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Basic Level Concepts as a Means to Better Interpretability of Boolean Matrix Factors and Their Application to Clustering

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Modeling Decisions for Artificial Intelligence (MDAI 2018)

Abstract

We present an initial study linking in cognitive psychology well known phenomenon of basic level concepts and a general Boolean matrix factorization method. The result of this fusion is a new algorithm producing factors that explain a large portion of the input data and that are easy to interpret. Moreover, the link with the cognitive psychology allowed us to design a new clustering algorithm that groups objects into clusters that are close to human perception. In addition we present experiments that provide insight to the relationship between basic level concepts and Boolean factors.

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Notes

  1. 1.

    In [6] this algorithm is named Algorithm 1.

References

  1. Andrews, S.: Making use of empty intersections to improve the performance of CbO-type algorithms. In: Bertet, K., Borchmann, D., Cellier, P., Ferré, S. (eds.) ICFCA 2017. LNCS (LNAI), vol. 10308, pp. 56–71. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59271-8_4

    Chapter  Google Scholar 

  2. Belohlavek, R., Outrata, J., Trnecka, M.: How to assess quality of BMF algorithms? In: Yager, R.R., Sgurev, V.S., Hadjiski, M., Jotsov, V.S. (eds.) Proceeding of International Conference on Intelligent Systems, IS 2016. pp. 227–233 (2016)

    Google Scholar 

  3. Belohlavek, R., Trnecka, M.: Basic Level of Concepts in Formal Concept Analysis. In: Domenach, F., Ignatov, D.I., Poelmans, J. (eds.) ICFCA 2012. LNCS (LNAI), vol. 7278, pp. 28–44. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29892-9_9

    Chapter  MATH  Google Scholar 

  4. Belohlavek, R., Trnecka, M.: Basic level in formal concept analysis: Interesting concepts and psychological ramifications. In: Rossi, F. (ed.) Proceedings of the 23rd International Joint Conference on Artificial Intelligence, IJCAI 2013. pp. 1233–1239 (2013)

    Google Scholar 

  5. Belohlavek, R., Trnecka, M.: From-below approximations in boolean matrix factorization: Geometry and new algorithm. J. Comput. Syst. Sci. 81(8), 1678–1697 (2015)

    Article  MathSciNet  Google Scholar 

  6. Belohlavek, R., Vychodil, V.: Discovery of optimal factors in binary data via a novel method of matrix decomposition. J. Comput. Syst. Sci. 76(1), 3–20 (2010)

    Article  MathSciNet  Google Scholar 

  7. Dheeru, D., Karra Taniskidou, E.: UCI machine learning repository (2017), http://archive.ics.uci.edu/ml

  8. Farhadi, A., Endres, I., Hoiem, D., Forsyth, D.A.: Describing objects by their attributes. In: Proceedings of Conference on Computer Vision and Pattern Recognition (CVPR 2009). pp. 1778–1785 (2009)

    Google Scholar 

  9. Ganter, B., Wille, R.: Formal concept analysis - mathematical foundations. Springer (1999)

    Google Scholar 

  10. Gottwald, S.: A Treatise on Many-Valued Logics, vol. 3. research studies press Baldock (2001)

    Google Scholar 

  11. Krajca, P., Outrata, J., Vychodil, V.: Computing formal concepts by attribute sorting. Fundam. Inform. 115(4), 395–417 (2012)

    MathSciNet  MATH  Google Scholar 

  12. Krajča, P.: Rank-aware clustering of relational data: Organizing search results. In: USB Proceedings The 13th International Conference on Modeling Decisions for Artificial Intelligence, pp. 61–72. (2016)

    Google Scholar 

  13. Lucchese, C., Orlando, S., Perego, R.: Mining top-\(k\) patterns from binary datasets in presence of noise. Proceedings of the International Conference on Data Mining, SDM 2010, 165–176 (2010)

    Google Scholar 

  14. Lucchese, C., Orlando, S., Perego, R.: A unifying framework for mining approximate top-\(k\) binary patterns. IEEE Trans. Knowl. Data Eng. 26(12), 2900–2913 (2014)

    Article  Google Scholar 

  15. Miettinen, P.: Matrix decomposition methods for data mining: Computational complexity and algorithms. Ph.D. thesis (2009)

    Google Scholar 

  16. Outrata, J., Vychodil, V.: Fast algorithm for computing fixpoints of galois connections induced by object-attribute relational data. Inf. Sci. 185(1), 114–127 (2012)

    Article  MathSciNet  Google Scholar 

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Correspondence to Petr Krajča .

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Krajča, P., Trnecka, M. (2018). Basic Level Concepts as a Means to Better Interpretability of Boolean Matrix Factors and Their Application to Clustering. In: Torra, V., Narukawa, Y., Aguiló, I., González-Hidalgo, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2018. Lecture Notes in Computer Science(), vol 11144. Springer, Cham. https://doi.org/10.1007/978-3-030-00202-2_14

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  • DOI: https://doi.org/10.1007/978-3-030-00202-2_14

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  • Print ISBN: 978-3-030-00201-5

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