The graph matching problem

Pattern Analysis and Applications

Volumn 16, Issue 3, 2013, Pages 253-283

  Livi, Lorenzo ^a   Rizzi, Antonello ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Graph edit distance; Graph embedding; Graph kernels; Graph based pattern recognition; Inexact graph matching

Indexed keywords

EID: 84880629975     PISSN: 14337541     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10044-012-0284-8     Document Type: Article

References (134)

1. Aggarwal C, Wang H (2010) Managing and mining graph data. Advances in Database Systems. Springer. http://books. google. com/books?id=Ox39uLyYh-wC.
2. Aizerman A, Braverman EM, Rozoner LI (1964) Theoretical foundations of the potential function method in pattern recognition learning. Automat Remote Control 25: 821-837.
3. Ambauen R, Fischer S, Bunke H (2003) Graph edit distance with node splitting and merging, and its application to diatom identification. In: Proceedings of the 4th IAPR international conference on Graph based representations in pattern recognition, GbRPR'03. Springer-Verlag, Berlin, Heidelberg, pp 95-106. http://portal. acm. org/citation. cfm?id=1757868. 1757880.
4. Bardaji I, Ferrer M, Sanfeliu A (2010) A comparison between two representatives of a set of graphs: median vs barycenter graph. In: Proceedings of the 2010 joint IAPR international conference on structural, syntactic, and statistical pattern recognition, SSPR-38; SPR'10. Springer-Verlag, Berlin, Heidelberg, pp 149-158. http://portal. acm. org/citation. cfm?id=1887003. 1887022.
5. Bargiela A, Pedrycz W (2003) Granular computing: an introduction. No. v. 2002 in Kluwer international series in engineering and computer science. Kluwer Academic Publishers. http://books. google. com/books?id=F_3t7XTMhBkC.
6. Berg C, Christensen J, Ressel P (1984) Harmonic analysis on semigroups: theory of positive definite and related functions. Graduate texts in mathematics. Springer-Verlag http://books. google. com/books?id=zz2DQgAACAAJ.
7. Bernard M, Boyer L, Habrard A, Sebban M (2008)Learning probabilistic models of tree edit distance. Pattern Recognit. 41: 2611-2629. doi: 10. 1016/j. patcog. 2008. 01. 011. http://portal. acm. org/citation. cfm?id=1367147. 1367314.
8. Bernstein D (2009) Matrix mathematics: theory, facts, and formulas. Princeton University Press. http://books. google. com/books?id=jgEiuHlTCYcC.
9. Bille P (2005) A survey on tree edit distance and related problems. Theor Comput Sci 337: 217-239. doi: 10. 1016/j. tcs. 2004. 12. 030. http://dx. doi. org/10. 1016/j. tcs. 2004. 12. 030.
10. Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D (2006) Complex networks: structure and dynamics. Phys. Rep. 424(4-5): 175-308. doi: 10. 1016/j. physrep. 2005. 10. 009. http://dx. doi. org/10. 1016/j. physrep. 2005. 10. 009.
11. Bollobás B (1998) Modern graph theory. Graduate texts in mathematics. Springer. http://books. google. ca/books?id=SbZKSZ-1qrwC.
12. Borg I, Groenen P (2005) Modern multidimensional scaling: theory and applications. Springer series in statistics. Springer. http://books. google. com/books?id=duTODldZzRcC.
13. Borgelt C (2002) Mining molecular fragments: finding relevant substructures of molecules. In: Proceedings of 2002 IEEE international conference on data mining (ICDM). IEEE Press, pp 51-58.
14. Borgwardt KM, Ong CS, Schönauer S, Vishwanathan SVN, Smola AJ, Kriegel HP (2005) Protein function prediction via graph kernels. Bioinformatics 21: 47-56. http://dx. doi. org/10. 1093/bioinformatics/bti1007.
15. Boser BE, Guyon IM, Vapnik VN (1992) A training algorithm for optimal margin classifiers. In: Proceedings of the fifth annual workshop on computational learning theory, COLT '92. ACM, New York, NY, USA, pp 144-152. doi: 10. 1145/130385. 130401. http://doi. acm. org/10. 1145/130385. 130401.
16. Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press. http://books. google. com/books?id=mYm0bLd3fcoC.
17. Bunke H, Allermann G (1983) Inexact graph matching for structural pattern recognition. Pattern Recognit Lett 1(4): 245-253 (1983). doi: 10. 1016/0167-8655(83)90033-8. http://www. sciencedirect. com/science/article/B6V15-48MPV00-1K/2/6f816d072c71e50b1a80858a8b488463.
18. Bunke H, Bühler U (1993) Applications of approximate string matching to 2D shape recognition. Pattern Recognit 26(12): 1797-1812. doi: 10. 1016/0031-3203(93)90177-X. http://www. sciencedirect. com/science/article/B6V14-48MPPK4-1V6/2/c7f7a4bd6aae48534f11137815852e32.
19. Bunke H, Shearer K (1998) A graph distance metric based on the maximal common subgraph. Pattern Recognit. Lett. 19: 255-259. doi: 10. 1016/S0167-8655(97)00179-7.
20. Burges CJC (1998) A tutorial on support vector machines for pattern recognition. Data Min Knowl Disc 2: 121-167.
21. Buriol LS, Castillo C, Donato D, Leonardi S, Millozzi S (2006) Temporal analysis of the wikigraph. In: Web intelligence conference. IEEE CS Press, pp 45-51.
22. Cinti A, Rizzi A (2011) Neurofuzzy min-max networks implementation on FPGA. In: International joint conference on computational intalligence (IJCCI), neural computation theories and analysis (NCTA).
23. Conte D, Foggia P, Sansone C, Vento M (2004) Thirty years of graph matching In pattern recognition. Int J Pattern Recognit Artif Intell 18: 265-298. doi: 10. 1142/S0218001404003228.
24. Cook D, Holder L (2007) Mining graph data. Wiley-Interscience. http://books. google. com/books?id=jp8ZIpMVB54C.
25. Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20: 273-297. http://dx. doi. org/10. 1023/A: 1022627411411. 10. 1023/A: 1022627411411.
26. Cox T, Cox M (2001) Multidimensional scaling. No. v. 1 in Monographs on statistics and applied probability. Chapman & Hall/CRC. http://books. google. com/books?id=SKZzmEZqvqkC.
27. Del Vescovo G, Livi L, Rizzi A, Frattale Mascioli FM (2011) Clustering structured data with the SPARE library. In: Proceeding of 2011 4th IEEE international conference on computer science and information technology, vol 9, pp 413-417.
28. Del Vescovo G, Rizzi A (2007) Automatic classification of graphs by symbolic histograms. In: Proceedings of the 2007 IEEE international conference on granular computing, GRC '07. IEEE Computer Society, pp 410-416. doi: 10. 1109/GRC. 2007. 46. http://dx. doi. org/10. 1109/GRC. 2007. 46.
29. Del Vescovo G, Rizzi A (2007) Online handwriting recognition by the symbolic histograms approach. In: Proceedings of the 2007 IEEE international conference on granular computing, GRC '07. IEEE Computer Society, Washington, DC, USA, p 686. doi: 10. 1109/GRC. 2007. 116. http://dx. doi. org/10. 1109/GRC. 2007. 116.
30. Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B 39(1): 1-38.
31. Diestel R (2006) Graph theory. Graduate texts in mathematics. Springer. http://books. google. com/books?id=aR2TMYQr2CMC.
32. Dijkstra EW (1959) A note on two problems in connexion with graphs. Numerische Mathematik 1: 269-271 http://dx. doi. org/10. 1007/BF01386390. 10. 1007/BF01386390.
33. Dorfler F, Bullo F (2011) Kron reduction of graphs with applications to electrical networks. ArXiv e-prints.
34. ElGhawalby H, Hancock ER (2008) Graph characteristic from the Gauss-Bonnet Theorem. In: Lobo NdV, Kasparis T, Roli F, Kwok JTY, Georgiopoulos M, Anagnostopoulos GC, Loog M (eds) SSPR/SPR, lecture notes in computer science, vol 5342. Springer, pp 207-216.
35. Emms, D., Wilson, R. C., Hancock, E. (2007) Graph embedding using quantum commute times. In: Proceedings of the 6th IAPR-TC-15 international conference on graph-based representations in pattern recognition, GbRPR'07. Springer-Verlag, Berlin, Heidelberg, pp 371-382. http://portal. acm. org/citation. cfm?id=1769371. 1769412.
36. Eshera MA, Fu KS (1984) A graph distance measure for image analysis. IEEE Trans Syst Man Cybern 14(3): 398-408.
37. Faloutsos C, Lin KI (1995) FastMap: a fast algorithm for indexing, data-mining and visualization of traditional and multimedia datasets. SIGMOD Rec 24: 163-174. doi: 10. 1145/568271. 223812. http://doi. acm. org/10. 1145/568271. 223812.
38. Fankhauser S, Riesen K, Bunke H (2011) Speeding up graph edit distance computation through fast bipartite matching. In: Jiang X, Ferrer M, Torsello A (eds) Graph-based representations in pattern recognition. Lecture notes in computer science, vol 6658. Springer, Berlin, pp 102-111. http://dx. doi. org/10. 1007/978-3-642-20844-7_11. 10. 1007/978-3-642-20844-7_11.
39. Fortune S, Wyllie J (1978) Parallelism in random access machines. In: Proceedings of the tenth annual ACM symposium on Theory of computing, STOC '78. ACM, New York, NY, USA, pp 114-118. doi: 10. 1145/800133. 804339. http://doi. acm. org/10. 1145/800133. 804339.
40. Gao X, Xiao B, Tao D, Li X (2008) Image categorization: graph edit direction histogram. Pattern Recognit 41(10): 3179-3191. doi: 10. 1016/j. patcog. 2008. 03. 025http://www. sciencedirect. com/science/article/pii/S0031320308001246.
41. Gao X, Xiao B, Tao D, Li X (2010) A survey of graph edit distance. Pattern Anal Appl 13(1): 113-129.
42. Garey MR, Johnson DS (1990) Computers and Intractability: a guide to the theory of NP-completeness. W. H. Freeman & Co., New York, NY, USA.
43. Gärtner T (2008) Kernels for structured data. No v 72 in kernels for structured data. World Scientific. http://books. google. com/books?id=ykomKZ5rD1gC.
44. Gartner T, Flach P, Wrobel S (2003) On graph kernels: hardness results and efficient alternatives. Lecture notes in computer science, pp 129-143.
45. Ghias A, Logan J, Chamberlin D, Smith BC (1995) Query by humming: musical information retrieval in an audio database. In: ACM Multimedia, pp 231-236.
46. Gibert J, Valveny E, Bunke H (2011) Dimensionality reduction for graph of words embedding. In: Jiang X, Ferrer M, Torsello A (eds) Graph-based representations in pattern recognition. Lecture notes in computer science, vol 6658. Springer Berlin, pp 22-31. http://dx. doi. org/10. 1007/978-3-642-20844-7_3. 10. 1007/978-3-642-20844-7_3.
47. Giuliani A, Benigni R, Zbilut JP, Webber Jr CL, Sirabella P, Colosimo A (2002) Nonlinear signal analysis methods in the Elucidation of protein sequence-structure relationships. ChemInform 33(28). doi: 10. 1002/chin. 200228300. http://dx. doi. org/10. 1002/chin. 200228300.
48. Goldfarb L (1984) A unified approach to pattern recognition. Pattern Recognit 17(5): 575-582. doi: 10. 1016/0031-3203(84)90056-6. http://www. sciencedirect. com/science/article/B6V14-48MPJHK-J1/2/b156c1fd23bfed84bd0db8f8ec523c88.
49. Goldschlager LM (1982) A universal interconnection pattern for parallel computers. J ACM 29: 1073-1086 doi: 10. 1145/322344. 322353. http://doi. acm. org/10. 1145/322344. 322353.
50. Gori M, Maggini M, Sarti L (2004) Graph matching using random walks. In: Proceedings of the pattern recognition, 17th international conference on (ICPR'04) volume 3, vol 03, ICPR '04. IEEE Computer Society, Washington, DC, USA, pp 394-397. doi: 10. 1109/ICPR. 2004. 422. http://dx. doi. org/10. 1109/ICPR. 2004. 422.
51. Hagmann P, Cammoun L, Gigandet X, Meuli R, Honey CJ, Sporns O (2008) Mapping the structural core of human cerebral cortex. PLoS Biol 6(7): e159. doi: 10. 1371/journal. pbio. 0060159. http://dx. doi. org/10. 1371/journal. pbio. 0060159.
52. Hart P, Nilsson N, Raphael B (1968) A formal basis for the heuristic determination of minimum cost paths. IEEE Trans Syst Sci Cybern 4(2): 100-107. doi: 10. 1109/TSSC. 1968. 300136. http://dx. doi. org/10. 1109/TSSC. 1968. 300136.
53. Haussler D (1999) Convolution kernels on discrete structures. Technical report.
54. Hell P, Nesšetřil J (2004) Graphs and homomorphisms. Oxford lecture series in mathematics and its applications. Oxford University Press. http://books. google. it/books?id=bJXWV-qK7kYC.
55. Hopcroft JE, Wong JK (1974) Linear time algorithm for isomorphism of planar graphs (Preliminary Report). In: Proceedings of the sixth annual ACM symposium on Theory of computing, STOC '74. ACM, New York, NY, USA, pp 172-184. doi: 10. 1145/800119. 803896. http://doi. acm. org/10. 1145/800119. 803896.
56. Imrich W, Klavžar S (2000) Product graphs, structure and recognition. Wiley-Interscience series in discrete mathematics and optimization. Wiley. http://books. google. com/books?id=EOnuAAAAMAAJ.
57. Izenman A (2008) Modern multivariate statistical techniques: regression, classification, and manifold learning. Springer texts in statistics. Springer. http://books. google. com/books?id=1CuznRORa3EC.
58. Jain B, Obermayer K (2011) Maximum likelihood for Gaussians on graphs. In: Jiang X, Ferrer M, Torsello A (eds) Graph-based representations in pattern recognition. Lecture notes in computer science, vol 6658. Springer, Berlin, pp 62-71. http://dx. doi. org/10. 1007/978-3-642-20844-7_7. 10. 1007/978-3-642-20844-7_7.
59. Jain BJ, Obermayer K (2009) Structure spaces. J Mach Learn Res 10: 2667-2714. http://portal. acm. org/citation. cfm?id=1577069. 1755876.
60. Jain BJ, Wysotzki F (2004) Central clustering of attributed graphs. Mach Learn 56: 169-207. doi: 10. 1023/B: MACH. 0000033119. 52532. ce. http://portal. acm. org/citation. cfm?id=1007760. 1007768.
61. Jiang X, Müunger A, Bunke H (2001) On median graphs: properties, algorithms, and applications. IEEE Trans Pattern Anal Mach Intell 23: 1144-1151. doi: 10. 1109/34. 954604. http://dx. doi. org/10. 1109/34. 954604.
62. Jolliffe I (2002) Principal component analysis. Springer series in statistics. Springer. http://books. google. com/books?id=_olByCrhjwIC.
63. Kashima H, Tsuda K, Inokuchi A (2003) Marginalized kernels between labeled graphs. In: Proceedings of the twentieth international conference on machine learning. AAAI Press, pp 321-328.
64. Kazius J, McGuire R, Bursi R (2005) Derivation and validation of toxicophores for mutagenicity prediction. J Med Chem 48(1): 312-320. doi: 10. 1021/jm040835a. http://pubs. acs. org/doi/abs/10. 1021/jm040835a.
65. Kohonen T (2001) Self-organizing maps. Springer series in information sciences. Springer. http://books. google. com/books?id=e4igHzyf078C.
66. Kondor RI, Lafferty J (2002) Diffusion kernels on graphs and other discrete structures. In: Proceedings of the ICML, pp 315-322.
67. Kruskal J (1962) Nonmetric multidimensional scaling: a numerical method. Psychometrika 29(2): 115-129. http://ideas. repec. org/a/spr/psycho/v29y1964i2p115-129. html.
68. Kruskal J, Wish M (1978) Multidimensional scaling. Quantitative applications in the social sciences. Sage Publications. http://books. google. com/books?id=ZzmIPcEXPf0C.
69. Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22(1): 79-86.
70. Kuramochi M, Karypis G (2002) An efficient algorithm for discovering frequent subgraphs. Technical report, IEEE Transactions on Knowledge and Data Engineering.
71. Leslie C, Kuang R (2004) Fast string kernels using inexact matching for protein sequences. J Mach Learn Res 5: 1435-1455. http://dl. acm. org/citation. cfm?id=1005332. 1044708.
72. Levenshtein VI (1966) Binary codes capable of correcting deletions, insertions, and reversals. Technical Report 8.
73. Levi G (1973) A note on the derivation of maximal common subgraphs of two directed or undirected graphs. Calcolo 9: 341-352. http://dx. doi. org/10. 1007/BF02575586. 10. 1007/BF02575586.
74. Livi L, Del Vescovo G, Rizzi A (2012) Graph recognition by seriation and frequent substructures mining. In: Proceeding of the first international conference on pattern recognition applications and methods 1: 186-191. doi: 10. 5220/0003733201860191.
75. Livi L, Del Vescovo G, Rizzi A (2012) Inexact graph matching through graph coverage. In: Proceeding of the first international conference on pattern recognition applications and methods 1: 269-272. doi: 10. 5220/0003732802690272.
76. Livi L, Rizzi A (2012) Parallel algorithms for tensor product-based inexact graph matching. In: Proceeding of the 2012 IEEE International Joint Conference on Neural Networks. IEEE, Brisbane, Australia, pp 2276-2283. doi: 10. 1109/IJCNN. 2012. 6252681. ISBN 978-1-4673-1489-3.
77. Luxburg UV, Bousquet O (2003) Distance-based classification with Lipschitz functions. J Mach Learn Res 5: 669-695.
78. Mascioli FMF, Rizzi A, Panella M, Martinelli G (2000) Scale-based approach to hierarchical fuzzy clustering. Signal Process 80(6): 1001-1016.
79. Menchetti S, Costa F, Frasconi P (2005) Weighted decomposition kernels. In: Proceedings of the 22nd international conference on Machine learning, ICML '05. ACM, New York, NY, USA, pp 585-592. doi: 10. 1145/1102351. 1102425. http://doi. acm. org/10. 1145/1102351. 1102425.
80. Mercer J (1909) Functions of positive and negative type, and their connection with the theory of integral equations. In: Philosophical transactions of the royal society of London. Series A, containing papers of a mathematical or physical character, vol 209, pp 415-446. http://www. jstor. org/stable/91043.
81. Munkres J (1957) Algorithms for the assignment and transportation problems. J Soc Ind Appl Math 5(1): 32-38. http://scitation. aip. org/getabs/servlet/GetabsServlet?prog=normal&id=SMJMAP000005000001000032000001&idtype=cvips&gifs=yes.
82. Munkres J (2000) Topology. Prentice Hall. http://books. google. com/books?id=XjoZAQAAIAAJ.
83. Neuhaus M, Bunke H (2004) A probabilistic approach to learning costs for graph edit distance. In: Proceedings of the 17th international conference on pattern recognition, pp 389-393.
84. Neuhaus M, Bunke H (2005) Self-organizing maps for learning the edit costs in graph matching. IEEE Trans Syst Man Cybern B 35: 503-514.
85. Neuhaus M, Bunke H (2006) A convolution edit kernel for error-tolerant graph matching. In: ICPR (4). IEEE Computer Society, pp 220-223.
86. Neuhaus M, Bunke H (2006) A random walk kernel derived from graph edit distance. In: Yeung DY, Kwok J, Fred A, Roli F, de Ridder D (eds) Structural, syntactic, and statistical pattern recognition. Lecture notes in computer science, vol 4109. Springer, Berlin, pp 191-199. http://dx. doi. org/10. 1007/11815921_20. 10. 1007/11815921_20.
87. Neuhaus M, Bunke H (2007) A quadratic programming approach to the graph edit distance problem. In: Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition, GbRPR'07. Springer-Verlag, Berlin, pp 92-102. http://portal. acm. org/citation. cfm?id=1769371. 1769382.
88. Neuhaus M, Bunke H (2007) Automatic learning of cost functions for graph edit distance. Inf Sci 177(1): 239-247.
89. Neuhaus M, Bunke H (2007) Bridging the gap between graph edit distance and kernel machines. Series in machine perception and artificial intelligence. World Scientific. http://books. google. com/books?id=xM_5hvL1AlkC.
90. Neuhaus M, Riesen K, Bunke H (2006) Fast suboptimal algorithms for the computation of graph edit distance. In: Structural, syntactic, and statistical pattern recognition. LNCS. Springer, pp 163-172.
91. Nocedal J, Wright S (2006) Numerical optimization. Springer series in operations research. Springer. http://books. google. com/books?id=eNlPAAAAMAAJ.
92. Pekalska E, Duin R (2005) The dissimilarity representation for pattern recognition: foundations and applications. Series in machine perception and artificial intelligence. World Scientific. http://books. google. com/books?id=YPPr6eypHFwC.
93. Peris G (2002) Fast cyclic edit distance computation with weighted edit costs in classification. In: Proceedings of the 16th international conference on pattern recognition (ICPR'02) volume 4, vol 4. ICPR '02. IEEE Computer Society, Washington, DC, USA, pp 40, 184. http://portal. acm. org/citation. cfm?id=846227. 848570.
94. Qiu H, Hancock ER (2006) Graph matching and clustering using spectral partitions. Pattern Recognit 39: 22-34. doi: 10. 1016/j. patcog. 2005. 06. 014. http://portal. acm. org/citation. cfm?id=1220964. 1221155.
95. Rao I, Sarma K (2010) On tensor product of standard graphs. Int J Comput Cognit 8(3): 99.
96. Ren P, Wilson RC, Hancock ER (2009) Characteristic polynomial analysis on matrix representations of graphs. In: Torsello A, Escolano F, Brun L (eds) GbRPR. Lecture notes in computer science, vol 5534. Springer, pp 243-252.
97. Riesen K, Bunke H (2008) IAM graph database repository for graph based pattern recognition and machine learning. In: Proceedings of the 2008 joint IAPR international workshop on structural, syntactic, and statistical pattern recognition, SSPR & SPR '08. Springer-Verlag, Berlin, pp 287-297. doi: 10. 1007/978-3-540-89689-0_33. http://dx. doi. org/10. 1007/978-3-540-89689-0_33.
98. Riesen K, Bunke H (2009) Approximate graph edit distance computation by means of bipartite graph matching. Image Vis Comput 27: 950-959. doi: 10. 1016/j. imavis. 2008. 04. 004. http://portal. acm. org/citation. cfm?id=1534927. 1534959.
99. Riesen K, Bunke H (2009) Reducing the dimensionality of dissimilarity space embedding graph kernels. Eng Appl Artif Intell 22: 48-56. doi: 10. 1016/j. engappai. 2008. 04. 006. http://portal. acm. org/citation. cfm?id=1497654. 1498530.
100. Riesen K, Bunke H (2010) Graph classification and clustering based on vector space embedding. Series in Machine Perception and Artificial Intelligence. World Scientific Pub Co Inc. http://books. google. com/books?id=hKr9QwAACAAJ.
101. Rizzi A, Del Vescovo G (2006) Automatic image classification by a granular computing approach. In: Machine learning for signal processing, 2006. Proceedings of the 2006 16th IEEE signal processing society workshop, pp 33-38. doi: 10. 1109/MLSP. 2006. 275517.
102. Rizzi A, Panella M, Frattale Mascioli FM (2002) Adaptive resolution min-max classifiers. IEEE Trans Neural Netw 13: 402-414.
103. Robles-Kelly A, Hancock E (2009) String edit distance, random walks and graph matching. In: Caelli T, Amin A, Duin RPW, Ridder D, Kamel M (eds) Structural, syntactic, and statistical pattern recognition. Lecture notes in computer science 2396, chap 10. Springer, Berlin, Berlin, pp. 107-129. doi: 10. 1007/3-540-70659-3_10. http://dx. doi. org/10. 1007/3-540-70659-3_10.
104. Robles-Kelly A, Hancock ER (2005) Graph edit distance from spectral seriation. IEEE Trans Pattern Anal Mach Intell 27: 365-378. doi: 10. 1109/TPAMI. 2005. 56. http://dx. doi. org/10. 1109/TPAMI. 2005. 56.
105. Robles-Kelly A, Hancock ER (2007) A Riemannian approach to graph embedding. Pattern Recognit 40(3): 1042-1056.
106. Sakoe H (1978) Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans Acoust Speech Signal Process 26: 43-49.
107. Sammon JW (1969) A nonlinear mapping for data structure analysis. IEEE Trans Comput 18: 401-409. doi: 10. 1109/T-C. 1969. 222678. http://dx. doi. org/10. 1109/T-C. 1969. 222678.
108. Sampathkumar E (1975) On tensor product graphs. J Aust Math Soc Ser A 20(03): 268-273.
109. Sanfeliu A, Fu KS (1983) A distance measure between attributed relational graphs for pattern recognition. IEEE Trans Syst Man Cybern 13(3): 353-362.
110. Schenker A, Bunke H, Last M, Kandel A (2005) Graph-theoretic techniques for web content mining 62. World Scientific Pub. http://books. google. com/books?hl=en&lr=&id=hNJozkPJAEwC&oi=fnd&pg=PP1&dq=Graph-Theoretic+Techniques+for+Web+Content+Mining&ots=PPVMc-VCA1&sig=d6Fok33vLb-WBFstYIpr7ijn4jM.
111. Schölkopf B, Smola A (2002) Learning with kernels: support vector machines, regularization, optimization, and beyond. Adapt Comput Mach Learn. MIT Press. http://books. google. com/books?id=y8ORL3DWt4sC.
112. Schölkopf B, Tsuda K, Vert J (2004) Kernel methods in computational biology. Comput Mol Biol. MIT Press. http://books. google. it/books?id=SwAooknaMXgC.
113. Shawe-Taylor J, Cristianini N (2004) Kernel methods for pattern analysis. Cambridge University Press. http://books. google. com/books?id=9i0vg12lti4C.
114. Smola AJ, Kondor RI (2003) Kernels and regularization on graphs. In: Scholkopf B, Warmuth MK (eds) Computational learning theory and kernel machines, 16th annual conference on computational learning theory and 7th Kernel workshop, COLT/Kernel 2003. Lecture notes in computer science, vol 2777. Springer, Washington, pp 144-158. ISBN 3-540-40720-0.
115. Tang J, Zhang C, Luo B (2006) A new approach to graph seriation. In: Proceedings of the first international conference on innovative computing, information and control, vol 3, ICICIC '06. IEEE Computer Society, Washington, DC, USA, pp 625-628. doi: 10. 1109/ICICIC. 2006. 385. http://dx. doi. org/10. 1109/ICICIC. 2006. 385.
116. Teo CH, Vishwanathan SVN (2006) Fast and space efficient string kernels using suffix arrays. In: Proceedings of the 23rd international conference on Machine learning, ICML 2006. ACM, New York, NY, USA, pp 929-936. doi: 10. 1145/1143844. 1143961. http://doi. acm. org/10. 1145/1143844. 1143961.
117. Theodoridis S, Koutroumbas K (2006) Pattern recognition. Elsevier, Academic Press. http://books. google. com/books?id=gAGRCmp8Sp8C.
118. Thomas LT, Valluri SR, Karlapalem K (2006) Margin: maximal frequent subgraph mining. In: Proceedings of the sixth international conference on data mining, ICDM'06. IEEE Computer Society, Washington, pp 1097-1101. doi: 10. 1109/ICDM. 2006. 102. http://dx. doi. org/10. 1109/ICDM. 2006. 102. ISBN 0-7695-2701-9.
119. Torsello A, Hancock ER (2007) Graph embedding using tree edit-union. Pattern Recognit 40: 1393-1405 doi: 10. 1016/j. patcog. 2006. 09. 006. http://portal. acm. org/citation. cfm?id=1224549. 1224568.
120. Torsello A, Robles-Kelly A, Hancock ER (2007) Discovering shape classes using tree edit-distance and pairwise clustering. Int J Comput Vis 72: 259-285. doi: 10. 1007/s11263-006-8929-y. http://portal. acm. org/citation. cfm?id=1210315. 1210321.
121. Tun K, Dhar P, Palumbo M, Giuliani A (2006) Metabolic pathways variability and sequence/networks comparisons. BMC Bioinf 7(1): 24. doi: 10. 1186/1471-2105-7-24. http://www. biomedcentral. com/1471-2105/7/24.
122. Valiant LG (1990) A bridging model for parallel computation. Commun. ACM 33: 103-111. doi: 10. 1145/79173. 79181. http://doi. acm. org/10. 1145/79173. 79181.
123. Vishwanathan SVN, Borgwardt KM, Kondor RI, Schraudolph NN (2010) Graph kernels. J Mach Learn Res 11: 1201-1242.
124. Vishwanathan SVN, Smola AJ (2002) Fast kernels for string and tree matching. In: Neural information processing systems, pp 569-576.
125. Washio T, Motoda H (2003) State of the art of graph-based data mining. SIGKDD Explor. Newsl 5: 59-68. doi: 10. 1145/959242. 959249. http://doi. acm. org/10. 1145/959242. 959249.
126. Wasserman S, Faust K (1994) Social network analysis: methods and applications. Cambridge University Press, Cambridge.
127. Watkins C (1999) Kernels from matching operations. Technical report, CSD-TR 98-07, University of London, Computer Science Department, Royal Holloway.
128. Weaver N (1999) Lipschitz algebras. World Scientific. http://books. google. com/books?id=45rnwyVjg_QC.
129. Xiao B, Gao X, Tao D, Li X (2008) HMM-based graph edit distance for image indexing. Int J Imaging Syst Technol 18(2-3): 209-218. doi: 10. 1002/ima. 20146. http://dx. doi. org/10. 1002/ima. 20146.
130. Yan X, Han J (2002) gSpan: graph-based substructure pattern mining. In: Proceedings of the 2002 IEEE international conference on data mining, ICDM '02. IEEE Computer Society, Washington, pp. 721-724. http://dl. acm. org/citation. cfm?id=844380. 844811. ISBN 0-7695-1754-4.
131. Yan X, Han J (2003) CloseGraph: mining closed frequent graph patterns. In: Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, KDD '03. ACM, New York, NY, USA, pp 286-295. doi: 10. 1145/956750. 956784. http://doi. acm. org/10. 1145/956750. 956784.
132. Yu H, Hancock ER (2006) String kernels for matching seriated graphs. In: Proceedings of the 18th international conference on pattern recognition, vol 04, ICPR '06. IEEE Computer Society, Washington, DC, USA, pp 224-228. doi: 10. 1109/ICPR. 2006. 1081. http://dx. doi. org/10. 1109/ICPR. 2006. 1081.
133. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3): 338-353. doi: 10. 1016/S0019-9958(65)90241-X. http://dx. doi. org/10. 1016/S0019-9958(65)90241-X.
134. Zinman GE, Zhong S, Bar-Joseph Z (2011) Biological interaction networks are conserved at the module level. BMC Syst Biol 5(1): 134+. doi: 10. 1186/1752-0509-5-134. http://dx. doi. org/10. 1186/1752-0509-5-134.