Abstract
We introduce the parameter of relevance of an attribute of a binary table to another attribute of the same table, computed with respect to an implicational basis of a closure system associated with the table. This enables a ranking of all attributes, by relevance parameter to the same fixed attribute, and, as a consequence, reveals the implications of the basis most relevant to this attribute. As an application of this new metric, we test the algorithm for D-basis extraction presented in Adaricheva and Nation [1] on biomedical data related to the survival groups of patients with particular types of cancer. Each test case requires a specialized approach in converting the real-valued data into binary data and careful analysis of the transformed data in a multi-disciplinary environment of cross-field collaboration.
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K. Adaricheva and J.B. Natio—Partial support provided by grant N 13/42 (2013–2015) of Nazarbayev University.
J.B. Nation, V. Adarichev, N. Seidalin and K. Alibek—Partial support provided by grant N 0112PK02175 (2012–2014) of Ministry of Healthcare and Social Development of RK.
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References
Adaricheva, K., Nation, J.B.: Discovery of the \(D\)-basis in binary tables based on hypergraph dualization, Theoretical Computer Science (submitted to)
Adaricheva, K., Nation, J.B., Rand, R.: Ordered direct implicational basis of a finite closure system. Disc. Appl. Math. 161, 707–723 (2013)
Adarichev, V.A., Vermes, C., Hanyecz, A., Mikecz, K., Bremer, E.G., Glant, T.T.: Gene expression profiling in murine autoimmune arthritis during the initiation and progression of joint inflammation. Arthritis Res. Ther. 7, 196–207 (2005)
Adarichev, V.A., Vermes, C., Hanyecz, A., Ludanyi, K., Tunyogi-Csapó, M., Mikecz, K., Glant, T.T.: Antigen-induced differential gene expression in lymphocytes and gene expression profile in synovium prior to the onset of arthritis. Autoimmunity 39, 663–673 (2006)
Agrawal, R., Mannila, H., Srikant, R., Toivonen, H., Verkamo, A.I.: Fast discovery of association rules. In: Fayyad, U.M., Piatetsky-Shapiro, G., Smyth, P., Uthurusamy, R. (eds.) Advances in Knowledge Discovery and Data Mining, pp. 307–328. AAAI Press, Menlo Park (1996)
Babin, M.A., Kuznetsov, S.O.: Computing premises of a minimal cover of functional dependencies is intractable. Disc. Appl. Math. 161, 742–749 (2013)
Balcázar, J.L.: Redundancy, deduction schemes, and minimum-size bases for association rules. Log. Meth. Comput. Sci. 6(2:3), 1–33 (2010)
Bertet, K., Monjardet, B.: The multiple facets of the canonical direct unit implicational basis. Theor. Comput. Sci. 411, 2155–2166 (2010)
Boros, E., Elbassioni, K., Gurvich, V., Khachiyan, L.: Generating dual-bounded hypergraphs. Optim. Methods Softw. 17, 749–781 (2002)
Distel, F., Sertkaya, B.: On the complexity of enumerating the pseudo-intents. Disc. Appl. Math. 159, 450–466 (2011)
Fredman, M., Khachiyan, L.: On the complexity of dualization of monotone disjunctive normal forms. J. Algorithms 21, 618–628 (1996)
Guigues, J.L., Duquenne, V.: Familles minimales d’implications informatives résultant d’une tables de données binares. Math. Sci. Hum. 95, 5–18 (1986)
Kaplan, E.L., Meier, P.: Nonparametric estimation from incomplete observations. J. Amer. Statist. Assn. 53(282), 457–481 (1958)
Kryszkiewicz, M.: Concise representations of association rules. In: Hand, D.J., Adams, N.M., Bolton, R.J. (eds.) Pattern Detection and Discovery. LNCS (LNAI), vol. 2447, p. 92. Springer, Heidelberg (2002)
Murakami, K., Uno, T.: Efficient algorithms for dualizing large scale hypergraphs. Disc. Appl. Math. 170, 83–94 (2014)
Ryssel, U., Distel, F., Borchmann, D.: Fast algorithms for implication bases and attribute exploration using proper premises. Ann. Math. Art. Intell. 70, 25–53 (2014)
Spearman, C.: The proof and measurement of association between two things. Amer. J. Psychol. 15, 72–101 (1904)
Network, T.C.G.A.R.: The cancer genome atlas pan-cancer analysis project. Nat. Genet. 45, 1113–1120 (2013)
R Core Team: R: a language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria (2013). URL http://www.R-project.org/
Acknowledgements
The C++ code for D-basis extraction on the binary table input used for testing in this project was created by undergraduate students of Yeshiva College in New York: Joshua Blumenkopf and Toviah Moldvin. We received the permission of Takeaki Uno, from the National Institute of Informatics in Tokyo, to implement the call to his subroutine performing the hypergraph dualization, within the structure of our programming code. We were assisted by colleagues Ulrich Norbisrath and Mark Sterling, from the Computer Science Department of School of Science and Technology of NU, when we needed tuning and debugging of the code, also to Rustam Bekishev and Anel Nurtay for assistance in the project. The first author is grateful to the bio-informatics group of the University of Hawaii Cancer Center, for the welcoming atmosphere and fruitful collaboration during her visit in June 2014, supported by Nazarbayev University grant N 13/42. The second author expresses his gratitude for support of his visit to Nazarbayev University in May–June 2013 and May 2014, which were partly funded by NU grant N 13/42 and grant N 0112PK02175 of Medical Holding of Astana. Tom Wenska, Ashkan Zeinalzadeh and Jenna Maligro contributed to the research and discussion in Honolulu.
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Adaricheva, K. et al. (2015). Measuring the Implications of the D-Basis in Analysis of Data in Biomedical Studies. In: Baixeries, J., Sacarea, C., Ojeda-Aciego, M. (eds) Formal Concept Analysis. ICFCA 2015. Lecture Notes in Computer Science(), vol 9113. Springer, Cham. https://doi.org/10.1007/978-3-319-19545-2_3
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