1 Intelligence Artificial on Conference Joint International Twenty-Second the of Proceedings LIMES—AT ime-Efficient Approach for Large-Scale Link Discovery on the Web of Data ̈ Axel-Cyrille Ngonga Ngomo, S oren Auer ̈ ur Informatik AKSW/BIS, Institut f ̈ at Leipzig Universit Postfach 100920, 04009 Leipzig, Germany ngonga @informatik.uni-leipzig.de } auer { | To carry out a matching task, the distance measure as de- Abstract fined by the user is usually applied to the value of some prop- The Linked Data paradigm has evolved into a pow- and target S erties of instances from the source so as to de- T erful enabler for the transition from the document- tect instances that should be linked. Instances whose distance oriented Web into the Semantic Web. While the is lower or equal to a given threshold are considered to be can- amount of data published as Linked Data grows didates for linkage. The a-priori complexity of a matching steadily and has surpassed 25 billion triples, less , an unpractical proposition as task is proportional to | S || T | than 5% of these triples are links between knowl- soon as the source and target knowledge bases become large. edge bases. Link discovery frameworks provide the [ For example, discovering duplicate cities in DBpedia Auer et 9 functionality necessary to discover missing links ] al. , 2008 10 × 15 . 0 alone would necessitate approximately between knowledge bases. Yet, this task requires distance computations. Hence, the provision of time-efficient a significant amount of time, especially when it is approaches for the reduction of the time complexity of link carried out on large data sets. This paper presents discovery is a key challenge of the Linked Data. and evaluates LIMES, a novel time-efficient ap- nk Discovery Frame- In this paper, we present LIMES (Li proach for link discovery in metric spaces. Our ap- tric s paces) - a time-efficient approach for the dis- work for me proach utilizes the mathematical characteristics of covery of links between Link Data sources. LIMES addresses metric spaces during the mapping process to filter tri- the scalability problem of link discovery by utilizing the out a large number of those instance pairs that do angle inequality in metric spaces to compute pessimistic es- not suffice the mapping conditions. We present the timates of instance similarities. Based on these approxima- mathematical foundation and the core algorithms tions, LIMES can filter out a large number of instance pairs employed in LIMES. We evaluate our algorithms that cannot suffice the matching condition set by the user. The with synthetic data to elucidate their behavior on real similarities of the remaining instance pairs are then com- small and large data sets with different configura- puted and the matching instances are returned. We show that tions and compare the runtime of LIMES with an- compar- LIMES requires a significantly smaller number of other state-of-the-art link discovery tool. than brute force approaches by using synthetic data. In isons addition, we show that our approach is superior to state-of- the-art link discovery frameworks by comparing their runtime 1 Introduction in real-world use cases. Our contributions are as follows: We present a lossless and time-efficient approach for the • The core idea behind the Linked Data paradigm is to facilitate large-scale matching of instances in metric spaces. the transition from the document-oriented Web to the Seman- tic Web by extending the Web with a data commons consist- • We present two novel algorithms for the efficient ap- [ ] Volz , 2009 ing of interlinked data sources . While the et al. proximation of distances within metric spaces based on number of triples in data sources increases steadily and has the triangle inequality. surpassed 25 billions, links still constitute less than 5% of the We evaluate LIMES on synthetic data by using the num- • 1 . total number of triples available on the Linked Data Web ber of comparisons necessary to complete the given In addition, while the number of tools for publishing Linked matching task and with real data against the SILK frame- Data on the Web grows steadily, there is a significant lack of ] [ with respect to the runtime. , 2009 et al. Volz work time-efficient solutions for discovering links between these data sets. Yet, links between knowledge bases play a key role The remainder of this paper is structured as follows: after in important tasks such as cross-ontology question answer- reviewing related work in Section 2 we develop the math- [ [ ] , 2009 Urbani et al. et al. Lopez ing , , large-scale inferences ematical framework underlying LIMES in Section 3. We [ ] ] , 2010 2010 and data integration . Ben-David et al. present the LIMES approach in Section 4 and report on the re- sults of an experimental evaluation in Section 5. We conclude 1 http://www4.wiwiss.fu-berlin.de/lodcloud/ with a discussion and an outlook on future work in Section 6. 2312

2 3.1 Preliminaries 2 Related Work In the remainder of this paper, we use the following notation. Using the triangle inequality for improving the runtime of , m , m symbolize metrics m , Let be an affine space. A m 2 1 3 algorithms is not a novel idea. This inequality has been γ , β , α and A represent points from z and y , x ; A δ on and [ Cilibrasi and Vitanyi, used for tasks such as data clustering are scalars, i.e., elements of R . Furthermore, we assume that ] ] [ 2005 , 2007 et al. Wong , spatial matching and query pro- ( ) A, m is a metric space. ] [ cessing , 2003 et al. Yao . Yet, to the best of our knowledge, it has never been used previously for link discovery. (source) and S Given two sets Definition 1 (Matching task) Current frameworks for link discovery on the Web of (target) of instances, a metric T ∈ θ and a threshold m Data can be subdivided into two categories: domain-specific M , the goal of a matching task is to compute the set [ ∞ , [0 and universal frameworks. Domain-specific link discov- )) s, t ( of all instances of triples (i.e., the matching) s, t, m ( ery frameworks aim at discovering links between knowledge m such that T ∈ t and S ∈ s . θ ≤ ) s, t ( bases from a particular domain. For example, the RKB com- a ) s, t ( m We call each computation of the distance ] [ , 2009 et al. Glaser knowledge base (RKB-CRS) computes parison . The time complexity of a mapping task can be mea- [ links between universities and conferences while GNAT Rai- sured by the number of comparisons necessary to complete ] discovers links between music data sets. , 2008 et al. mond this task. A-priori, the completion of a matching task re- Universal link discovery frameworks are designed to carry comparisons. In this paper, we show how ) | T || S | ( O quires out mapping tasks independently from the domain of the the number of comparisons necessary to map two knowledge source and target knowledge bases. For example, RDF- bases can be reduced significantly by using the mathematical [ ] AI et al. , 2009 Scharffe implements a five-step approach characteristics of metric spaces. For this purpose, we make that comprises the preprocessing, matching, fusion, interlink particularly use of the triangle inequality (TI) that holds in [ ] Volz and post-processing of data sets. SILK , 2009 et al. metric spaces. (Version 2.0) is a time-optimized tool for link discovery. In- 3.2 Distance Approximation Based on the Triangle stead of utilizing the characteristics of metric spaces, SILK uses rough index pre-matching to reach a quasi-linear time- Inequality complexity. The drawback of the pre-matching approach is z and y , in A, Given a metric space ( A, m ) and three points x that the recall is not guaranteed to be 1. In addition, SILK al- the TI entails that lows the manual configuration of data blocks to minimize the ≤ m m ( x, y ) ) (1) ( x, z )+ m ( z,y . runtime of the matching process. Yet, this blocking approach Without restriction of generality, the TI also entails that is not lossless. The task of discovering links between knowledge bases is )+ (2) , ) y,z ( x, y ( m ≤ ) x, z m ( m [ closely related with record linkageand de-duplication Blei- thus leading to the following boundary conditions in metric ] holder and Naumann, 2008 . The database community has spaces: produced a vast amount of literature on efficient algorithms ≤ ) x, z m ) y,z ( m − ) x, y ( m ( (3) . ) y,z ( m )+ x, y ( m ≤ for solving these problems. Different blocking techniques such as standard blocking, sorted-neighborhood, bigram in- Inequality 3 has two major implications. First, the distance dexing, canopy clustering and adaptive blocking (see e.g. x in a metric space can be ap- z to any point from a point ] [ ̈ , 2009 K ) have been developed to address the opcke et al. to a reference proximated when knowing the distance from x problem of the quadratic time complexity of brute force com- y y and the distance from the reference point point .We z to parison methods. The rationale is to filter out obvious non- [ Frey and (following exemplar call such a reference point an matches efficiently before executing the more detailed and ] ). The role of an exemplar is to be used as a Dueck, 2007 time-consuming comparisons. sample of a portion of the metric space . Given an input A The difference between the approaches described above y to an exemplar x , knowing the distance from x point allows and our approach is that LIMES uses the triangle inequal- to to compute lower and upper bounds of the distance from x ity to portion the metric space. Each of these portions of the at a known distance from z any other point y . [ Frey and Dueck, space is then represented by an exemplar The second implication of inequality 3 is that the real dis- ] that allows to compute an accurate approximation of 2007 z if the lower θ tance from x to can only be smaller than the distance between each instance in this region and others z bound of the approximation of the distance from x to via instances. By these means, we can discovery links between any exemplar y is also smaller than θ . Thus, if the lower Linked Data sources efficiently without sacrificing precision. ( bound of the approximation of the distance m x, z ) is larger itself must be larger than θ , then . Formally, than θ ) m ( x, z 3 Mathematical Framework ( >θ. m ( x, y ) − m (4) y,z ) >θ ⇒ m ( x, z ) In this section, we present the mathematical principles under- to exem- T Supposing that all distances from instances t ∈ lying the LIMES framework. We present the formal defini- plars are known, reducing the number of comparisons simply tion of a matching task within metric spaces. Then, we use consists of using inequality 4 to compute an approximation this definition to infer upper and lower boundary conditions of the distance from all s and computing the S to all t ∈ T ∈ for distances based on the triangle inequality. Finally, we real distance only for the ( s, t ) pairs for which the first term show how these boundary conditions can be used to reduce of inequality 4 does not hold. This is the core of the approach the number of comparisons necessary to complete a mapping. implemented by LIMES. 2313

3 4 The LIMES framework Data : Number of exemplars n , target knowledge base T : Set E of exemplars and their matching to the Result In this section, we present the LIMES framework in more T instances in detail. First, we give an overview of the workflow it imple- ∈ T ; e 1. Pick random point 1 ments. Thereafter, we present the two core algorithms under- ; } , η = e 2. Set E = E ∪{ e 1 1 lying our framework. Finally, we present the architecture of to all ; T ∈ t 3. Compute the distance from e 1 the current implementation.

4 of the distance is less than the threshold. We terminate the Table 1: Average number of comparisons (in millions) for e as soon as the first similarity computation for an exemplar matching knowledge bases of different sizes (in thousands). e is found such that the lower bound of the distance is larger λ The columns are the size of the source knowledge base, while is sorted, i.e., if . This is possible since the list L than θ e the rows are the size of the target knowledge base. e >θ , then the same inequality holds for ) s, e ) − m ( m ( e, λ i 6 5 4 3 2 10 9 8 7 e . In the worst case, our matching algorithm with j>i all λ j 0.9 2.7 2 2.3 2.5 2.0 1.6 1.4 1.2 0.6 ) | , leading to a total worst- T has the time complexity O ( | S || 3 3.6 3.4 2.9 2.7 2.1 2.0 1.6 1.2 0.9 S + E , which is larger than (( O time complexity of | | | ) | T | ) | 3.9 1.1 4 1.6 2.0 2.5 2.9 3.1 3.6 4.5 that of the brute force approach. However, as our evaluation 5.5 5 1.4 1.9 2.3 2.8 3.4 3.9 4.2 4.8 with both synthetic and real data shows, a correct parameter- 3.3 1.6 6 2.8 3.9 4.4 5.0 5.4 6.1 2.1 ization of LIMES leads to dramatically reduced comparisons 5.7 3.2 3.7 4.4 5.1 2.6 6.4 6.6 7 1.9 and runtime. 2.8 3.4 4.1 5.0 5.5 6.6 7.1 7.5 8 2.0 7.6 3.0 5.4 6.3 6.9 4.7 8.2 3.9 2.4 9 5 Evaluation 4.3 5.0 6.0 6.3 7.8 8.3 9.2 10 2.6 3.5 Our evaluation is based on the implementation of the LIMES framework consisting of seven main modules (including a An analysis of the results displayed in Figure 2 also allows dashboard) of which each can be extended to accommodate 2 , the smaller the num- . The higher the value of θ to answer Q new or improved functionality 2 ber of comparisons. This is due to the stricter filtering that We elucidate the following four central evaluation ques- results from the higher threshold and consequently leads to a tions: smaller number of required comparisons. An important ob- What is the best number of exemplars? : Q 1 S servation is that, the larger the size of the knowledge bases θ and the What is the relation between the threshold : Q 2 , the higher the speedup obtained by using the LIMES T and total number of comparisons? approach. For example, while LIMES necessitates approxi- : Does the assignment of matter? T and S Q 3 mately 7 times less comparisons than a brute force approach : How does LIMES compare to other approaches? Q 4 =0 and θ 2 . 95 , in the for the knowledge bases of size 000 to Q , we performed an evaluation on syn- Q To answer 1 3 best case, it requires approximately 17 times less comparisons was thetic data as described in the subsequent section. Q 4 10 000 with the same threshold for knowledge bases of size , elucidated by comparing the runtimes of LIMES and SILK settings. on three different real-world matching tasks. , we measured the average number of com- To address Q 3 parisons required to map synthetic knowledge bases of sizes 5.1 Evaluation with Synthetic Data between 1,000 and 10,000 in all possible combinations of The general experimental setup for the evaluation on syn- S sizes for and T . For this experiment, the number of ex- √ thetic data was as follows: The source and target knowl- emplars was set to | θ . | T was set to 0.9. The results of this edge bases were filled with random strings having a maxi- experiment are summarized in Table 1. mal length of 10 characters. We used the Levenshtein metric Overall, the experiment shows that whether source or target to measure string similarity. Each of the matching tasks was knowledge base is larger does not affect the number of com- carried out five times and we report average values in the fol- parisons significantly. It appears that the results are slightly lowing. better when | S |≤| T | . Yet, the difference between the num- , we considered four match- and Q To address the first Q 1 2 ber of comparisons lies below 5% in most cases and is thus 2 000 ing tasks on knowledge bases of sizes between and , not significant. Therefore, the link discovery can always be . 000 95 and and 75 , . We varied the thresholds between 0 . 10 0 carried out by simply following the specification of the user the number of exemplars between 300 . We measured and 10 with respect to which endpoint is source resp. target of the the average number of comparisons necessary to carry out matching. each of the matching tasks (see Figure 2). Two main conclu- sions can be inferred from the results. First, the results clearly 5.2 Evaluation with Real Data indicate that the best number of exemplars diminishes when , we evaluated the performance of Q To answer the question θ is increased. In general, the best the similarity threshold 4 √ LIMES on real data by comparing its runtime with that of the | E | lies around value for | T 9 for θ | ≥ 0 , which answers . (to the best of our knowledge) only time-optimized link dis- E | θ . The relation between | is a direct cause of our and Q 1 covery framework SILK. Non-optimized frameworks would approach being based on the triangle inequality. Given a high perform like a brute-force approach, which is clearly infe- threshold, even a rough approximation of the distances is suf- rior to LIMES. To ensure an objective comparison of the run- ficient to rule out a significant number of target instances as times, we only considered the time necessary for both frame- being similar to a source instance. However, a low threshold works to carry out the comparisons in our evaluation . Each of demands a high number of exemplars to be able to rule out a the time measurements was carried out three times and only significant number of target instances. the best runtime was considered. Note that there was no sig- 2 nificant different between the different runtimes of LIMES. http:// LIMES is available as an open-source framework at limes.sf.net . Every time measurement experiment was carried out as a sin- 2315

5 100 45 90 40 80 35 70 30 0.75 0.75 60 25 0.8 0.8 50 20 0.85 0.85 40 15 0.9 30 0.9 10 20 0.95 0.95 comparisons 5 comparisons 10 5 Brute force 5 Brute force 10 0 0 10 50 200 250 300 0 100 150 0 50 300 250 200 150 100 Exemplars Exemplars (b) Size = 3000 (a) Size = 2000 1200 300 1000 250 800 200 0.75 0.75 0.8 0.8 600 150 0.85 0.85 400 100 0.9 0.9 0.95 0.95 50 200 comparisons comparisons 5 5 Brute force Brute force 10 10 0 0 250 300 0 50 100 150 200 300 200 150 100 50 0 250 Exemplars Exemplars (d) Size = 10000 (c) Size = 5000 Figure 2: Comparisons required by LIMES for different numbers of exemplars on knowledge bases of different sizes. The 5 . x-axis shows the number of exemplars, the y-axis the number of comparisons in multiples of 10 5 6 gle thread on a 32-bit system with a 2.5GHz Intel Core Duo from MESH with the corresponding diseases in LinkedCT CPU and 4GB RAM. For our experiments, we used version by comparing their labels. The configuration files for all three 0.3.2 of LIMES and version 2.0 of SILK. We did not use experiments are available in the LIMES distribution. SILK’s blocking feature because it loses some links and we were interested in lossless approaches. The number of exem- √ Table 3: Absolute runtimes of LIMES and SILK. All times plars for LIMES was set to . | T | are given in seconds. The values in the second row of the table are the similarity thresholds. LIMES SILK Table 2: Overview of runtime experiments. | S | is the size 0.75 0.95 0.9 0.85 0.8 is the size of the target | T of the source knowledge base, | 211 Drugs 86 120 175 252 1,732 is the number of exemplars used by E | knowledge base and | 1,403 523 SimCities 1,547 1,722 33,786 979 LIMES during the experiment. Diseases 546 949 1,327 1,784 1,882 17,451 Drugs Diseases SimCities 23,618 12,701 4,346 | S | Figure 3 shows a relative comparison of the runtimes of 4,772 12,701 5,000 | T | SILK and LIMES. The absolute runtimes are given in Ta- 112 69 | E | 70 ble 3. LIMES outperforms SILK in all experimental settings. Source DBpedia DBpedia MESH It is important to notice that the difference in performance Target DBpedia LinkedCT Drugbank grows with the (product of the) size of the source and target knowledge bases. While LIMES ( θ = 0.75) necessitates ap- The experiments on real data were carried out in three dif- proximately 30% of SILK’s computation time for the Drugs ferent settings as shown in Table 2. The goal of the first ex- experiment, it requires only roughly 5% of SILK’s time for 3 and periment, named Drugs, was to map drugs in DBpedia the SimCities experiments. The difference in performance is 4 by comparing their labels. The goal of the second Drugbank even more significant when the threshold is set higher. For experiment, named SimCities, was to detect duplicate cities example, θ = 0.95 leads to LIMES necessitating only 1.6% within DBpedia by comparing their labels. The purpose of of SILK’s runtime in the SimCities experiment. The poten- the last experiment, named Diseases, was to map diseases tial of our approach becomes even more obvious when one 3 5 http://dbpedia.org/sparql http://mesh.bio2rdf.org/sparql 4 6 http://www4.wiwiss.fu-berlin.de/drugbank/sparql http://data.linkedct.org/sparql 2316

6 References takes into consideration that we did not vary the number of exemplars in this experiment. Setting optimal values for the ] [ ̈ oren Auer, Chris Bizer, Georgi Kobi- et al. , 2008 Auer S number of exemplars would have led to even smaller runtimes larov, Jens Lehmann, Richard Cyganiak, and Zachary Ives. as shown by our experiments with synthetic data. ISWC2008 DBpedia: A nucleus for a web of open data. In , pages 722–735. Springer, 2008. 100,00% [ ] David Ben-David, Tamar Domany, , 2010 Ben-David et al. 90,00% and Abigail Tarem. Enterprise data classification using 80,00% , 2010. ISWC2010 semantic web technologies. In 70,00% ] [ Jens Bleiholder and Felix Bleiholder and Naumann, 2008 LIMES (0.95) 60,00% LIMES (0.90) , 41(1):1–41, ACM Comput. Surv. Naumann. Data fusion. LIMES (0.85) 2008. 50,00% LIMES (0.80) 40,00% [ ] Cilibrasi and Vitanyi, 2005 R. Cilibrasi and P.M.B. Vi- LIMES (0.75) IEEE Transactions on tanyi. Clustering by compression. 30,00% SILK Information Theory , 51(4):1523–1545, April 2005. 20,00% [ ] Brendan J. Frey and Delbert Dueck. Frey and Dueck, 2007 10,00% Sci- Clustering by passing messages between data points. 0,00% Drugbank SimCities Diseases ence , 315:972–976, 2007. [ ] Glaser et al. , 2009 Hugh Glaser, Ian C. Millard, Won- Figure 3: Comparison of the relative runtimes of SILK and Kyung Sung, Seungwoo Lee, Pyung Kim, and Beom-Jong LIMES. The number in brackets in the legend are the values You. Research on linked data and co-reference resolution. threshold. of the θ Technical report, University of Southampton, 2009. [ ] ̈ ̈ , 2009 opcke, Andreas Thor, and Er- et al. K opcke Hanna K hard Rahm. Comparative evaluation of entity resolution 6 Discussion and Future Work approaches with fever. Proc. VLDB Endow. , 2(2):1574– 1577, 2009. We presented the LIMES framework, which implements a ] [ Vanessa Lopez, Victoria Uren, Lopez et al. , 2009 very time-efficient approach for the discovery of links be- Marta Reka Sabou, and Enrico Motta. Cross ontol- tween knowledge bases on the Linked Data Web. We eval- ogy query answering on the semantic web: an initial uated our approach both with synthetic and real data and evaluation. In K-CAP ’09 , pages 17–24, 2009. showed that it outperforms state-of-the-art approaches with respect to the number of comparisons and runtime. In partic- [ ] et al. , 2008 Yves Raimond, Christopher Sutton, Raimond ular, we showed that the speedup of our approach grows with and Mark Sandler. Automatic interlinking of music the a-priori time complexity of the mapping task, making our 1st Workshop about datasets on the semantic web. In framework especially suitable for handling large-scale match- Linked Data on the Web , 2008. ing tasks (cf. results of the SimCities experiment). [ ] Franois Scharffe, Yanbin Liu, and , 2009 et al. Scharffe The current approach to the computation of exemplars does Chuguang Zhou. Rdf-ai: an architecture for rdf datasets not take the distribution of data in the metric into considera- matching, fusion and interlink. In Proc. IJCAI 2009 IR- tion. In future work, we will integrate this feature. The main KR Workshop , 2009. drawback of LIMES is that it is restricted to metric spaces. ] [ Jacopo Urbani, Spyros Kotoulas, Jason Urbani , 2010 et al. [ Thus, some popular semi-metrics such as JaroWinkler Win- Maassen, Frank van Harmelen, and Henri Bal. Owl rea- ] kler, 1999 can not be accelerated with LIMES. To ensure soning with webpie: calculating the closure of 100 billion that our framework can be used even with these measures, triples. In ESWC2010 , 2010. we have implemented the brute force approach as a fall-back ] [ for comparing instances in such cases. One can easily show Julius Volz, Christian Bizer, Martin , 2009 et al. Volz that our approach can be extended to semi-metrics. In future Gaedke, and Georgi Kobilarov. Discovering and main- work, we will take a closer look at semi-metrics and aim at taining links on the web of data. In , pages ISWC 2009 finding a relaxed triangular inequality that applies to each of 650–665. Springer, 2009. them. Based on these inequalities, our framework will also [ ] Winkler, 1999 William Winkler. The state of record link- use semi-metrics to compute exemplar and render link dis- age and current research problems. Technical report, U.S. covery based on these measures more efficient. We also aim Bureau of the Census, 1999. to explore the combination of LIMES with active learning [ ] Wong et al. , 2007 Raymond Chi-Wing Wong, Yufei Tao, strategies in a way, that a manual configuration of the tool Ada Wai-Chee Fu, and Xiaokui Xiao. On efficient spatial becomes unnecessary. VLDB , pages 579–590, 2007. matching. In [ ] et al. Yao , 2003 Zhengrong Yao, Like Gao, and X. Sean Acknowledgement Wang. Using triangle inequality to efficiently process con- tinuous queries on high-dimensional streaming time series. This work was supported by the Eurostars grant SCMS In SSDBM , pages 233–236. IEEE, 2003. E!4604 and the EU FP7 grant LOD2 (GA no. 257943). 2317

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