Measuring the Implications of the D-Basis in Analysis of Data in Biomedical Studies
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  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.
KeywordsBinary table Galois lattice Implicational basis D-basis Support Relevance Gene expression Survival Response to treatment Immune markers Blood biochemistry Infection
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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