Comparison between ontology distances (preliminary results)

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Comparison between ontology distances (preliminary results) Jérôme David, Jérôme Euzenat ISWC 2008 1 / 17

Context A distributed and heterogenous environment: the semantic Web Several ontologies on the same domain Problem: how to facilitate the communication between programs using different ontologies?? software program, peer, etc. software program, peer, etc. 2 / 17

Context A distributed and heterogenous environment: the semantic Web Several ontologies on the same domain Problem: how to facilitate the communication between programs using different ontologies? alignment = mediator software program, peer, etc. software program, peer, etc. 2 / 17

Context How to deal with many ontologies at Web scale? A solution: Distances between ontologies In peer-to-peer systems: find a peer using a close ontology In ontology engineering: find related ontologies for facilitating ontologies reuse etc. Objectives: Review some distances between ontologies distances issued from ontology matching Make a preliminary evaluation of these measures accuracy vs. speed 3 / 17

Various kinds of ontology distances Two kinds of ontology distances evaluated: Vectorial distances: ontologies are viewed as bags of terms 1. which weight scheme to use? 2. which vector distance to use? Entity-based distances: the distance between ontologies is function of the distance between their entities 1. entity distances: structural or/and lexical? 2. aggregating entity distance values: which collection distance to use? 4 / 17

Vectorial ontology distances RedWine Ontology Ontology vector... Médoc individual MyChateauMargauxBottle Château Margaux label comment ProducedIn GrapeVariety Producer Cantenac Médoc Ṁédoc wines are french red wine produced in the Bordeaux wine region. BordeauxArea Cabarnet Sauvignon Vintage Appellation Name City Merlot Margaux 1998 ChateauMargaux wine red médoc french bordeaux cabarnet sauvignon merlot margaux chateau cantenac 1998 grape appelation producer... 3 2 2 1 1 1 1... Vector measures Cosine Jaccard (Tanimoto index) Possible weights Boolean Frequency TF.IDF 5 / 17

Entity distances Label-based distance: String-distance between entity annotations : Jaro-Winkler Minimum Weight pairing + arithmetic mean Structural distances: OLA similarity Structural iterative similarity for OWL ontologies Triple-based iterative similarity Structural iterative similarity for RDF graphs Problem: How to aggregate entity measures values? concepts of o entity distance values concepts of o' 0.1 0.5 0.9 0.4 1 0.7 0.8 0.7 0.3? ontology distance value? 6 / 17

Collection measures Goal: compute ontology measure from concept measure values. Collection measures used Average linkage : the arithmetic mean of concept measure values. concepts of o' concepts of o 0.1 0.5 0.9 0.4 1 0.7 0.8 0.7 0.3 mean = 0.5 7 / 17

Collection measures Goal: compute ontology measure from concept measure values. Collection measures used Average linkage : the arithmetic mean of concept measure values. Hausdorff : Hausdorff (o, o ) = max(max e o min e o δ K (e, e ), max e o min e o δ K (e, e )) concepts of o' concepts of o 0.1 0.5 0.9 0.4 1 0.7 0.8 0.7 0.3 7 / 17

Collection measures Goal: compute ontology measure from concept measure values. Collection measures used Average linkage : the arithmetic mean of concept measure values. Hausdorff : Hausdorff (o, o ) = max(max e o min e o δ K (e, e ), max e o min e o δ K (e, e )) concepts of o' concepts of o 0.1 0.5 0.9 0.4 1 0.7 0.8 0.7 0.3 7 / 17

Collection measures Goal: compute ontology measure from concept measure values. Collection measures used Average linkage : the arithmetic mean of concept measure values. Hausdorff : Hausdorff (o, o ) = max(max e o min e o δ K (e, e ), max e o min e o δ K (e, e )) concepts of o' concepts of o 0.1 0.5 0.9 0.4 1 0.7 0.8 0.7 0.3 7 / 17

Collection measures Goal: compute ontology measure from concept measure values. Collection measures used Average linkage : the arithmetic mean of concept measure values. Hausdorff : Hausdorff (o, o ) = max(max e o min e o δ K (e, e ), max e o min e o δ K (e, e )) Minimum Weight Maximum Graph Matching distance: concepts of o' concepts of o 0.1 0.5 0.9 0.4 1 0.7 0.8 0.7 0.3 mean = 0.4 7 / 17

Selected Measures 12 measures evaluated: 3 vectorial measures: Jaccard: the most basic measure (proportion of common terms) Cosine + TF weights Cosine + TF IDF weights 3 entity measures: EntityLexicalMeasure TripleBasedEntitySim OLAEntitySim 9 entity based measures combined with 3 collections measures: AverageLinkage Hausdorff MWMGM 8 / 17

Benchmark suite OAEI benchmark test set: 1 reference ontology 101 and altered ontologies 6 kinds of alterations: Name: suppressed, randomized, synonyms, convention, other language Comment: suppressed, other language Specialization hierarchy: suppressed, expanded, flattened Instances: suppressed Properties: suppressed, discarded restrictions Classes: split, flattened Order between alterations Example on name: {suppressed, randomized} < { synonym, convention, other language } ontology with synonym names is closer to the reference one than ontology with no names 9 / 17

Benchmark suite Induced proximity order: 101 is closer to 225 than 228 103_101_104 207 225 230 231 distance 204 205 203 206 223 201 208 209 210 222 224 228 221 252 238 240 202 251 249 250 248 237 239 236 232 233 259 261 247 258 260 257 253 254 246 241 266 265 262 10 / 17

Benchmark suite Induced proximity order (with partial alterations): 11 / 17

Tests We performed 3 different tests: Order comparison on benchmark test set check if the similarity orders are compatible with the order induced by alterations For each o, o check if 101 < o < o δ(101, o) < δ(101, o ) - Test set is biased towards 1-1 matching: some measure favored 12 / 17

Tests We performed 3 different tests: Order comparison on benchmark test set check if the similarity orders are compatible with the order induced by alterations For each o, o check if 101 < o < o δ(101, o) < δ(101, o ) - Test set is biased towards 1-1 matching: some measure favored Different cardinality matching compare with related but different ontologies compare with unrelated ontologies 12 / 17

Tests We performed 3 different tests: Order comparison on benchmark test set check if the similarity orders are compatible with the order induced by alterations For each o, o check if 101 < o < o δ(101, o) < δ(101, o ) - Test set is biased towards 1-1 matching: some measure favored Different cardinality matching compare with related but different ontologies compare with unrelated ontologies Time consumption test compare the time consumption of evaluated measures 12 / 17

Order comparison Proportion of o, o satisfying the induced order: Measure Tests Passed (ratio) Original Enhanced MWMGM (EntityLexicalMeasure) 0.53 0.72 Hausdorff (EntityLexicalMeasure) NaN NaN AverageLinkage (EntityLexicalMeasure) 0.44 0.31 MWMGM (OLAEntitySim) 0.75 0.78 Hausdorff (OLAEntitySim) 0.75 0.65 AverageLinkage (OLAEntitySim) 0.79 0.74 MWMGM (TripleBasedEntitySim) 0.86 0.92 Hausdorff (TripleBasedEntitySim) 0.86 0.89 AverageLinkage (TripleBasedEntitySim) 0.82 0.91 CosineVM (TF) 0.82 0.92 CosineVM (TFIDF) 0.57 0.81 JaccardVM (TF) 0.71 0.87 best entity measure : TripleBasedEntitySim 13 / 17

Order comparison Proportion of o, o satisfying the induced order: Measure Tests Passed (ratio) Original Enhanced MWMGM (EntityLexicalMeasure) 0.53 0.72 Hausdorff (EntityLexicalMeasure) NaN NaN AverageLinkage (EntityLexicalMeasure) 0.44 0.31 MWMGM (OLAEntitySim) 0.75 0.78 Hausdorff (OLAEntitySim) 0.75 0.65 AverageLinkage (OLAEntitySim) 0.79 0.74 MWMGM (TripleBasedEntitySim) 0.86 0.92 Hausdorff (TripleBasedEntitySim) 0.86 0.89 AverageLinkage (TripleBasedEntitySim) 0.82 0.91 CosineVM (TF) 0.82 0.92 CosineVM (TFIDF) 0.57 0.81 JaccardVM (TF) 0.71 0.87 best entity measure : TripleBasedEntitySim best collection measure : MWMGM 13 / 17

Order comparison Proportion of o, o satisfying the induced order: Measure Tests Passed (ratio) Original Enhanced MWMGM (EntityLexicalMeasure) 0.53 0.72 Hausdorff (EntityLexicalMeasure) NaN NaN AverageLinkage (EntityLexicalMeasure) 0.44 0.31 MWMGM (OLAEntitySim) 0.75 0.78 Hausdorff (OLAEntitySim) 0.75 0.65 AverageLinkage (OLAEntitySim) 0.79 0.74 MWMGM (TripleBasedEntitySim) 0.86 0.92 Hausdorff (TripleBasedEntitySim) 0.86 0.89 AverageLinkage (TripleBasedEntitySim) 0.82 0.91 CosineVM (TF) 0.82 0.92 CosineVM (TFIDF) 0.57 0.81 JaccardVM (TF) 0.71 0.87 best entity measure : TripleBasedEntitySim best collection measure : MWMGM best vectorial measure : Cosine with TF weights 13 / 17

Order comparison Proportion of o, o satisfying the induced order: Measure Tests Passed (ratio) Original Enhanced MWMGM (EntityLexicalMeasure) 0.53 0.72 Hausdorff (EntityLexicalMeasure) NaN NaN AverageLinkage (EntityLexicalMeasure) 0.44 0.31 MWMGM (OLAEntitySim) 0.75 0.78 Hausdorff (OLAEntitySim) 0.75 0.65 AverageLinkage (OLAEntitySim) 0.79 0.74 MWMGM (TripleBasedEntitySim) 0.86 0.92 Hausdorff (TripleBasedEntitySim) 0.86 0.89 AverageLinkage (TripleBasedEntitySim) 0.82 0.91 CosineVM (TF) 0.82 0.92 CosineVM (TFIDF) 0.57 0.81 JaccardVM (TF) 0.71 0.87 best entity measure : TripleBasedEntitySim best collection measure : MWMGM best vectorial measure : Cosine with TF weights Best results: TripleBasedEntitySim with MWMGM Cosine with TF weights: basic measure but works well Hausdorff works only with TripleBasedEntitySim Is MWMGM favored by the 1-1 nature of this test? 13 / 17

Different cardinality matching Objective: Ensure that MWMGM is still the best measure when we use different cardinality ontologies Test set: A reference ontology: 101 Highly altered ontologies: 2xx Different but similar ontologies: 3xx Irrelevant ontologies: conference test set (could share some vocabulary with benchmark ontologies) Expected results: δ(101, 2xx) < δ(101, 3xx) < δ(101, conference) 14 / 17

Different cardinality matching Results: MWMGM still performs best, vectorial measures fail when ontologies are lexically altered Main misorderings: MWMGM Hausdorff : only one altered (250) with similar (3xx) and conference ontologies some similar (3xx) with conference ontologies with TripleBasedEntitySim: only 250 with similar (3xx) and a conference ontology with OLAEntitySim: 228, 248, 250, 251, 252 with 304 and conference ontologies AverageLinkage with LexicalEntitySim: does not work highly altered (2xx) and similar (3xx) ontologies Vectorial measures many altered (248, 250, 251, 252) ontologies with similar (3xx) ontologies 15 / 17

Time consumption Are measures useable in real-time applications? Vectorial measures are more time efficient Time consumption on benchmark test: Measure Total time Average time (s) per similarity value (s) MWMGM(EntityLexicalMeasure) 558 0.46 MWMGM (OLAEntitySim) 39 074 31.9 MWMGM (TripleBasedEntitySim) 7 950 6.49 Hausdorff (EntityLexicalMeasure) 451 0.37 Hausdorff (OLAEntitySim) 38 912 31.76 Hausdorff (TripleBasedEntitySim) 7 410 6.05 AverageLinkage (EntityLexicalMeasure) 444 0.36 AverageLinkage (OLAEntitySim) 38 995 31.83 AverageLinkage (TripleBasedEntitySim) 7 671 6.26 CosineVM (TF) 101 0.08 CosineVM (TFIDF) 102 0.08 JaccardVM (TF) 101 0.08 16 / 17

Time consumption Are measures useable in real-time applications? Vectorial measures are more time efficient Not significant differences between MWMGM (N 3 ), Hausdorff and AverageLinkage(N 2 ) Time consumption on benchmark test: Measure Total time Average time (s) per similarity value (s) MWMGM(EntityLexicalMeasure) 558 0.46 MWMGM (OLAEntitySim) 39 074 31.9 MWMGM (TripleBasedEntitySim) 7 950 6.49 Hausdorff (EntityLexicalMeasure) 451 0.37 Hausdorff (OLAEntitySim) 38 912 31.76 Hausdorff (TripleBasedEntitySim) 7 410 6.05 AverageLinkage (EntityLexicalMeasure) 444 0.36 AverageLinkage (OLAEntitySim) 38 995 31.83 AverageLinkage (TripleBasedEntitySim) 7 671 6.26 CosineVM (TF) 101 0.08 CosineVM (TFIDF) 102 0.08 JaccardVM (TF) 101 0.08 16 / 17

Time consumption Are measures useable in real-time applications? Vectorial measures are more time efficient Not significant differences between MWMGM (N 3 ), Hausdorff and AverageLinkage(N 2 ) Structural measures are not really useable in real-time applications Time consumption on benchmark test: Measure Total time Average time (s) per similarity value (s) MWMGM(EntityLexicalMeasure) 558 0.46 MWMGM (OLAEntitySim) 39 074 31.9 MWMGM (TripleBasedEntitySim) 7 950 6.49 Hausdorff (EntityLexicalMeasure) 451 0.37 Hausdorff (OLAEntitySim) 38 912 31.76 Hausdorff (TripleBasedEntitySim) 7 410 6.05 AverageLinkage (EntityLexicalMeasure) 444 0.36 AverageLinkage (OLAEntitySim) 38 995 31.83 AverageLinkage (TripleBasedEntitySim) 7 671 6.26 CosineVM (TF) 101 0.08 CosineVM (TFIDF) 102 0.08 JaccardVM (TF) 101 0.08 16 / 17

Conclusion Why use complex measures when basic measures performs well? for discriminating highly related ontologies More precise test set is needed Characterize confidence intervals Is there a threshold from which returned values are always correct? Other ontology distances measures: alignment based 17 / 17

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