Skip to main content
Erschienen in: Artificial Intelligence Review 7/2020

27.02.2020

An overview of distance and similarity functions for structured data

verfasst von: Santiago Ontañón

Erschienen in: Artificial Intelligence Review | Ausgabe 7/2020

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The notions of distance and similarity play a key role in many machine learning approaches, and artificial intelligence in general, since they can serve as an organizing principle by which individuals classify objects, form concepts and make generalizations. While distance functions for propositional representations have been thoroughly studied, work on distance functions for structured representations, such as graphs, frames or logical clauses, has been carried out in different communities and is much less understood. Specifically, a significant amount of work that requires the use of a distance or similarity function for structured representations of data usually employs ad-hoc functions for specific applications. Therefore, the goal of this paper is to provide an overview of this work to identify connections between the work carried out in different areas and point out directions for future work.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Fußnoten
1
Notice that in the description logics notation, subsumption is written in the reverse order since it is seen as “set inclusion” of their interpretations. Here, \(x_1 \sqsubseteq x_2\) means that \(x_1\) is more general than \(x_2\), while in description logics it has the opposite meaning.
 
2
Interestingly, the Weisfeiler–Lehman test is related to the expressive power of Graph Neural Networks (discussed in Sect. 3.5), as it has been shown that a some classes of GNNs are at least as powerful as the Weisfeiler–Lehman in detecting graph isomorphism (Xu et al. 2018).
 
Literatur
Zurück zum Zitat Aamodt A, Plaza E (1994) Case-based reasoning: foundational issues, methodological variations, and system approaches. Artif Intell Commun 7(1):39–59 Aamodt A, Plaza E (1994) Case-based reasoning: foundational issues, methodological variations, and system approaches. Artif Intell Commun 7(1):39–59
Zurück zum Zitat Abu-Khzam FN, Samatova NF, Rizk MA, Langston MA (2007) The maximum common subgraph problem: faster solutions via vertex cover. In: IEEE/ACS international conference on computer systems and applications, 2007. AICCSA’07. IEEE, pp 367–373 Abu-Khzam FN, Samatova NF, Rizk MA, Langston MA (2007) The maximum common subgraph problem: faster solutions via vertex cover. In: IEEE/ACS international conference on computer systems and applications, 2007. AICCSA’07. IEEE, pp 367–373
Zurück zum Zitat Agrawal R, Faloutsos C, Swami A (1993) Efficient similarity search in sequence databases. In: International conference on foundations of data organization and algorithms. Springer, pp 69–84 Agrawal R, Faloutsos C, Swami A (1993) Efficient similarity search in sequence databases. In: International conference on foundations of data organization and algorithms. Springer, pp 69–84
Zurück zum Zitat Aha DW, Kibler D, Albert MK (1991) Instance-based learning algorithms. Mach Learn 6(1):37–66 Aha DW, Kibler D, Albert MK (1991) Instance-based learning algorithms. Mach Learn 6(1):37–66
Zurück zum Zitat Almohamad H, Duffuaa SO (1993) A linear programming approach for the weighted graph matching problem. IEEE Trans Pattern Anal Mach Intell 15(5):522–525 Almohamad H, Duffuaa SO (1993) A linear programming approach for the weighted graph matching problem. IEEE Trans Pattern Anal Mach Intell 15(5):522–525
Zurück zum Zitat Armengol E, Plaza E (2001) Similarity assessment for relational cbr. In: International conference on case-based reasoning. Springer, pp 44–58 Armengol E, Plaza E (2001) Similarity assessment for relational cbr. In: International conference on case-based reasoning. Springer, pp 44–58
Zurück zum Zitat Armengol E, Plaza E (2002) Similarity of structured cases in CBR. In: Proceedings from the CCIA held in Castellon, Spain Armengol E, Plaza E (2002) Similarity of structured cases in CBR. In: Proceedings from the CCIA held in Castellon, Spain
Zurück zum Zitat Assali AA, Lenne D, Debray B (2009) Case retrieval in ontology-based cbr systems. In: Annual conference on artificial intelligence. Springer, pp 564–571 Assali AA, Lenne D, Debray B (2009) Case retrieval in ontology-based cbr systems. In: Annual conference on artificial intelligence. Springer, pp 564–571
Zurück zum Zitat Baader F, Calvanese D, McGuinness DL, Nardi D, Patel-Schneider PF (eds) (2003) The description logic handbook: theory, implementation, and applications. Cambridge University Press, CambridgeMATH Baader F, Calvanese D, McGuinness DL, Nardi D, Patel-Schneider PF (eds) (2003) The description logic handbook: theory, implementation, and applications. Cambridge University Press, CambridgeMATH
Zurück zum Zitat Baader F, Horrocks I, Sattler U (2005) Description logics as ontology languages for the semantic web. In: Hutter D, Stephan W (eds) Mechanizing mathematical reasoning. Springer, pp 228–248 Baader F, Horrocks I, Sattler U (2005) Description logics as ontology languages for the semantic web. In: Hutter D, Stephan W (eds) Mechanizing mathematical reasoning. Springer, pp 228–248
Zurück zum Zitat Babai L (2018) Groups, graphs, algorithms: the graph isomorphism problem. In: Proceedings of international congress of mathematicians 2018 Babai L (2018) Groups, graphs, algorithms: the graph isomorphism problem. In: Proceedings of international congress of mathematicians 2018
Zurück zum Zitat Badea L, Nienhuys-Cheng SH (1999) A refinement operator for description logics. In: Cussens J, Frisch A (eds) Inductive logic programming, no. 1866 in Lecture notes in computer science. Springer, pp 40–59 Badea L, Nienhuys-Cheng SH (1999) A refinement operator for description logics. In: Cussens J, Frisch A (eds) Inductive logic programming, no. 1866 in Lecture notes in computer science. Springer, pp 40–59
Zurück zum Zitat Battaglia PW, Hamrick JB, Bapst V, Sanchez-Gonzalez A, Zambaldi V, Malinowski M, Tacchetti A, Raposo D, Santoro A, Faulkner R et al (2018) Relational inductive biases, deep learning, and graph networks. arXiv:180601261 Battaglia PW, Hamrick JB, Bapst V, Sanchez-Gonzalez A, Zambaldi V, Malinowski M, Tacchetti A, Raposo D, Santoro A, Faulkner R et al (2018) Relational inductive biases, deep learning, and graph networks. arXiv:180601261
Zurück zum Zitat Bellet A, Habrard A, Sebban M (2012) Good edit similarity learning by loss minimization. Mach Learn 89(1–2):5–35MathSciNetMATH Bellet A, Habrard A, Sebban M (2012) Good edit similarity learning by loss minimization. Mach Learn 89(1–2):5–35MathSciNetMATH
Zurück zum Zitat Bellet A, Habrard A, Sebban M (2013) A survey on metric learning for feature vectors and structured data. arXiv:13066709 Bellet A, Habrard A, Sebban M (2013) A survey on metric learning for feature vectors and structured data. arXiv:13066709
Zurück zum Zitat Bergmann R, Stahl A (1998) Similarity measures for object-oriented case representations. In: Advances in case-based reasoning, pp 25–36 Bergmann R, Stahl A (1998) Similarity measures for object-oriented case representations. In: Advances in case-based reasoning, pp 25–36
Zurück zum Zitat Bergmann R, Gil Y (2014) Similarity assessment and efficient retrieval of semantic workflows. Inf Syst 40:115–127 Bergmann R, Gil Y (2014) Similarity assessment and efficient retrieval of semantic workflows. Inf Syst 40:115–127
Zurück zum Zitat Bergmann R, Kolodner J, Plaza E (2005) Representation in case-based reasoning. Knowl Eng Rev 20(3):209–213 Bergmann R, Kolodner J, Plaza E (2005) Representation in case-based reasoning. Knowl Eng Rev 20(3):209–213
Zurück zum Zitat Bille P (2005) A survey on tree edit distance and related problems. Theor Comput Sci 337(1):217–239MathSciNetMATH Bille P (2005) A survey on tree edit distance and related problems. Theor Comput Sci 337(1):217–239MathSciNetMATH
Zurück zum Zitat Bisson G (1990) Kbg: a knowledge based generalizer. In: Porter B, Mooney R (eds) Machine learning proceedings 1990. Elsevier, Amsterdam, pp 9–15 Bisson G (1990) Kbg: a knowledge based generalizer. In: Porter B, Mooney R (eds) Machine learning proceedings 1990. Elsevier, Amsterdam, pp 9–15
Zurück zum Zitat Bisson G (1992) Learing in FOL with a similarity measure. In: Proceedings of AAAI, vol 1992, pp 82–87 Bisson G (1992) Learing in FOL with a similarity measure. In: Proceedings of AAAI, vol 1992, pp 82–87
Zurück zum Zitat Borgida A, Walsh TJ, Hirsh H et al (2005) Towards measuring similarity in description logics. Descr Log 147 Borgida A, Walsh TJ, Hirsh H et al (2005) Towards measuring similarity in description logics. Descr Log 147
Zurück zum Zitat Bournaud I, Courtine M, Jean-Daniel Z (2002) Propositionalization for clustering symbolic relational descriptions. In: International conference on inductive logic programming. Springer, pp 1–16 Bournaud I, Courtine M, Jean-Daniel Z (2002) Propositionalization for clustering symbolic relational descriptions. In: International conference on inductive logic programming. Springer, pp 1–16
Zurück zum Zitat Bunke H (1997) On a relation between graph edit distance and maximum common subgraph. Pattern Recogn Lett 18(8):689–694 Bunke H (1997) On a relation between graph edit distance and maximum common subgraph. Pattern Recogn Lett 18(8):689–694
Zurück zum Zitat Bunke H (1999) Error correcting graph matching: on the influence of the underlying cost function. IEEE Trans Pattern Anal Mach Intell 21(9):917–922 Bunke H (1999) Error correcting graph matching: on the influence of the underlying cost function. IEEE Trans Pattern Anal Mach Intell 21(9):917–922
Zurück zum Zitat Bunke H (2000) Graph matching: theoretical foundations, algorithms, and applications. Proc Vis Interface 2000:82–88 Bunke H (2000) Graph matching: theoretical foundations, algorithms, and applications. Proc Vis Interface 2000:82–88
Zurück zum Zitat Bunke H, Shearer K (1998) A graph distance metric based on the maximal common subgraph. Pattern Recogn Lett 19(3):255–259MATH Bunke H, Shearer K (1998) A graph distance metric based on the maximal common subgraph. Pattern Recogn Lett 19(3):255–259MATH
Zurück zum Zitat Carpenter B (1992) The logic of typed feature structures. Cambridge University Press, New YorkMATH Carpenter B (1992) The logic of typed feature structures. Cambridge University Press, New YorkMATH
Zurück zum Zitat Champin PA, Solnon C (2003) Measuring the similarity of labeled graphs. In: International conference on case-based reasoning, ICCBR. Springer Champin PA, Solnon C (2003) Measuring the similarity of labeled graphs. In: International conference on case-based reasoning, ICCBR. Springer
Zurück zum Zitat Chen PPS (1988) The entity-relationship model—toward a unified view of data. Readings in artificial intelligence and databases. Elsevier, Amsterdam, pp 98–111 Chen PPS (1988) The entity-relationship model—toward a unified view of data. Readings in artificial intelligence and databases. Elsevier, Amsterdam, pp 98–111
Zurück zum Zitat Cilibrasi R, Vitányi PM (2005) Clustering by compression. IEEE Trans Inf Theory 51(4):1523–1545MathSciNetMATH Cilibrasi R, Vitányi PM (2005) Clustering by compression. IEEE Trans Inf Theory 51(4):1523–1545MathSciNetMATH
Zurück zum Zitat Collins M, Duffy N (2002) Convolution kernels for natural language. In: Becker S, Thrun S, Obermayer K (eds) Advances in neural information processing systems. Vancouver, Canada, pp 625–632 Collins M, Duffy N (2002) Convolution kernels for natural language. In: Becker S, Thrun S, Obermayer K (eds) Advances in neural information processing systems. Vancouver, Canada, pp 625–632
Zurück zum Zitat Conte D, Foggia P, Sansone C, Vento M (2004) Thirty years of graph matching in pattern recognition. Int J Pattern Recogn Artif Intell 18(03):265–298 Conte D, Foggia P, Sansone C, Vento M (2004) Thirty years of graph matching in pattern recognition. Int J Pattern Recogn Artif Intell 18(03):265–298
Zurück zum Zitat Cover T, Hart P (1967) Nearest neighbor pattern classification. IEEE Trans Inf Theory 13(1):21–27MATH Cover T, Hart P (1967) Nearest neighbor pattern classification. IEEE Trans Inf Theory 13(1):21–27MATH
Zurück zum Zitat d’Amato C, Fanizzi N, Esposito F (2006) A dissimilarity measure for alc concept descriptions. In: Proceedings of the 2006 ACM symposium on applied computing. ACM, pp 1695–1699 d’Amato C, Fanizzi N, Esposito F (2006) A dissimilarity measure for alc concept descriptions. In: Proceedings of the 2006 ACM symposium on applied computing. ACM, pp 1695–1699
Zurück zum Zitat d’Amato C, Staab S, Fanizzi N (2008) On the influence of description logics ontologies on conceptual similarity. In: Proceedings of the 16th international conference on knowledge engineering. Lecture notes in computer science, vol 5268. Springer, pp 48–63 d’Amato C, Staab S, Fanizzi N (2008) On the influence of description logics ontologies on conceptual similarity. In: Proceedings of the 16th international conference on knowledge engineering. Lecture notes in computer science, vol 5268. Springer, pp 48–63
Zurück zum Zitat Datar M, Immorlica N, Indyk P, Mirrokni VS (2004) Locality-sensitive hashing scheme based on p-stable distributions. In: Proceedings of the twentieth annual symposium on computational geometry. ACM, pp 253–262 Datar M, Immorlica N, Indyk P, Mirrokni VS (2004) Locality-sensitive hashing scheme based on p-stable distributions. In: Proceedings of the twentieth annual symposium on computational geometry. ACM, pp 253–262
Zurück zum Zitat de Vries GKD, de Rooij S (2015) Substructure counting graph kernels for machine learning from rdf data. Web Semant Sci Serv Agents World Wide Web 35:71–84 de Vries GKD, de Rooij S (2015) Substructure counting graph kernels for machine learning from rdf data. Web Semant Sci Serv Agents World Wide Web 35:71–84
Zurück zum Zitat Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. Journal R Stat Soc Ser B (Methodol) 39:1–38MathSciNetMATH Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. Journal R Stat Soc Ser B (Methodol) 39:1–38MathSciNetMATH
Zurück zum Zitat Dobrushin RL (1970) Prescribing a system of random variables by conditional distributions. Theory Probab Appl 15(3):458–486MathSciNetMATH Dobrushin RL (1970) Prescribing a system of random variables by conditional distributions. Theory Probab Appl 15(3):458–486MathSciNetMATH
Zurück zum Zitat Doyle PG, Snell JL (1984) Random walks and electric networks, vol 22. American Mathematical Society, ProvidenceMATH Doyle PG, Snell JL (1984) Random walks and electric networks, vol 22. American Mathematical Society, ProvidenceMATH
Zurück zum Zitat Emde W, Wettschereck D (1996) Relational instance based learning. In: Saitta L (ed) Machine learning—proceedings 13th international conference on machine learning. Morgan Kaufmann Publishers, pp 122–130 Emde W, Wettschereck D (1996) Relational instance based learning. In: Saitta L (ed) Machine learning—proceedings 13th international conference on machine learning. Morgan Kaufmann Publishers, pp 122–130
Zurück zum Zitat Emele MC, Zajac R (1990) Typed unification grammars. In: Proceedings of the 13th conference on computational linguistics, vol 3. Association for Computational Linguistics, pp 293–298 Emele MC, Zajac R (1990) Typed unification grammars. In: Proceedings of the 13th conference on computational linguistics, vol 3. Association for Computational Linguistics, pp 293–298
Zurück zum Zitat Emmert-Streib F, Dehmer M, Shi Y (2016) Fifty years of graph matching, network alignment and network comparison. Inf Sci 346:180–197MathSciNetMATH Emmert-Streib F, Dehmer M, Shi Y (2016) Fifty years of graph matching, network alignment and network comparison. Inf Sci 346:180–197MathSciNetMATH
Zurück zum Zitat Ester M, Kriegel HP, Sander J, Xu X et al (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. Kdd 96:226–231 Ester M, Kriegel HP, Sander J, Xu X et al (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. Kdd 96:226–231
Zurück zum Zitat Falkenhainer B, Forbus KD, Gentner D (1989) The structure-mapping engine: algorithm and examples. Artif intell 41(1):1–63MATH Falkenhainer B, Forbus KD, Gentner D (1989) The structure-mapping engine: algorithm and examples. Artif intell 41(1):1–63MATH
Zurück zum Zitat Fanizzi N, d’Amato C (2006) A declarative kernel for $\cal{ALC}$ concept descriptions. In: International symposium on methodologies for intelligent systems. Springer, pp 322–331 Fanizzi N, d’Amato C (2006) A declarative kernel for $\cal{ALC}$ concept descriptions. In: International symposium on methodologies for intelligent systems. Springer, pp 322–331
Zurück zum Zitat Fanizzi N, d’Amato C, Esposito F (2008) Learning with kernels in description logics. In: Zelezny F, Lavrac N (eds) Inductive logic programming. Springer, pp 210–225 Fanizzi N, d’Amato C, Esposito F (2008) Learning with kernels in description logics. In: Zelezny F, Lavrac N (eds) Inductive logic programming. Springer, pp 210–225
Zurück zum Zitat Fernández ML, Valiente G (2001) A graph distance metric combining maximum common subgraph and minimum common supergraph. Pattern Recognition Letters 22(6):753–758MATH Fernández ML, Valiente G (2001) A graph distance metric combining maximum common subgraph and minimum common supergraph. Pattern Recognition Letters 22(6):753–758MATH
Zurück zum Zitat French RM (2002) The computational modeling of analogy-making. Trends Cogn Sci 6(5):200–205 French RM (2002) The computational modeling of analogy-making. Trends Cogn Sci 6(5):200–205
Zurück zum Zitat Gao X, Xiao B, Tao D, Li X (2010) A survey of graph edit distance. Pattern Anal Appl 13(1):113–129MathSciNetMATH Gao X, Xiao B, Tao D, Li X (2010) A survey of graph edit distance. Pattern Anal Appl 13(1):113–129MathSciNetMATH
Zurück zum Zitat Gärtner T (2003) A survey of kernels for structured data. ACM SIGKDD Explor Newsl 5(1):49–58 Gärtner T (2003) A survey of kernels for structured data. ACM SIGKDD Explor Newsl 5(1):49–58
Zurück zum Zitat Gärtner T, Lloyd JW, Flach PA (2002) Kernels for structured data. Springer, BerlinMATH Gärtner T, Lloyd JW, Flach PA (2002) Kernels for structured data. Springer, BerlinMATH
Zurück zum Zitat Gärtner T, Flach P, Wrobel S (2003) On graph kernels: Hardness results and efficient alternatives. In: Schölkopf B, Warmuth MK (eds) Learning theory and kernel machines. Springer, Berlin, pp 129–143MATH Gärtner T, Flach P, Wrobel S (2003) On graph kernels: Hardness results and efficient alternatives. In: Schölkopf B, Warmuth MK (eds) Learning theory and kernel machines. Springer, Berlin, pp 129–143MATH
Zurück zum Zitat Gärtner T, Lloyd JW, Flach PA (2004) Kernels and distances for structured data. Mach Learn 57(3):205–232MATH Gärtner T, Lloyd JW, Flach PA (2004) Kernels and distances for structured data. Mach Learn 57(3):205–232MATH
Zurück zum Zitat Gentner D (1983) Structure-mapping: a theoretical framework for analogy. Cogn Sci 7(2):155–170 Gentner D (1983) Structure-mapping: a theoretical framework for analogy. Cogn Sci 7(2):155–170
Zurück zum Zitat Getoor L, Taskar B (2007) Introduction to statistical relational learning. MIT Press, CambridgeMATH Getoor L, Taskar B (2007) Introduction to statistical relational learning. MIT Press, CambridgeMATH
Zurück zum Zitat Göker MH, Roth-Berghofer T (1999) The development and utilization of the case-based help-desk support system homer. Eng Appl Artif Intell 12(6):665–680 Göker MH, Roth-Berghofer T (1999) The development and utilization of the case-based help-desk support system homer. Eng Appl Artif Intell 12(6):665–680
Zurück zum Zitat Goldstone RL, Medin DL, Gentner D (1991) Relational similarity and the nonindependence of features in similarity judgments. Cogn Psychol 23(2):222–262 Goldstone RL, Medin DL, Gentner D (1991) Relational similarity and the nonindependence of features in similarity judgments. Cogn Psychol 23(2):222–262
Zurück zum Zitat Gollery M (2005) Bioinformatics: sequence and genome analysis. Clin Chem 51(11):2219–2219 Gollery M (2005) Bioinformatics: sequence and genome analysis. Clin Chem 51(11):2219–2219
Zurück zum Zitat Golub GH, Van Loan CF (2012) Matrix computations, vol 3. JHU Press, BaltimoreMATH Golub GH, Van Loan CF (2012) Matrix computations, vol 3. JHU Press, BaltimoreMATH
Zurück zum Zitat González-Calero PA, Díaz-Agudo B, Gómez-Albarrán M et al (1999) Applying dls for retrieval in case-based reasoning. In: In Proceedings of the 1999 description logics workshop (Dl’99). Linkopings Universitet, Citeseer González-Calero PA, Díaz-Agudo B, Gómez-Albarrán M et al (1999) Applying dls for retrieval in case-based reasoning. In: In Proceedings of the 1999 description logics workshop (Dl’99). Linkopings Universitet, Citeseer
Zurück zum Zitat Haussler D (1999) Convolution kernels on discrete structures. Technical report, Department of Computer Science, University of California at Santa Cruz Haussler D (1999) Convolution kernels on discrete structures. Technical report, Department of Computer Science, University of California at Santa Cruz
Zurück zum Zitat Hearst MA, Dumais ST, Osuna E, Platt J, Scholkopf B (1998) Support vector machines. IEEE Intell Syst Their Appl 13(4):18–28 Hearst MA, Dumais ST, Osuna E, Platt J, Scholkopf B (1998) Support vector machines. IEEE Intell Syst Their Appl 13(4):18–28
Zurück zum Zitat Heckerman D, Meek C, Koller D (2007) Probabilistic entity-relationship models, prms, and plate models. In: Getoor L, Taskar B (eds) Introduction to statistical relational learning, MIT Press, pp 201–238 Heckerman D, Meek C, Koller D (2007) Probabilistic entity-relationship models, prms, and plate models. In: Getoor L, Taskar B (eds) Introduction to statistical relational learning, MIT Press, pp 201–238
Zurück zum Zitat Holyoak KJ, Koh K (1987) Surface and structural similarity in analogical transfer. Mem Cogn 15(4):332–340 Holyoak KJ, Koh K (1987) Surface and structural similarity in analogical transfer. Mem Cogn 15(4):332–340
Zurück zum Zitat Horváth T, Wrobel S, Bohnebeck U (2001) Relational instance-based learning with lists and terms. Mach Learn 43(1–2):53–80MATH Horváth T, Wrobel S, Bohnebeck U (2001) Relational instance-based learning with lists and terms. Mach Learn 43(1–2):53–80MATH
Zurück zum Zitat Horváth T, Gärtner T, Wrobel S (2004) Cyclic pattern kernels for predictive graph mining. In: Proceedings of the tenth ACM SIGKDD international conference on knowledge discovery and data mining. ACM, pp 158–167 Horváth T, Gärtner T, Wrobel S (2004) Cyclic pattern kernels for predictive graph mining. In: Proceedings of the tenth ACM SIGKDD international conference on knowledge discovery and data mining. ACM, pp 158–167
Zurück zum Zitat Hu B, Kalfoglou Y, Alani H, Dupplaw D, Lewis P, Shadbolt N (2006) Semantic metrics. In: International conference on knowledge engineering and knowledge management. Springer, pp 166–181 Hu B, Kalfoglou Y, Alani H, Dupplaw D, Lewis P, Shadbolt N (2006) Semantic metrics. In: International conference on knowledge engineering and knowledge management. Springer, pp 166–181
Zurück zum Zitat Hutchinson A (1997) Metrics on terms and clauses. In: ECML ’97: proceedings of the 9th European conference on machine learning. Lecture notes in computer science, vol 1224. Springer, pp 138–145 Hutchinson A (1997) Metrics on terms and clauses. In: ECML ’97: proceedings of the 9th European conference on machine learning. Lecture notes in computer science, vol 1224. Springer, pp 138–145
Zurück zum Zitat Itakura F (1975) Minimum prediction residual principle applied to speech recognition. IEEE Trans Acoust Speech Signal Process 23(1):67–72 Itakura F (1975) Minimum prediction residual principle applied to speech recognition. IEEE Trans Acoust Speech Signal Process 23(1):67–72
Zurück zum Zitat Jaakkola T, Haussler D (1999) Exploiting generative models in discriminative classifiers. In: Solla SA, Leen TK, Müller K-R (eds) Advances in neural information processing systems. MIT Press, Denver, Colarado, pp 487–493 Jaakkola T, Haussler D (1999) Exploiting generative models in discriminative classifiers. In: Solla SA, Leen TK, Müller K-R (eds) Advances in neural information processing systems. MIT Press, Denver, Colarado, pp 487–493
Zurück zum Zitat Janowicz K (2006) Sim-dl: towards a semantic similarity measurement theory for the description logic $\cal{ALCNR}$ in geographic information retrieval. In: OTM confederated international conferences “on the move to meaningful internet systems. Springer, pp 1681–1692 Janowicz K (2006) Sim-dl: towards a semantic similarity measurement theory for the description logic $\cal{ALCNR}$ in geographic information retrieval. In: OTM confederated international conferences “on the move to meaningful internet systems. Springer, pp 1681–1692
Zurück zum Zitat Jeh G, Widom J (2002) Simrank: a measure of structural-context similarity. In: Proceedings of the eighth ACM SIGKDD international conference on knowledge discovery and data mining. ACM, pp 538–543 Jeh G, Widom J (2002) Simrank: a measure of structural-context similarity. In: Proceedings of the eighth ACM SIGKDD international conference on knowledge discovery and data mining. ACM, pp 538–543
Zurück zum Zitat Jiang JJ, Conrath DW (1997) Semantic similarity based on corpus statistics and lexical taxonomy. arXiv:cmp-lg/9709008 Jiang JJ, Conrath DW (1997) Semantic similarity based on corpus statistics and lexical taxonomy. arXiv:cmp-lg/9709008
Zurück zum Zitat Kalfoglou Y, Schorlemmer M (2003) Ontology mapping: the state of the art. Knowl Eng Rev 18(1):1–31MATH Kalfoglou Y, Schorlemmer M (2003) Ontology mapping: the state of the art. Knowl Eng Rev 18(1):1–31MATH
Zurück zum Zitat Kashima H, Koyanagi T (2002) Kernels for semi-structured data. ICML 2:291–298 Kashima H, Koyanagi T (2002) Kernels for semi-structured data. ICML 2:291–298
Zurück zum Zitat Kashima H, Tsuda K, Inokuchi A (2003) Marginalized kernels between labeled graphs. In: Proceedings of the twentieth international conference (ICML 2003). AAAI Press, pp 321–328 Kashima H, Tsuda K, Inokuchi A (2003) Marginalized kernels between labeled graphs. In: Proceedings of the twentieth international conference (ICML 2003). AAAI Press, pp 321–328
Zurück zum Zitat Katz L (1953) A new status index derived from sociometric analysis. Psychometrika 18(1):39–43MATH Katz L (1953) A new status index derived from sociometric analysis. Psychometrika 18(1):39–43MATH
Zurück zum Zitat Kaufman L, Rousseeuw P (1987) Clustering by means of medoids. North-Holland, Amsterdam Kaufman L, Rousseeuw P (1987) Clustering by means of medoids. North-Holland, Amsterdam
Zurück zum Zitat Keogh E, Kasetty S (2003) On the need for time series data mining benchmarks: a survey and empirical demonstration. Data Min Knowl Discov 7(4):349–371MathSciNet Keogh E, Kasetty S (2003) On the need for time series data mining benchmarks: a survey and empirical demonstration. Data Min Knowl Discov 7(4):349–371MathSciNet
Zurück zum Zitat Klein PN (1998) Computing the edit-distance between unrooted ordered trees. In: European symposium on algorithms. Springer, pp 91–102 Klein PN (1998) Computing the edit-distance between unrooted ordered trees. In: European symposium on algorithms. Springer, pp 91–102
Zurück zum Zitat Kok S, Domingos P (2007) Statistical predicate invention. In: Proceedings of the 24th international conference on machine learning. ACM, pp 433–440 Kok S, Domingos P (2007) Statistical predicate invention. In: Proceedings of the 24th international conference on machine learning. ACM, pp 433–440
Zurück zum Zitat Kolmogorov AN (1965) Three approaches to the quantitative definition of information. Probl Inf Transm 1(1):1–7MathSciNet Kolmogorov AN (1965) Three approaches to the quantitative definition of information. Probl Inf Transm 1(1):1–7MathSciNet
Zurück zum Zitat Kramer S, Lavrač N, Flach P (2001) Propositionalization approaches to relational data mining. In: Dzeroski S, Lavrac N (eds) Relational data mining. Springer, pp 262–291 Kramer S, Lavrač N, Flach P (2001) Propositionalization approaches to relational data mining. In: Dzeroski S, Lavrac N (eds) Relational data mining. Springer, pp 262–291
Zurück zum Zitat Krieger HU, Schäfer U (1995) Efficient parameterizable type expansion for typed feature formalisms Krieger HU, Schäfer U (1995) Efficient parameterizable type expansion for typed feature formalisms
Zurück zum Zitat Krogel MA, Rawles S, Železnỳ F, Flach PA, Lavrač N, Wrobel S (2003) Comparative evaluation of approaches to propositionalization. In: International conference on inductive logic programming. Springer, pp 197–214 Krogel MA, Rawles S, Železnỳ F, Flach PA, Lavrač N, Wrobel S (2003) Comparative evaluation of approaches to propositionalization. In: International conference on inductive logic programming. Springer, pp 197–214
Zurück zum Zitat Kulis B, et al (2013) Metric learning: a survey. Found Trends® Mach Learn 5(4):287–364 Kulis B, et al (2013) Metric learning: a survey. Found Trends® Mach Learn 5(4):287–364
Zurück zum Zitat Lavrac N, Dzeroski S (1994) Inductive logic programming. In: Fuchs NE, Gottlob G (eds) WLP. Springer, Berlion, pp 146–160 Lavrac N, Dzeroski S (1994) Inductive logic programming. In: Fuchs NE, Gottlob G (eds) WLP. Springer, Berlion, pp 146–160
Zurück zum Zitat Lehmann J, Hitzler P (2007) A refinement operator based learning algorithm for the LC description logic. In: Blockeel H, Ramon J, Shavlik JW, Tadepalli P (eds) ILP. Lecture notes in computer science, vol 4894. Springer, Berlin, pp 147–160 Lehmann J, Hitzler P (2007) A refinement operator based learning algorithm for the LC description logic. In: Blockeel H, Ramon J, Shavlik JW, Tadepalli P (eds) ILP. Lecture notes in computer science, vol 4894. Springer, Berlin, pp 147–160
Zurück zum Zitat Lehmann J, Haase C (2009) Ideal downward refinement in the EL description logic. In: Raedt LD (ed) ILP. Lecture notes in computer science, vol 5989. Springer, Berlin pp 73–87 Lehmann J, Haase C (2009) Ideal downward refinement in the EL description logic. In: Raedt LD (ed) ILP. Lecture notes in computer science, vol 5989. Springer, Berlin pp 73–87
Zurück zum Zitat Leishman D (1989) Analogy as a constrained partial correspondence over conceptual graphs. In: KR, pp 223–234 Leishman D (1989) Analogy as a constrained partial correspondence over conceptual graphs. In: KR, pp 223–234
Zurück zum Zitat Levenshtein VI (1966) Binary codes capable of correcting deletions, insertions, and reversals. Sov Phys Dokl 10:707–710MathSciNet Levenshtein VI (1966) Binary codes capable of correcting deletions, insertions, and reversals. Sov Phys Dokl 10:707–710MathSciNet
Zurück zum Zitat Levi G (1973) A note on the derivation of maximal common subgraphs of two directed or undirected graphs. Calcolo 9(4):341MathSciNetMATH Levi G (1973) A note on the derivation of maximal common subgraphs of two directed or undirected graphs. Calcolo 9(4):341MathSciNetMATH
Zurück zum Zitat Li Y, Gu C, Dullien T, Vinyals O, Kohli P (2019) Graph matching networks for learning the similarity of graph structured objects. arXiv preprint arXiv:190412787 Li Y, Gu C, Dullien T, Vinyals O, Kohli P (2019) Graph matching networks for learning the similarity of graph structured objects. arXiv preprint arXiv:190412787
Zurück zum Zitat Lü L, Zhou T (2011) Link prediction in complex networks: a survey. Phys A Stat Mech Its Appl 390(6):1150–1170 Lü L, Zhou T (2011) Link prediction in complex networks: a survey. Phys A Stat Mech Its Appl 390(6):1150–1170
Zurück zum Zitat Luss R, d’Aspremont A (2008) Support vector machine classification with indefinite kernels. In: Advances in neural information processing systems, pp 953–960 Luss R, d’Aspremont A (2008) Support vector machine classification with indefinite kernels. In: Advances in neural information processing systems, pp 953–960
Zurück zum Zitat Mahé P, Ueda N, Akutsu T, Perret JL, Vert JP (2005) Graph kernels for molecular structure–activity relationship analysis with support vector machines. J Chem Inf Model 45(4):939–951 Mahé P, Ueda N, Akutsu T, Perret JL, Vert JP (2005) Graph kernels for molecular structure–activity relationship analysis with support vector machines. J Chem Inf Model 45(4):939–951
Zurück zum Zitat Manago M, Bergmann R, Conruyt N, Traphöner R, Pasley J, Le Renard J, Maurer F, Wess S, Althoff KD, Dumont S (1994) Casuel: a common case representation language. INRECA Consortium Available on the World-Wide Web at http://wwwagr informatik unikl de/bergmann/casuel/CASUEL toc2 4 Manago M, Bergmann R, Conruyt N, Traphöner R, Pasley J, Le Renard J, Maurer F, Wess S, Althoff KD, Dumont S (1994) Casuel: a common case representation language. INRECA Consortium Available on the World-Wide Web at http://​wwwagr informatik unikl de/bergmann/casuel/CASUEL toc2 4
Zurück zum Zitat Marteau PF (2009) Time warp edit distance with stiffness adjustment for time series matching. IEEE Trans Pattern Anal Mach Intell 31(2):306–318 Marteau PF (2009) Time warp edit distance with stiffness adjustment for time series matching. IEEE Trans Pattern Anal Mach Intell 31(2):306–318
Zurück zum Zitat Miller GA (1995) Wordnet: a lexical database for english. Commun ACM 38(11):39–41 Miller GA (1995) Wordnet: a lexical database for english. Commun ACM 38(11):39–41
Zurück zum Zitat Minsky M (1974) A framework for representing knowledge, MIT-AI LAboratory Memo 306 Minsky M (1974) A framework for representing knowledge, MIT-AI LAboratory Memo 306
Zurück zum Zitat Mishne G, De Rijke M (2004) Source code retrieval using conceptual similarity. In: Coupling approaches, coupling media and coupling languages for information retrieval, pp 539–554 Mishne G, De Rijke M (2004) Source code retrieval using conceptual similarity. In: Coupling approaches, coupling media and coupling languages for information retrieval, pp 539–554
Zurück zum Zitat Mitchell TM (1980) The need for biases in learning generalizations. Department of Computer Science, Laboratory for Computer Science Research, Rutgers Univ, New Jersey Mitchell TM (1980) The need for biases in learning generalizations. Department of Computer Science, Laboratory for Computer Science Research, Rutgers Univ, New Jersey
Zurück zum Zitat Mitchell TM, Keller RM, Kedar-Cabelli ST (1986) Explanation-based generalization: a unifying view. Mach Learn 1(1):47–80 Mitchell TM, Keller RM, Kedar-Cabelli ST (1986) Explanation-based generalization: a unifying view. Mach Learn 1(1):47–80
Zurück zum Zitat Montani S, Leonardi G, Quaglini S, Cavallini A, Micieli G et al (2015) A knowledge-intensive approach to process similarity calculation. Expert Syst Appl 42(9):4207–4215 Montani S, Leonardi G, Quaglini S, Cavallini A, Micieli G et al (2015) A knowledge-intensive approach to process similarity calculation. Expert Syst Appl 42(9):4207–4215
Zurück zum Zitat Muggleton S, Lodhi H, Amini A, Sternberg MJ (2005) Support vector inductive logic programming. In: International conference on discovery science. Springer, pp 163–175 Muggleton S, Lodhi H, Amini A, Sternberg MJ (2005) Support vector inductive logic programming. In: International conference on discovery science. Springer, pp 163–175
Zurück zum Zitat Munkres J (1957) Algorithms for the assignment and transportation problems. J Soc Ind Appl Math 5(1):32–38MathSciNetMATH Munkres J (1957) Algorithms for the assignment and transportation problems. J Soc Ind Appl Math 5(1):32–38MathSciNetMATH
Zurück zum Zitat Needleman SB, Wunsch CD (1970) A general method applicable to the search for similarities in the amino acid sequence of two proteins. J Mol Biol 48(3):443–453 Needleman SB, Wunsch CD (1970) A general method applicable to the search for similarities in the amino acid sequence of two proteins. J Mol Biol 48(3):443–453
Zurück zum Zitat Neuhaus M, Bunke H (2006a) A convolution edit kernel for error-tolerant graph matching. In: 18th international conference on pattern recognition, 2006. ICPR 2006, vol 4. IEEE, pp 220–223 Neuhaus M, Bunke H (2006a) A convolution edit kernel for error-tolerant graph matching. In: 18th international conference on pattern recognition, 2006. ICPR 2006, vol 4. IEEE, pp 220–223
Zurück zum Zitat Neuhaus M, Bunke H (2006b) Edit distance-based kernel functions for structural pattern classification. Pattern Recogn 39(10):1852–1863MATH Neuhaus M, Bunke H (2006b) Edit distance-based kernel functions for structural pattern classification. Pattern Recogn 39(10):1852–1863MATH
Zurück zum Zitat Neuhaus M, Bunke H (2007) Automatic learning of cost functions for graph edit distance. Inf Sci 177(1):239–247MathSciNetMATH Neuhaus M, Bunke H (2007) Automatic learning of cost functions for graph edit distance. Inf Sci 177(1):239–247MathSciNetMATH
Zurück zum Zitat Ng AY, Jordan MI, Weiss Y et al (2002) On spectral clustering: analysis and an algorithm. Adv Neural Inf Process Syst 2:849–856 Ng AY, Jordan MI, Weiss Y et al (2002) On spectral clustering: analysis and an algorithm. Adv Neural Inf Process Syst 2:849–856
Zurück zum Zitat Nienhuys-Cheng SH (1997) Distance between Herbrand interpretations: a measure for approximations to a target concept. In: Lavrac N, Dzeroski S (eds) Inductive logic programming. Springer, Berlin, pp 213–226MATH Nienhuys-Cheng SH (1997) Distance between Herbrand interpretations: a measure for approximations to a target concept. In: Lavrac N, Dzeroski S (eds) Inductive logic programming. Springer, Berlin, pp 213–226MATH
Zurück zum Zitat Nikolentzos G, Meladianos P, Limnios S, Vazirgiannis M (2018) A degeneracy framework for graph similarity. Proc IJCAI 2018:2595–2601 Nikolentzos G, Meladianos P, Limnios S, Vazirgiannis M (2018) A degeneracy framework for graph similarity. Proc IJCAI 2018:2595–2601
Zurück zum Zitat Ontañón S, Zhu J (2011) The SAM algorithm for analogy-based story generation. In: Seventh artificial intelligence and interactive digital entertainment conference Ontañón S, Zhu J (2011) The SAM algorithm for analogy-based story generation. In: Seventh artificial intelligence and interactive digital entertainment conference
Zurück zum Zitat Ontañón S, Shokoufandeh A (2016) Refinement-based similarity measures for directed labeled graphs. In: International conference on case-based reasoning. Springer, pp 311–326 Ontañón S, Shokoufandeh A (2016) Refinement-based similarity measures for directed labeled graphs. In: International conference on case-based reasoning. Springer, pp 311–326
Zurück zum Zitat Ontañón S, Montaña JL, Gonzalez AJ (2014) A dynamic-bayesian network framework for modeling and evaluating learning from observation. Expert Syst Appl 41(11):5212–5226 Ontañón S, Montaña JL, Gonzalez AJ (2014) A dynamic-bayesian network framework for modeling and evaluating learning from observation. Expert Syst Appl 41(11):5212–5226
Zurück zum Zitat Page L, Brin S, Motwani R, Winograd T (1999) The pagerank citation ranking: bringing order to the web. Technical report, Stanford InfoLab Page L, Brin S, Motwani R, Winograd T (1999) The pagerank citation ranking: bringing order to the web. Technical report, Stanford InfoLab
Zurück zum Zitat Plaza E (1995) Cases as terms: a feature term approach to the structured representation of cases. In: International conference on case-based reasoning. Springer, pp 265–276 Plaza E (1995) Cases as terms: a feature term approach to the structured representation of cases. In: International conference on case-based reasoning. Springer, pp 265–276
Zurück zum Zitat Plaza E, Armengol E, Ontañón S (2005) The explanatory power of symbolic similarity in case-based reasoning. Artif Intell Rev 24(2):145–161MATH Plaza E, Armengol E, Ontañón S (2005) The explanatory power of symbolic similarity in case-based reasoning. Artif Intell Rev 24(2):145–161MATH
Zurück zum Zitat Plotkin GD (1970) A note on inductive generalization. In: Meltzer B, Michie D (eds) Machine intelligence, vol 5. Edinburgh University Press, Edinburgh, pp 153–163 Plotkin GD (1970) A note on inductive generalization. In: Meltzer B, Michie D (eds) Machine intelligence, vol 5. Edinburgh University Press, Edinburgh, pp 153–163
Zurück zum Zitat Pons P, Latapy M (2005) Computing communities in large networks using random walks. In: International symposium on computer and information sciences. Springer, pp 284–293 Pons P, Latapy M (2005) Computing communities in large networks using random walks. In: International symposium on computer and information sciences. Springer, pp 284–293
Zurück zum Zitat Poole J, Campbell J (1995) A novel algorithm for matching conceptual and related graphs. In: International conference on conceptual structures. Springer, pp 293–307 Poole J, Campbell J (1995) A novel algorithm for matching conceptual and related graphs. In: International conference on conceptual structures. Springer, pp 293–307
Zurück zum Zitat Rada R, Mili H, Bicknell E, Blettner M (1989) Development and application of a metric on semantic nets. IEEE Trans Syst Man Cybern 19(1):17–30 Rada R, Mili H, Bicknell E, Blettner M (1989) Development and application of a metric on semantic nets. IEEE Trans Syst Man Cybern 19(1):17–30
Zurück zum Zitat Ralaivola L, Swamidass SJ, Saigo H, Baldi P (2005) Graph kernels for chemical informatics. Neural Netw 18(8):1093–1110 Ralaivola L, Swamidass SJ, Saigo H, Baldi P (2005) Graph kernels for chemical informatics. Neural Netw 18(8):1093–1110
Zurück zum Zitat Ramon J, Bruynooghe M (1998) A framework for defining distances between first-order logic objects. In: International conference on inductive logic programming. Springer, pp 271–280 Ramon J, Bruynooghe M (1998) A framework for defining distances between first-order logic objects. In: International conference on inductive logic programming. Springer, pp 271–280
Zurück zum Zitat Ramon J, Gärtner T (2003) Expressivity versus efficiency of graph kernels. In: Proceedings of the first international workshop on mining graphs, trees and sequences, pp 65–74 Ramon J, Gärtner T (2003) Expressivity versus efficiency of graph kernels. In: Proceedings of the first international workshop on mining graphs, trees and sequences, pp 65–74
Zurück zum Zitat Ramoni M, Sebastiani P, Cohen P (2002) Bayesian clustering by dynamics. Mach Learn 47(1):91–121MATH Ramoni M, Sebastiani P, Cohen P (2002) Bayesian clustering by dynamics. Mach Learn 47(1):91–121MATH
Zurück zum Zitat Resnik P (1995) Using information content to evaluate semantic similarity in a taxonomy. arXiv:cmp-lg/9511007 Resnik P (1995) Using information content to evaluate semantic similarity in a taxonomy. arXiv:cmp-lg/9511007
Zurück zum Zitat Resnik P et al (1999) Semantic similarity in a taxonomy: an information-based measure and its application to problems of ambiguity in natural language. J Artif Intell Res: JAIR 11:95–130MATH Resnik P et al (1999) Semantic similarity in a taxonomy: an information-based measure and its application to problems of ambiguity in natural language. J Artif Intell Res: JAIR 11:95–130MATH
Zurück zum Zitat Riesen K, Bunke H (2008) Iam graph database repository for graph based pattern recognition and machine learning. In: da Vitoria Lobo N, Kasparis T, Roli F, Kwok JT, Georgiopoulos M, Anagnostopoulos GC, Loog M (eds) Structural, syntactic, and statistical pattern recognition. Springer, Orlando, pp 287–297 Riesen K, Bunke H (2008) Iam graph database repository for graph based pattern recognition and machine learning. In: da Vitoria Lobo N, Kasparis T, Roli F, Kwok JT, Georgiopoulos M, Anagnostopoulos GC, Loog M (eds) Structural, syntactic, and statistical pattern recognition. Springer, Orlando, pp 287–297
Zurück zum Zitat Riesen K, Bunke H (2009) Approximate graph edit distance computation by means of bipartite graph matching. Image Vis Comput 27(7):950–959 Riesen K, Bunke H (2009) Approximate graph edit distance computation by means of bipartite graph matching. Image Vis Comput 27(7):950–959
Zurück zum Zitat Rubner Y, Tomasi C, Guibas LJ (2000) The earth mover’s distance as a metric for image retrieval. Int J Comput Vis 40(2):99–121MATH Rubner Y, Tomasi C, Guibas LJ (2000) The earth mover’s distance as a metric for image retrieval. Int J Comput Vis 40(2):99–121MATH
Zurück zum Zitat Sánchez-Ruiz AA, Ontañón S, González-Calero PA, Plaza E (2011) Measuring similarity in description logics using refinement operators. In: ICCBR, pp 289–303 Sánchez-Ruiz AA, Ontañón S, González-Calero PA, Plaza E (2011) Measuring similarity in description logics using refinement operators. In: ICCBR, pp 289–303
Zurück zum Zitat Sánchez-Ruiz AA, Ontañón S, González-Calero PA, Plaza E (2016) Measuring similarity of individuals in description logics over the refinement space of conjunctive queries. J Intell Inf Syst 47(3):447–467 Sánchez-Ruiz AA, Ontañón S, González-Calero PA, Plaza E (2016) Measuring similarity of individuals in description logics over the refinement space of conjunctive queries. J Intell Inf Syst 47(3):447–467
Zurück zum Zitat Sanfeliu A, Fu KS (1983) A distance measure between attributed relational graphs for pattern recognition. IEEE Trans Syst Man Cybern 3:353–362MATH Sanfeliu A, Fu KS (1983) A distance measure between attributed relational graphs for pattern recognition. IEEE Trans Syst Man Cybern 3:353–362MATH
Zurück zum Zitat Santini S, Jain R (1999) Similarity measures. IEEE Trans Pattern Anal Mach Intell 21(9):871–883 Santini S, Jain R (1999) Similarity measures. IEEE Trans Pattern Anal Mach Intell 21(9):871–883
Zurück zum Zitat Schaaf JW (1996) Fish and shrink. A next step towards efficient case retrieval in large scaled case bases. In: European workshop on advances in case-based reasoning. Springer, pp 362–376 Schaaf JW (1996) Fish and shrink. A next step towards efficient case retrieval in large scaled case bases. In: European workshop on advances in case-based reasoning. Springer, pp 362–376
Zurück zum Zitat Schädler K, Wysotzki F (1999) Comparing structures using a hopfield-style neural network. Appl Intell 11(1):15–30 Schädler K, Wysotzki F (1999) Comparing structures using a hopfield-style neural network. Appl Intell 11(1):15–30
Zurück zum Zitat Sebag M (1997) Distance induction in first order logic. In: International conference on inductive logic programming. Springer, pp 264–272 Sebag M (1997) Distance induction in first order logic. In: International conference on inductive logic programming. Springer, pp 264–272
Zurück zum Zitat Serra J, Arcos JL (2014) An empirical evaluation of similarity measures for time series classification. Knowl Based Syst 67:305–314 Serra J, Arcos JL (2014) An empirical evaluation of similarity measures for time series classification. Knowl Based Syst 67:305–314
Zurück zum Zitat Shapiro LG, Haralick RM (1981) Structural descriptions and inexact matching. IEEE Trans Pattern Anal Mach Intell 5:504–519 Shapiro LG, Haralick RM (1981) Structural descriptions and inexact matching. IEEE Trans Pattern Anal Mach Intell 5:504–519
Zurück zum Zitat Shervashidze N, Schweitzer P, van Leeuwen EJ, Mehlhorn K, Borgwardt KM (2011) Weisfeiler–Lehman graph kernels. J Mach Learn Res 12(1):2539–2561MathSciNetMATH Shervashidze N, Schweitzer P, van Leeuwen EJ, Mehlhorn K, Borgwardt KM (2011) Weisfeiler–Lehman graph kernels. J Mach Learn Res 12(1):2539–2561MathSciNetMATH
Zurück zum Zitat Shieber SM (2003) An introduction to unification-based approaches to grammar. Microtome Publishing, New YorkMATH Shieber SM (2003) An introduction to unification-based approaches to grammar. Microtome Publishing, New YorkMATH
Zurück zum Zitat Singhal A (2001) Modern information retrieval: a brief overview. IEEE Data Eng Bull 24(4):35–43 Singhal A (2001) Modern information retrieval: a brief overview. IEEE Data Eng Bull 24(4):35–43
Zurück zum Zitat Small H (1973) Co-citation in the scientific literature: a new measure of the relationship between two documents. J Assoc Inf Sci Technol 24(4):265–269MathSciNet Small H (1973) Co-citation in the scientific literature: a new measure of the relationship between two documents. J Assoc Inf Sci Technol 24(4):265–269MathSciNet
Zurück zum Zitat Smola AJ, Vishwanathan S (2003) Fast kernels for string and tree matching. In: Thrun S, Saul LK, Schölkopf B (eds) Advances in neural information processing systems. MIT Press, Vancouver, Canada, pp 585–592 Smola AJ, Vishwanathan S (2003) Fast kernels for string and tree matching. In: Thrun S, Saul LK, Schölkopf B (eds) Advances in neural information processing systems. MIT Press, Vancouver, Canada, pp 585–592
Zurück zum Zitat Sørensen TJ (1948) A method of establishing groups of equal amplitude in plant sociology based on similarity of species content. Kongelige Danske Videnskabernes Selskab 5(1–34):4–7 Sørensen TJ (1948) A method of establishing groups of equal amplitude in plant sociology based on similarity of species content. Kongelige Danske Videnskabernes Selskab 5(1–34):4–7
Zurück zum Zitat Sowa JF (1979) Semantics of conceptual graphs. In: Proceedings of the 17th annual meeting on Association for Computational Linguistics. Association for Computational Linguistics, pp 39–44 Sowa JF (1979) Semantics of conceptual graphs. In: Proceedings of the 17th annual meeting on Association for Computational Linguistics. Association for Computational Linguistics, pp 39–44
Zurück zum Zitat Spielman DA (2010) Algorithms, graph theory, and linear equations in laplacian matrices. In: Proceedings of the international congress of mathematicians 2010 (ICM 2010) (In 4 Volumes) vol I: plenary lectures and ceremonies vols. II–IV: invited lectures. World Scientific, pp 2698–2722 Spielman DA (2010) Algorithms, graph theory, and linear equations in laplacian matrices. In: Proceedings of the international congress of mathematicians 2010 (ICM 2010) (In 4 Volumes) vol I: plenary lectures and ceremonies vols. II–IV: invited lectures. World Scientific, pp 2698–2722
Zurück zum Zitat Sussenguth EH (1964) Structure matching in information processing. Harvard University, CambridgeMATH Sussenguth EH (1964) Structure matching in information processing. Harvard University, CambridgeMATH
Zurück zum Zitat Tsai WH, Fu KS (1979) Error-correcting isomorphisms of attributed relational graphs for pattern analysis. IEEE Trans Syst Man Cybern 9(12):757–768MATH Tsai WH, Fu KS (1979) Error-correcting isomorphisms of attributed relational graphs for pattern analysis. IEEE Trans Syst Man Cybern 9(12):757–768MATH
Zurück zum Zitat Tsuda K, Kin T, Asai K (2002) Marginalized kernels for biological sequences. Bioinformatics 18(Suppl 1):S268–S275 Tsuda K, Kin T, Asai K (2002) Marginalized kernels for biological sequences. Bioinformatics 18(Suppl 1):S268–S275
Zurück zum Zitat Tversky A (1977) Features of similarity. Psychol Rev 84:327–352 Tversky A (1977) Features of similarity. Psychol Rev 84:327–352
Zurück zum Zitat Umeyama S (1988) An eigendecomposition approach to weighted graph matching problems. IEEE Trans Pattern Anal Machine Intell 10(5):695–703MATH Umeyama S (1988) An eigendecomposition approach to weighted graph matching problems. IEEE Trans Pattern Anal Machine Intell 10(5):695–703MATH
Zurück zum Zitat Valls-Vargas J, Ontanón S, Zhu J (2014) Toward automatic character identification in unannotated narrative text. In: Seventh intelligent narrative technologies workshop Valls-Vargas J, Ontanón S, Zhu J (2014) Toward automatic character identification in unannotated narrative text. In: Seventh intelligent narrative technologies workshop
Zurück zum Zitat van der Laag PRJ, Nienhuys-Cheng SH (1998) Completeness and properness of refinement operators in inductive logic programming. J Log Program 34(3):201–225MathSciNetMATH van der Laag PRJ, Nienhuys-Cheng SH (1998) Completeness and properness of refinement operators in inductive logic programming. J Log Program 34(3):201–225MathSciNetMATH
Zurück zum Zitat Vert JP, Tsuda K, Schölkopf B (2004) A primer on kernel methods. Kernel Methods Comput Biol 47:35–70 Vert JP, Tsuda K, Schölkopf B (2004) A primer on kernel methods. Kernel Methods Comput Biol 47:35–70
Zurück zum Zitat Wallis WD, Shoubridge P, Kraetz M, Ray D (2001) Graph distances using graph union. Pattern Recogn Lett 22(6):701–704MATH Wallis WD, Shoubridge P, Kraetz M, Ray D (2001) Graph distances using graph union. Pattern Recogn Lett 22(6):701–704MATH
Zurück zum Zitat Wang Y, Ishii N (1997) A method of similarity metrics for structured representations. Expert Syst Appl 12(1):89–100 Wang Y, Ishii N (1997) A method of similarity metrics for structured representations. Expert Syst Appl 12(1):89–100
Zurück zum Zitat Weisfeiler B, Lehman AA (1968) A reduction of a graph to a canonical form and an algebra arising during this reduction. Nauchno-Technicheskaya Informatsia 2(9):12–16 Weisfeiler B, Lehman AA (1968) A reduction of a graph to a canonical form and an algebra arising during this reduction. Nauchno-Technicheskaya Informatsia 2(9):12–16
Zurück zum Zitat Welch TA (1984) A technique for high-performance data compression. Computer 6(17):8–19 Welch TA (1984) A technique for high-performance data compression. Computer 6(17):8–19
Zurück zum Zitat Wess S (1995) Fallbasiertes Problemlösen in wissensbasierten systemen zur entscheidungsunterst ützung und diagnostik Wess S (1995) Fallbasiertes Problemlösen in wissensbasierten systemen zur entscheidungsunterst ützung und diagnostik
Zurück zum Zitat Wettschereck D, Aha DW, Mohri T (1997) A review and empirical evaluation of feature weighting methods for a class of lazy learning algorithms. Artif Intell Rev 11(1–5):273–314 Wettschereck D, Aha DW, Mohri T (1997) A review and empirical evaluation of feature weighting methods for a class of lazy learning algorithms. Artif Intell Rev 11(1–5):273–314
Zurück zum Zitat Wolpert DH (1996) The lack of a priori distinctions between learning algorithms. Neural Comput 8(7):1341–1390 Wolpert DH (1996) The lack of a priori distinctions between learning algorithms. Neural Comput 8(7):1341–1390
Zurück zum Zitat Wu Z, Palmer M (1994) Verbs semantics and lexical selection. In: Proceedings of the 32nd annual meeting on Association for Computational Linguistics. Association for Computational Linguistics, pp 133–138 Wu Z, Palmer M (1994) Verbs semantics and lexical selection. In: Proceedings of the 32nd annual meeting on Association for Computational Linguistics. Association for Computational Linguistics, pp 133–138
Zurück zum Zitat Xu L, King I (2001) A pca approach for fast retrieval of structural patterns in attributed graphs. IEEE Trans Syst Man Cybern Part B (Cybern) 31(5):812–817 Xu L, King I (2001) A pca approach for fast retrieval of structural patterns in attributed graphs. IEEE Trans Syst Man Cybern Part B (Cybern) 31(5):812–817
Zurück zum Zitat Xu K, Hu W, Leskovec J, Jegelka S (2018) How powerful are graph neural networks? arXiv:181000826 Xu K, Hu W, Leskovec J, Jegelka S (2018) How powerful are graph neural networks? arXiv:181000826
Zurück zum Zitat Yang L, Jin R (2006) Distance metric learning: a comprehensive survey. Mich State Univ 2(2):4 Yang L, Jin R (2006) Distance metric learning: a comprehensive survey. Mich State Univ 2(2):4
Zurück zum Zitat Zhang K (1989) The editing distance between trees: algorithms and applications. PhD thesis from the New York University Zhang K (1989) The editing distance between trees: algorithms and applications. PhD thesis from the New York University
Zurück zum Zitat Zhang Z, Wang M, Xiang Y, Huang Y, Nehorai A (2018) Retgk: graph kernels based on return probabilities of random walks. In: Bengio S, Wallach HM, Larochelle H, Grauman K, Cesa-Bianchi N, Garnett R, Neural Information Processing Systems Conference (eds) Advances in neural information processing systems, Vancouver, Canada, pp 3964–3974 Zhang Z, Wang M, Xiang Y, Huang Y, Nehorai A (2018) Retgk: graph kernels based on return probabilities of random walks. In: Bengio S, Wallach HM, Larochelle H, Grauman K, Cesa-Bianchi N, Garnett R, Neural Information Processing Systems Conference (eds) Advances in neural information processing systems, Vancouver, Canada, pp 3964–3974
Metadaten
Titel
An overview of distance and similarity functions for structured data
verfasst von
Santiago Ontañón
Publikationsdatum
27.02.2020
Verlag
Springer Netherlands
Erschienen in
Artificial Intelligence Review / Ausgabe 7/2020
Print ISSN: 0269-2821
Elektronische ISSN: 1573-7462
DOI
https://doi.org/10.1007/s10462-020-09821-w

Weitere Artikel der Ausgabe 7/2020

Artificial Intelligence Review 7/2020 Zur Ausgabe

Premium Partner