geometry from each dataset. For each pair (s, t) of geometries, where s ∈ S and t ∈ T , we then employ a filtering step before actually triggering the potentially expensive (in cases of large ge- ometries) computation that checks if the given relation holds. Let (g) denote the MBB of geometry g. The filtering step leverages the fact that ¬r((s), (t)) ⇒ ¬r(s, t) holds for every relation r, where one geometry has no interior or boundary points in the ex- terior of the other geometry, i.e. s ⊆ t or t ⊆ s. For these relations, we can return false and skip further computations, iff the geometries MBB’s do not satisfy the relation. 2 Adaptations made for the evaluation No specific adaptations were made to the original Radon algorithm [5], we only provide a Java SystemAdapter according to the campaign guidelines3 . The final Radon Java SystemAdapter source code is available online in the project website4 . 3 Evaluation Results Radon has been evaluated only in the Hobbit Link Discovery Track Task 2 (Spatial). The basic idea behind this task was to measure how well the systems can identify DE- 9IM (Dimensionally Extended nine-Intersection Model) topological relations. The sup- ported spatial relations were: Disjoint, Touches, Contains/Within, Covers/CoveredBy, 3 https://goo.gl/cWmZ5P 4 https://goo.gl/awkvvo Intersects, Crosses, Overlaps. The geospatial resources traces were represented in Well- known text (WKT) format as LineStrings . Given two sets of LineString geometries S and T and a DE-9IM topological re- lation R, the participants were assigned the task of retrieving the mapping M = {(s, t) ∈ S ×T : R(s, t)}. All the systems were tested against two datasets: (1) the sandbox dataset, with a scale of 10 instances, and (2) the mainbox dataset with a scale of 2K instances. The other participants to this task in addition to Radon were AgreementMakerLight (AML), OntoIdea, and Silk. The systems were judged on the basis of precision, recall, F-Measure and run time. The final results are shown in Table 1 and Figures 1 and 2. Note that we are only presenting the time performance and not precision, recall and F-Measure, as all were equal to 1.0 except OntoIdea Touches and Overlaps which is equal to 0.99. From these results we can see that, while Radon performs in the middle field of the the sandbox dataset, Radon outperforms the other participants on most relations for the sandbox dataset. Notably, the optimization described in Section 1.2 speeds up the relations Equals, Contains, Within, Covers and CoveredBy significantly in comparison to the remaining relations. The differences in performance between Touches, Intersects, where AML outperforms Radon, and Overlaps cannot be explained from an implemen- tation point of view, as these three relations share the exact optimizations. However, due to the datasets consisting exclusively of LineStrings, it is apparent that Touches and Intersects are much more likely to hold between any two geometries than Overlaps. Therefore, the benchmarks on these relations are the hardest in this task. 4 Conclusion We priefly presented Radon, an approach for rapid discovery of topological relations among geo-spatial resources. To achieve a high scalability, Radon combines space tiling, minimum bounding box approximation and a sparse index. The presented evalu- ation during the OAEI 2017 showed that, in addition to being complete and correct (i.e. achieving an F-Measure of 1.0), Radon also outperforms the other participating systems in most of the cases. In future work, we aim to apply the particle-swarm-optimization load balancing approaches [6]. To improve the performance of Radon on high resolu- tion datasets, i.e. datasets whose containing geometries consist of a large set of points, we will optimize the computation of relation checks. In order to further reduce the amount of computations, we will consider adaptive granularity factors, i.e. granularity factors as functions of latitude and longitude. In addition, we aim to combine Radon with the machine learning approaches already implemented in Limes such as the Wom- bat [4] algorithm. Finally, we will consider the discovery of temporospatial relations, by integrating the Aegle[2] algorithm with the Radon approach. Acknowledgments This work has been supported by the eurostars project SAGE (GA no. E!10882), the H2020 projects SLIPO (GA no. 731581) and HOBBIT (GA no. 688227) as well as the Fig. 1. Runtime comparison for Sandbox dataset Fig. 2. Runtime comparison for Mainbox dataset Table 1. Hobbit link discovery task evaluation results for all participants. Note that we used — for systems which were not participating in the specified sub-task and × for systems that exceeded the time limit. Relation System Sandbox Mainbox AML 8157 10284 OntoIdea 1531 567169 Equals Radon 2215 4680 Silk 4059 125967 AML 7173 × OntoIdea — — Disjoint Radon 1558 19214 Silk 3224 257877 AML 11207 20252 OntoIdea 4712 473430 Touches Radon 2672 485765 Silk 4805 1777747 AML 9191 16966 OntoIdea 1489 223857 Contains Radon 2228 6937 Silk 4160 83958 AML 10186 12308 OntoIdea 4517 236506 Within Radon 2203 5036 Silk 4037 88758 AML 7177 11859 OntoIdea 1503 313298 Covers Radon 2180 6772 Silk — — AML 8184 14703 OntoIdea 1467 304509 CoveredBy Radon 2132 4721 Silk — — AML 9269 66681 OntoIdea 1505 510938 Intersects Radon 2737 339742 Silk 3582 1718035 AML 8224 19385 OntoIdea 1509 461693 Crosses Radon 2131 8490 Silk 3917 203763 AML 10223 194838 OntoIdea 1486 530752 Overlaps Radon 2167 60801 Silk 4217 464382 DFG project LinkingLOD (project no. NG 105/3-2) and the BMWI Project GEISER (project no. 01MD16014E). References 1. E. Clementini, J. Sharma, and M. J. Egenhofer. Modelling topological spatial relations: Strate- gies for query processing. Computers & graphics, 18(6):815–822, 1994. 2. K. Georgala, M. A. Sherif, and A.-C. N. Ngomo. An efficient approach for the generation of allen relations. In Proceedings of the 22nd European Conference on Artificial Intelligence (ECAI) 2016, The Hague, 29. August - 02. September 2016, 2016. 3. A.-C. Ngonga Ngomo and S. Auer. Limes - a time-efficient approach for large-scale link discovery on the web of data. In Proceedings of IJCAI, 2011. 4. M. Sherif, A.-C. Ngonga Ngomo, and J. Lehmann. WOMBAT - A Generalization Approach for Automatic Link Discovery. In 14th Extended Semantic Web Conference, Portorož, Slove- nia, 28th May - 1st June 2017. Springer, 2017. 5. M. A. Sherif, K. Dreßler, P. Smeros, and A.-C. N. Ngomo. Radon-rapid discovery of topolog- ical relations. In AAAI, pages 175–181, 2017. 6. M. A. Sherif and A.-C. N. Ngomo. An optimization approach for load balancing in parallel link discovery. 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