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A research summary about triadic concept analysis

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Abstract

Triadic concept analysis (TCA) is an extension of formal concept analysis (FCA), which can be applied to machine learning, data mining, information retrieval, and so on. This paper summarizes the current situation and the development tendency of TCA. We introduce TCA in this paper from four aspects: basic notions of triadic concept analysis, triadic implications and triadic association rules, triadic factor analysis and triadic fuzzy concept analysis.

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References

  1. Ashfaq RAR, He YL, Ghen DG (2016) Toward an efficient fuzziness based instance selection methodology for intrusion detection system. Int J Machine Learn Cybernet (in press). doi:10.1007/s13042-016-0557-4

  2. Ashfaq RAR, Wang XZ, et al (2016) Fuzziness based semi-supervised learning approach for Intrusion Detection System. Info Sci (in press). doi:10.1016/j.ins.2016.04.019

  3. Biedermann K (1997) Tradic galois connections. In: Denecke K, Luders O (eds) General algebra and applications in discrete mathematics. Aachen, Shaker Verlag, pp 23–33

    Google Scholar 

  4. Biedermann K (1997) How triadic diagrams represent conceptual structures. In: ICCS 304–317

  5. Biedermann K (1999) An equational theory for trilattices. Algebra Universalis 42:253–268

    Article  MathSciNet  MATH  Google Scholar 

  6. Belohlavek R, Glodeanu C, Vychodil V (2013) Optimal factorization of three-way binary data. Order 30:437–454

    Article  MathSciNet  MATH  Google Scholar 

  7. Belohlavek R, Osicka P (2010) Triadic concept analysis of data with fuzzy attributes. 2010 IEEE, International Conference on Granular Computing. 661–665

  8. Belohlavek R, Osicka P, Vychodil V (2011) Factorzing three-way ordinal data using triadic formal concepts, Lecture Notes in Artificial Intelligence. Ninth International conference on Flexible Query Answering System, Ghent

    Google Scholar 

  9. Belohlavek R, Osicka P (2012) Triadic concept lattices of data with graded attributes. Int J General Syst 41(2):93–108

    Article  MathSciNet  MATH  Google Scholar 

  10. Belohlavek R, Osicka P (2012) Triadic fuzzy Galois connections as ordinary connections. WCCI 2012, FUZZ IEEE 10–15

  11. Belohlavek R, Vychodil V (2010) Optimal factorization of three-way binary data. In: Hu X, Lin TY, Raghavan V, Grzymala-Busse J, Liu Q, Broder, IEEE International Conference on Granual Computing, 61–66

  12. Belohlavek R, Vychodil V (2010) Factorzing three-way binary data with triadic formal concepts. KES, (2010) Part I. LNAI 6276:471–480

  13. Belohlavek R, Vychodil V (2010) Discovery of optimal factors in binary data via a novel method of matrix decomposition. J Comp Syst Sci 76:3–20

    Article  MathSciNet  MATH  Google Scholar 

  14. Cerf L, Besson J et al (2009) Closed pattern meet n-ary relations. ACM Trans Knowl Discovery Data 3:1–36

    Article  Google Scholar 

  15. Dau F, Wille R (2000) On the modal understanding of triadic context. Classification and Information Processing at the Turn of the Millennium Studies in Classification, Data Analysis, and Knowledge Organization 83–94

  16. Glodeanu C (2010) Triadic factor analysis. In: Kryszkiewicz M 127–138

  17. Glodeanu C (2011) Factorization methods of binary, triadic, real and fuzzy data. Informatica 2:81–86

    MathSciNet  Google Scholar 

  18. Glodeanu C (2011) Fuzzy-valued triadic implications. CLA, Amedeo Napoli

    Google Scholar 

  19. Glodeanu C (2011) Fuzzy-valued triadic concept analysis and its applications. Technical Report MATH-AL-07-2011, Technische Uniersitat Dresden

  20. Glodeanu C (2013) Tri-ordinal factor analysis. ICFCA, LNAI 7880:125–140

    MATH  Google Scholar 

  21. Ganter B, Obiedkov SA (2004) Implications in triadic formal contexts. In: ICCS 2004, LNAI 3127, 186–195

  22. Ganter B, Wille R (1999) Formal concept analysis-mathematical foundations. Springer-Verlay Heidelberg, New York

    Book  MATH  Google Scholar 

  23. Gnatyshak D, Ignatov D, Semenov A, Poelmans J (2012) Gaining insight in social networks with biclustering and triclustering. BIR, (2012) LNBIP 128. Springer-Verlag, Berlin Heidelberg BIR 128, 162–171

  24. He YL, Wang XZ, Huang JZX (2016) Fuzzy nonlinear regression analysis using a random weight network. Info Sci 364–365:222–240

    Article  Google Scholar 

  25. He YL, Liu JNK, Hu YX, Wang XZ, Huang JZX (2015) OWA operator based link prediction ensemble for social network. Expert Syst Appl 42(1):21–50

    Article  Google Scholar 

  26. Ignatov D, Kuznetsov S, Magizov R, Zhukov L (2011) From triconcepts to triclusters. RSFDGrC 6743:257–264

    Google Scholar 

  27. Jaschke R, Hotho A, Schmitz C el at (2006) TRIAS-an algorithm for mining iceberg tri-lattices. In: Proceeding of the sixth international conference on data mining (ICDM’06) 907–911

  28. Jelassi N, Yahia S, Nguifo E (2012) A scalable mining of frequent quadratic concepts in d-folksonomies. arXiv:1212.0087

  29. Kavtoue M, Kuznetsov S, Macko J, Meira W, Napoli A (2011) Minging biclusters of similar values with triadic concept analysis. CLA 2011 175–190

  30. Konecny J, Osicka P (2014) Triadic concept lattices in the framework of aggregation structures. Info Sci 279:512–527

    Article  MathSciNet  MATH  Google Scholar 

  31. Lehmann F, Wille R (1995) A triadic approach to formal concept analysis. ICCS 954:32–43

    Google Scholar 

  32. Missaoui R, Kwuida L (2011) Mining triadic association rules from ternary relations. ICFCA, LNAI 6628, 204–218

  33. Osicka P, Konecny J (2010) General approach to triadic concept analysis. In: Kryszkiewicz M (2010): 116–126

  34. Osicka P (2012) Algorithms for computation of concept trilattices of triadic fuzzy context. IPMU, (2012) Prat III. CCIS 299:221–230

  35. Osicka P (2012) Concept analysis of three-way ordinal matrices. Olomouc: Palacky University

  36. Trabelsi C, Jelassi N, Yahia S (2012) Scalable mining of frequent tri-concepts from folksonomies. PAKDD, (2012) Part II. LNAI 7302(2012):231–244

  37. Voutsadakis G (2002) Polyadic concept analysis. Order 19(3):295–304

    Article  MathSciNet  MATH  Google Scholar 

  38. Voutsadakis G (2006) n-closure systems and n-closure operators. Algebra Universalis 55:369–386

    Article  MathSciNet  MATH  Google Scholar 

  39. Wang XZ (2015) Learning from big data with uncertainty-editorial. J Intel Fuzzy Syst 28(5):2329–2330

    Article  MathSciNet  Google Scholar 

  40. Wang XZ, Ashfaq RAR, Fu AM (2015) Fuzziness based sample categorization for classifier performance improvement. J Intell Fuzzy Syst 29(3):1185–1196

    Article  MathSciNet  Google Scholar 

  41. Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival I (ed) Ordered sets. Reidel, Dordrecht-Boston, pp 445–470

    Chapter  Google Scholar 

  42. Wille R (1995) The basic theorem of triadic concept analysis. Order 12(2):149–158

    Article  MathSciNet  MATH  Google Scholar 

  43. Wille R (1996) Restructuring mathematical logic: an approach based on Peirce’s pragmatism[J]. lecture notes in pure and applied mathematics, 267–282

  44. Wu WZ, Leung Y, Mi JS (2009) Granular computing and knowledge reduction in formal contexts. IEEE Trans Knowl Data Eng 21(10):1461–1474

    Article  Google Scholar 

  45. Wu WZ (2008) Attribute reduction based on evidence theory in incomplete decision systems. Info Sci 178:1355–1371

    Article  MathSciNet  MATH  Google Scholar 

  46. Tang YQ, Fan M, Li JH (2016) An information fusion technology for triadic decision contexts. Int J Mach Learn Cybernet 7(1):13–24

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Acknowledgments

This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 11371014 and 11071281), the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2014JM8306) and the State Scholarship Fund of China.

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Correspondence to Ling Wei.

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Wei, L., Qian, T., Wan, Q. et al. A research summary about triadic concept analysis. Int. J. Mach. Learn. & Cyber. 9, 699–712 (2018). https://doi.org/10.1007/s13042-016-0599-7

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