Cayley graphs as classifiers for data mining: the influence of asymmetries. (English) Zbl 1206.05050
This is strictly an expository article. From the authors’ abstract: “The endomorphism monoids of graphs have been actively investigated. They are convenient tools expressing asymmetries of the graphs. One of the most important classes of graphs considered in this framework is that of Cayley graphs. Our paper proposes a new method of using Cayley graphs for classification of data. We give a survey of recent results devoted to the Cayley graphs also involving their endomorphism monoids.”
Reviewer: Mark E. Watkins (Syracuse)
MSC:
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
| 20M35 | Semigroups in automata theory, linguistics, etc. |
Keywords:
Cayley graphs; endomorphism monoids; classification: monoid; finite state automaton; periodic semigroupReferences:
| [1] | S.B. Akers, B. Krishnamurthy, Group graphs as interconnection networks, in: Proc. 14th Int. Conf. Fault Tolerance Comp, 1984, pp. 422-427; S.B. Akers, B. Krishnamurthy, Group graphs as interconnection networks, in: Proc. 14th Int. Conf. Fault Tolerance Comp, 1984, pp. 422-427 |
| [2] | Akers, S. B.; Krishnamurthy, B., A group-theoretical model for symmetric interconnection networks, IEEE Trans. Comput., 38, 555-566 (1989) · Zbl 0678.94026 |
| [3] | Alspach, B., Cayley graphs with optimal fault tolerance, IEEE Trans. Computers, 41, 10, 1337-1339 (1992) · Zbl 1395.05078 |
| [4] | Annexstein, F.; Baumslag, M.; Rosenberg, A. L., Group action graphs and parallel architectures, SIAM J. Comput., 19, 544-569 (1990) · Zbl 0698.68064 |
| [5] | Arden, B. W.; Tang, K. W., Representations and routing for Cayley graphs, IEEE Trans. Commun., 39, 11, 1533-1537 (1991) · Zbl 0737.05072 |
| [6] | Arworn, S.; Knauer, U.; Na Chiangmai, N., Characterization of digraphs of right (left) zero unions of groups, Thai J. Math., 1, 131-140 (2003) · Zbl 1055.05075 |
| [7] | Babai, L., Automorphism groups, isomorphism, reconstruction, (Handbook of Combinatorics (1995), Elsevier Sci), 1447-1540 · Zbl 0846.05042 |
| [8] | Bača, M.; Jendroľ, S.; Miller, M.; Ryan, J., Antimagic labelings of generalized Petersen graphs that are plane, Ars Combin., 73, 115-128 (2004) · Zbl 1072.05050 |
| [9] | Bagirov, A. M.; Rubinov, A. M.; Yearwood, J., A global optimization approach to classification, Optim. Eng., 3, 129-155 (2002) · Zbl 1035.90060 |
| [10] | Bagirov, A. M.; Rubinov, A. M.; Soukhoroukova, N. V.; Yearwood, J., Unsupervised and supervised data classification via nonsmooth and global optimization, Top, 11, 1-93 (2003) · Zbl 1048.65059 |
| [11] | Bagirov, A. M.; Yearwood, J. L., A new nonsmooth optimization algorithm for minimum sum-of-squares clustering problems, European J. Operational Research, 170, 578-596 (2006) · Zbl 1085.90045 |
| [12] | Barth, D.; Berthomé, P., Periodic gossiping in commuted networks, Theory Comput. Syst., 37, 5, 559-584 (2004) · Zbl 1088.68012 |
| [13] | Baumslag, M., On the fault tolerance of quasi-minimal Cayley networks, Lect. Notes Comput. Inform., 497, 424-431 (1992) |
| [14] | Biggs, N., Algebraic Graph Theory (1994), Cambridge University Press · Zbl 0797.05032 |
| [15] | Böttcher, M.; Knauer, U., Endomorphism spectra of graphs, Discrete Math., 109, 45-57 (1992) · Zbl 0792.05135 |
| [16] | Chartland, G.; Lesniak, L., Graphs and Digraphs (1996), Chapman & Hall: Chapman & Hall London · Zbl 0890.05001 |
| [17] | Chung, F.; Coman, E.; Reiman, M.; Simon, B., On the capacity and vertex forwarding index of communication networks, IEEE Trans. Inform. Theory, 33, 224-232 (1987) · Zbl 0626.94019 |
| [18] | Clifford, A. H.; Preston, G. B., The Algebraic Theory of Semigroups (1961), Amer. Math. Soc.: Amer. Math. Soc. Providence, R.I · Zbl 0111.03403 |
| [19] | The Data Mine, http://www.the-data-mine.com/; The Data Mine, http://www.the-data-mine.com/ |
| [20] | Day, K.; Tripathi, A., A comparative study of topological properties of hypercubes and star graphs, IEEE Trans. Parallel Distrib. Systems, 31-38 (1994) |
| [21] | R.P. Dazeley, B.H. Kang, Weighted MCRDR: Deriving information about relationships between classifications in MCRDR, in: Proc. Advances in Artificial Intelligence 2003, pp. 245-255; R.P. Dazeley, B.H. Kang, Weighted MCRDR: Deriving information about relationships between classifications in MCRDR, in: Proc. Advances in Artificial Intelligence 2003, pp. 245-255 |
| [22] | R.P. Dazeley, B.H. Kang, An online classification and prediction hybrid system for knowledge discovery in databases, in: Proc. 2nd Internat. Conf. Artificial Intelligence in Science and Technology, 2004, pp. 114-119; R.P. Dazeley, B.H. Kang, An online classification and prediction hybrid system for knowledge discovery in databases, in: Proc. 2nd Internat. Conf. Artificial Intelligence in Science and Technology, 2004, pp. 114-119 |
| [23] | R. Dazeley, A.V. Kelarev, J.L. Yearwood, M.A. Mammadov, Optimization of multiple classifiers in data mining based on string rewriting systems, Asian-European Journal of Mathematics (in press); R. Dazeley, A.V. Kelarev, J.L. Yearwood, M.A. Mammadov, Optimization of multiple classifiers in data mining based on string rewriting systems, Asian-European Journal of Mathematics (in press) · Zbl 1178.68405 |
| [24] | Dénes, J., Connections between transformation semigroups and graphs, (Theory of Graphs (1967), Gordon and Breach: Gordon and Breach New York, Paris), 93-101 · Zbl 0188.05701 |
| [25] | Dutt, S.; Hayes, J. P., Designing fault-tolerant systems using automorphisms, J. Parallel Distrib. Computing, 12, 249-268 (1991) · Zbl 0741.68018 |
| [26] | Eilenberg, S., Automata, Languages, and Machines, vol. A, B (1974), Academic Press: Academic Press New York · Zbl 0317.94045 |
| [27] | Fan, S.; Zeng, Y., On Cayley graphs of bands, Semigroup Forum, 74, 99-105 (2007) · Zbl 1125.05051 |
| [28] | Fertin, G.; Raspaud, A., Families of graphs having broadcasting and gossiping properties, Lect. Notes Comp. Sci., 1517, 63-77 (1998) · Zbl 0918.68083 |
| [29] | Fraigniaud, P.; Lazard, E., Methods and problems of communication in usual networks, Discrete Appl. Math., 53, 79-133 (1994) · Zbl 0818.94029 |
| [30] | J.A. Gallian, Graph labeling, Electronic J. Combinatorics, Dynamic Survey DS6, January 20, 2005, pp.148; J.A. Gallian, Graph labeling, Electronic J. Combinatorics, Dynamic Survey DS6, January 20, 2005, pp.148 |
| [31] | Grillet, P. A., Semigroups (1995), Marcel Dekker: Marcel Dekker New York · Zbl 0830.20079 |
| [32] | Han, J.; Kamber, M., Data Mining: Concepts and Techniques (2000), Elsevier, Morgan Kaufmann |
| [33] | Hedetniemi, S. M.; Hedetniemi, S. T., A survey of gossiping and broadcasting in communication networks, Networks, 18, 319-349 (1988) · Zbl 0649.90047 |
| [34] | Heydemann, M.-C., Cayley graphs and interconnection networks, (Graph Symmetry: Algebraic Methods and Applications (1997), Kluwer: Kluwer Dordrecht), 167-224 · Zbl 0885.05075 |
| [35] | J. Holub, C.S. Iliopoulos, B. Melichar, L. Mouchard, Distributed string matching using finite automata, in: Proc. Australasian workshop on Combinatorial Algorithms, 1999, pp. 114-127; J. Holub, C.S. Iliopoulos, B. Melichar, L. Mouchard, Distributed string matching using finite automata, in: Proc. Australasian workshop on Combinatorial Algorithms, 1999, pp. 114-127 · Zbl 0978.68085 |
| [36] | Howie, J. M., Automata and Languages (1991), Clarendon Press: Clarendon Press Oxford · Zbl 0778.68065 |
| [37] | Howie, J. M., Fundamentals of Semigroup Theory (1995), Clarendon Press: Clarendon Press Oxford · Zbl 0835.20077 |
| [38] | Ito, M., Algebraic Theory of Automata and Languages (2001), World Scientific: World Scientific New York |
| [39] | Jiang, Z., An answer to a question of Kelarev and Praeger on Cayley graphs of semigroups, Semigroup Forum, 69, 457-461 (2004) · Zbl 1065.20069 |
| [40] | B.H. Kang, Pacific Knowledge Acquisition Workshop, Auckland, New Zealand, 2004; B.H. Kang, Pacific Knowledge Acquisition Workshop, Auckland, New Zealand, 2004 |
| [41] | B.H. Kang, A.V. Kelarev, A.H.J. Sale, R.N. Williams, A model for classifying DNA code embracing neural networks and FSA, in: Proc. Pacific Knowledge Acquisition Workshop, 2006, pp. 201-212; B.H. Kang, A.V. Kelarev, A.H.J. Sale, R.N. Williams, A model for classifying DNA code embracing neural networks and FSA, in: Proc. Pacific Knowledge Acquisition Workshop, 2006, pp. 201-212 |
| [42] | Kang, B. H.; Kelarev, A. V.; Sale, A. H.J.; Williams, R. N., A new model for classifying DNA code inspired by neural networks and FSA, Lect. Notes Computer Science, 4303, 187-198 (2006) |
| [43] | R. Kaschek, Endomorphism monoids of certain lexicographic products as wreath products of monoids, in: Proc. 1st Estonian Conference on Graphs and Applications, 1991, pp. 90-101; R. Kaschek, Endomorphism monoids of certain lexicographic products as wreath products of monoids, in: Proc. 1st Estonian Conference on Graphs and Applications, 1991, pp. 90-101 · Zbl 0854.05096 |
| [44] | A.V. Kelarev, Combinatorial properties of sequences in groups and semigroups, in: Proc. Intern. Conf. Combinatorics, Complexity and Logic, 1996, pp. 289-298; A.V. Kelarev, Combinatorial properties of sequences in groups and semigroups, in: Proc. Intern. Conf. Combinatorics, Complexity and Logic, 1996, pp. 289-298 · Zbl 0914.68155 |
| [45] | Kelarev, A. V., Ring Constructions and Applications (2002), World Scientific · Zbl 0999.16036 |
| [46] | Kelarev, A. V., On undirected Cayley graphs, Australasian J. Combinatorics, 25, 73-78 (2002) · Zbl 0993.05085 |
| [47] | Kelarev, A. V., Graph Algebras and Automata (2003), Marcel Dekker · Zbl 1070.68097 |
| [48] | Kelarev, A. V., Labelled Cayley graphs and minimal automata, Australasian J. Combinatorics, 30, 95-101 (2004) · Zbl 1152.68482 |
| [49] | A.V. Kelarev, B.H. Kang, A.H.J. Sale, R.N. Williams, Labeled directed graphs and FSA as classifiers of strings, in: Proc. 17th Australasian Workshop on Combinatorial Algorithms, 2006, pp. 93-109; A.V. Kelarev, B.H. Kang, A.H.J. Sale, R.N. Williams, Labeled directed graphs and FSA as classifiers of strings, in: Proc. 17th Australasian Workshop on Combinatorial Algorithms, 2006, pp. 93-109 |
| [50] | Kelarev, Andrei; Kang, Byeong; Steane, Dorothy, Clustering algorithms for ITS sequence data with alignment metrics, Lect. Notes Artificial Intelligence, 4304, 1027-1031 (2006) |
| [51] | A.V. Kelarev, M. Miller, O.V. Sokratova, Directed graphs and closure properties for languages, in: Proc. 12th Australasian Workshop on Combinatorial Algorithms, 2001, pp. 118-125; A.V. Kelarev, M. Miller, O.V. Sokratova, Directed graphs and closure properties for languages, in: Proc. 12th Australasian Workshop on Combinatorial Algorithms, 2001, pp. 118-125 |
| [52] | Kelarev, A. V.; Miller, M.; Sokratova, O. V., Languages recognized by two-sided automata of graphs, Proc. Estonian Academy of Science, 54, 1, 46-54 (2005) · Zbl 1081.68046 |
| [53] | Kelarev, A. V.; Passman, D. S., A description of incidence rings of group automata, Contemp. Math., 456, 27-33 (2008) · Zbl 1154.16015 |
| [54] | Kelarev, A. V.; Praeger, C. E., On transitive Cayley graphs of groups and semigroups, European J. Combin., 24, 1, 59-72 (2003) · Zbl 1011.05027 |
| [55] | Kelarev, A. V.; Quinn, S. J., A combinatorial property and power graphs of groups, Contrib. General Algebra, 12, 229-235 (2000) · Zbl 0966.05040 |
| [56] | Kelarev, A. V.; Quinn, S. J., Directed graphs and combinatorial properties of semigroups, J. Algebra, 251, 1, 16-26 (2002) · Zbl 1005.20043 |
| [57] | Kelarev, A. V.; Quinn, S. J., A combinatorial property and Cayley graphs of semigroups, Semigroup Forum, 66, 89-96 (2003) · Zbl 1016.20047 |
| [58] | A.V. Kelarev, J. Ryan, J.L. Yearwood, A combinatorial algorithm for the optimization of multiple classifiers in data mining based on graphs, J. Combin. Math. Comb. Computing (in press); A.V. Kelarev, J. Ryan, J.L. Yearwood, A combinatorial algorithm for the optimization of multiple classifiers in data mining based on graphs, J. Combin. Math. Comb. Computing (in press) · Zbl 1197.05146 |
| [59] | Kelarev, A. V.; Sokratova, O. V., Languages recognized by a class of finite automata, Acta Cybernetica, 15, 45-52 (2001) · Zbl 0981.68074 |
| [60] | Kelarev, A. V.; Sokratova, O. V., Directed graphs and syntactic algebras of tree languages, J. Automata, Languages & Combinatorics, 6, 3, 305-311 (2001) · Zbl 0993.68055 |
| [61] | Kelarev, A. V.; Sokratova, O. V., Two algorithms for languages recognized by graph algebras, Internat. J. Computer Math., 79, 12, 1317-1327 (2002) · Zbl 1008.68071 |
| [62] | Kelarev, A. V.; Sokratova, O. V., On congruences of automata defined by directed graphs, Theoretical Computer Science, 301, 31-43 (2003) · Zbl 1022.68068 |
| [63] | A.V. Kelarev, P.G. Trotter, A combinatorial property of languages and monoids, in: Proc. 3rd Internat. Conf. Words, Languages and Combinatorics, 2003, pp. 228-239; A.V. Kelarev, P.G. Trotter, A combinatorial property of languages and monoids, in: Proc. 3rd Internat. Conf. Words, Languages and Combinatorics, 2003, pp. 228-239 |
| [64] | A.V. Kelarev, J.L. Yearwood, M.A. Mammadov, A formula for multiple classifiers in data mining based on Brandt semigroups, Semigroup Forum (in press); A.V. Kelarev, J.L. Yearwood, M.A. Mammadov, A formula for multiple classifiers in data mining based on Brandt semigroups, Semigroup Forum (in press) · Zbl 1168.94007 |
| [65] | A.V. Kelarev, J.L. Yearwood, P. Vamplew, A polynomial ring construction for classification of data, Bulletin Austral. Math. Soc. (in press); A.V. Kelarev, J.L. Yearwood, P. Vamplew, A polynomial ring construction for classification of data, Bulletin Austral. Math. Soc. (in press) · Zbl 1181.16024 |
| [66] | A.V. Kelarev, J.L. Yearwood, P. Watters, Rees matrix construction for clustering of data (submitted for publication); A.V. Kelarev, J.L. Yearwood, P. Watters, Rees matrix construction for clustering of data (submitted for publication) · Zbl 1233.16021 |
| [67] | L.H. Khachatrian, H.S. Haroutunian, Construction of new classes of minimal broadcast networks, in: Proc. 3rd Intern. Colloquium on Coding Theory 1990, pp. 69-77; L.H. Khachatrian, H.S. Haroutunian, Construction of new classes of minimal broadcast networks, in: Proc. 3rd Intern. Colloquium on Coding Theory 1990, pp. 69-77 |
| [68] | Kilp, M.; Knauer, U., Graph operations and categorical constructions, Acta Comment. Univ. Tartu. Math., 5, 43-57 (2001) · Zbl 1003.05100 |
| [69] | Kilp, M.; Knauer, U.; Mikhalev, A. V., Monoids, Acts and Categories with Applications to Wreath Products and Graphs (2000), Walter de Gruyter & Co: Walter de Gruyter & Co Berlin · Zbl 0945.20036 |
| [70] | Knauer, U., Endomorphism types of bipartite graphs, Words, languages and combinatorics, II (1994), World Sci.: World Sci. River Edge, NJ, pp. 234-251 · Zbl 0877.05051 |
| [71] | Knauer, U.; Mikhalev, A. V., Endomorphism monoids of generators in the category of \(S\)-acts, (Semigroups with Applications (1992), World Sci.: World Sci. River Edge, NJ), 132-151 |
| [72] | Kuske, D.; Lohrey, M., Decidable theories of Cayley-graphs, Lect. Notes Comp. Sci., 2607, 463-474 (2003) · Zbl 1036.03009 |
| [73] | Kuske, D.; Lohrey, M., Logical aspects of Cayley graphs: The group case, Ann. Pure Appl. Logic, 131, 263-286 (2005) · Zbl 1063.03005 |
| [74] | Kuske, D.; Lohrey, M., Logical aspects of Cayley-graphs: The monoid case, Internat. J. Algebra Comput., 16, 307-340 (2006) · Zbl 1151.03003 |
| [75] | Lakshmivarahan, S.; Jwo, J.-S.; Dhall, S. K., Symmetry in interconnection networks based on Cayley graphs of permutation groups: A survey, Parallel Computing, 19, 4, 361-407 (1993) · Zbl 0777.05064 |
| [76] | Lallement, G., Semigroups and Combinatorial Applications (1979), Wiley: Wiley New York · Zbl 0421.20025 |
| [77] | Li, C. H.; Praeger, C. E., On the isomorphism problem for finite Cayley graphs of bounded valency, European J. Combin., 20, 4, 279-292 (1999) · Zbl 0924.05035 |
| [78] | Li, C. H.; Praeger, C. E., Self-complementary vertex-transitive graphs need not be Cayley graphs, Bull. London Math. Soc., 33, 6, 653-661 (2001) · Zbl 1026.05058 |
| [79] | Lohrey, M., Decidability and complexity in automatic monoids, Internat. J. Found. Comput. Sci., 16, 4, 707-722 (2005) · Zbl 1146.20314 |
| [80] | Luger, G. F., Artificial Intelligence. Structures and Strategies for Complex Problem Solving (2005), Addison-Wesley: Addison-Wesley New York |
| [81] | Margolis, S. W.; Meakin, J. C., \(E\)-unitary inverse monoids and the Cayley graph of a group representation, J. Pure Appl. Algebra, 58, 45-76 (1989) · Zbl 0676.20037 |
| [82] | Miller, M.; Patel, D.; Ryan, J.; Sugeng, K. A.; Slamin; Tuga, M., Exclusive sum labeling of graphs, J. Combin. Math. Combin. Comput., 55, 137-148 (2005) · Zbl 1103.05076 |
| [83] | Muzychuk, M.; Tinhofer, G.; Dutt, S.; Hayes, J. P., Designing fault-tolerant systems using automorphisms, J. Parallel Distrib. Computing, 12, 249-268 (1991) · Zbl 0741.68018 |
| [84] | N. Na Chiangmai, On graphs defined from algebraic systems, Masters Thesis, Chulalongkorn University, Bangkok, 1975; N. Na Chiangmai, On graphs defined from algebraic systems, Masters Thesis, Chulalongkorn University, Bangkok, 1975 |
| [85] | Negnevitsky, M., Artificial Intelligence: A Guide to Intelligent Systems (2001), Addison Wesley: Addison Wesley Harlow |
| [86] | Oliveira, A.; Silva, P., Inverse automata and monoids and the undecidability of the Cayley subgraph problem for groups, Glasgow Math. J., 42, 3, 421-437 (2000) · Zbl 0986.20063 |
| [87] | Panma, S.; Knauer, U.; Arworn, S., On transitive Cayley graphs of right (left) groups and of Clifford semigroups, Thai J. Math., 2, 1, 183-195 (2004) · Zbl 1063.05068 |
| [88] | S. Panma, U. Knauer, S. Arworn, On transitive Cayley graphs of strong semilattices of right (left) groups (in press); S. Panma, U. Knauer, S. Arworn, On transitive Cayley graphs of strong semilattices of right (left) groups (in press) · Zbl 1198.05095 |
| [89] | Panma, S.; Na Chiangmai, N.; Knauer, U.; Arworn, S., Characterizations of Clifford semigroup digraphs, Discrete Math., 306, 12, 1247-1252 (2006) · Zbl 1096.05045 |
| [90] | Formal Properties of Finite Automata and Applications, (Pin, J. E., Lect. Notes Computer Science, vol. 386 (1989), Springer: Springer New York) · Zbl 0702.68024 |
| [91] | Praeger, C. E., Finite transitive permutation groups and finite vertex-transitive graphs, (Graph Symmetry: Algebraic Methods and Applications (1997), Kluwer: Kluwer Dordrecht), 277-318 · Zbl 0885.05072 |
| [92] | Praeger, C. E., Finite normal edge-transitive Cayley graphs, Bull. Austral. Math. Soc., 60, 2, 207-220 (1999) · Zbl 0939.05047 |
| [93] | Robinson, D. J.S., A Course in the Theory of Groups (1982), Springer: Springer New York, Berlin · Zbl 0496.20038 |
| [94] | J. Rosenthal, P.O. Vontobel, Construction of LDPC codes using Ramanujan graphs and ideas from Margulis, in: Proc. 38th Allerton Conf. on Communication, 2000; J. Rosenthal, P.O. Vontobel, Construction of LDPC codes using Ramanujan graphs and ideas from Margulis, in: Proc. 38th Allerton Conf. on Communication, 2000 |
| [95] | J. Rosenthal, P O Vontobel, Constructions of regular and irregular LDPC codes using Ramanujangraphs and ideas from Margulis, in: Proc. Information Theory, 06/24/2001-06/29/2001, Washington, DC, USA; J. Rosenthal, P O Vontobel, Constructions of regular and irregular LDPC codes using Ramanujangraphs and ideas from Margulis, in: Proc. Information Theory, 06/24/2001-06/29/2001, Washington, DC, USA |
| [96] | (Rozenberg, G.; Salomaa, A., Handbook of Formal Languages, vol. 1, 2, 3 (1997), Springer: Springer New York) · Zbl 0866.68057 |
| [97] | Schibell, S. T.; Stafford, R. M., Processor interconnection networks from Cayley graphs, Discrete Appl. Math., 40, 333-357 (1992) · Zbl 0782.68014 |
| [98] | Shevrin, L. N.; Ovsyannikov, A. J., Semigroups and their Subsemigroup Lattices (1996), Kluwer: Kluwer Dordrecht · Zbl 0858.20054 |
| [99] | Steinberg, B., Finite state automata: A geometric approach, Trans. Amer. Math. Soc., 353, 9, 3409-3464 (2001) · Zbl 0980.20067 |
| [100] | Tinhofer, G., Cayley graphs in computer science, Proc. Algebraic Combin. Comput. Algebra, 1-34 (2000) |
| [101] | Tuga, M.; Miller, M.; Ryan, J.; Ryjáček, Z., Exclusive sum labelings of trees, J. Combin. Math. Combin. Comput., 55, 109-121 (2005) · Zbl 1110.05088 |
| [102] | Vadapalli, P.; Srimani, P. K., A new family of Cayley graph interconnection networks of constant degree four, IEEE Trans. Parallel Distributed Syst., 7, 1, 26-32 (1996) |
| [103] | Witten, I. H.; Frank, E., Data Mining: Practical Machine Learning Tools and Techniques (2005), Elsevier, Morgan Kaufmann · Zbl 1076.68555 |
| [104] | Xiao, W.; Parhami, B., Some mathematical properties of Cayley digraphs with applications to interconnection network design, Internat. J. Computer Math., 82, 5, 521-528 (2005) · Zbl 1064.05082 |
| [105] | J.L. Yearwood, A.M. Bagirov, A.V. Kelarev, Optimization methods and the k-committees algorithm for clustering of sequence data (submitted for publication); J.L. Yearwood, A.M. Bagirov, A.V. Kelarev, Optimization methods and the k-committees algorithm for clustering of sequence data (submitted for publication) · Zbl 1184.49027 |
| [106] | J.L. Yearwood, B.H. Kang, A.V. Kelarev, Experimental investigation of classification algorithms for ITS dataset, Lect. Notes Computer Science (in press); J.L. Yearwood, B.H. Kang, A.V. Kelarev, Experimental investigation of classification algorithms for ITS dataset, Lect. Notes Computer Science (in press) |
| [107] | Yearwood, J. L.; Mammadov, M., Classification Technologies: Optimization Approaches to Short Text Categorization (2007), Idea Group Inc. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
