Abstract
Models of interactions between multiple fetaures (genes) can be obtained from collinear data sets consisting of multivariate feature vectors. Such models can be designed by minimizing the collinearity criterion function with the basis echange algorithm.
The collinearity criterion functions are defined on learning data subsets representing selected categories (e.g. diseases). Based on the minimization of the collinearity functions, interaction models specific to each category can be defined.
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References
Hand, D., Smyth, P., Mannila, H.: Principles of Data Mining. MIT Press, Cambridge (2001)
Duda, O.R., Hart, P.E., Stork, D.G.: Pattern classification. J. Wiley, New York (2001)
Bishop, C.M.: Pattern Recognition and Machine Learning. Springer Verlag (2006)
Johnson, R.A., Wichern, D.W.: Applied Multivariate Statistical Analysis. Prentice- Hall Inc, Englewood Cliffs (2002)
Bobrowski, L.: Computing on vertices in data mining. In: Data Mining – Concepts and Applications, Ed. by Ciza Thomas, INTECH OPEN 2021. ISBN 978-1-83969-267-3
Bobrowski, L.: Small samples of multidimensional feature vectors. In: Hernes, M., Wojtkiewicz, K., Szczerbicki, E. (eds.) ICCCI 2020. CCIS, vol. 1287, pp. 87–98. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-63119-2_8
Bobrowski, L.: Data Exploration and Linear Separability, pp. 1–172, Lambert Academic Publishing (2019)
Bobrowski, L.: Complexes of low dimensional linear classifiers with L1 margins. In: Nguyen, N.T., Chittayasothorn, S., Niyato, D., Trawiński, B. (eds.) ACIIDS 2021. LNCS (LNAI), vol. 12672, pp. 29–40. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-73280-6_3
Bobrowski, L., Zabielski, P.: Flat patterns extraction with collinearity models. In: 9th EUROSIM Congress on Modelling and Simulation, EUROSIM 2016 , 12–16 September 2016, Oulu Finland, IEEE Conference Publishing Services (CPS)
Simonnard, M.: Linear Programming, Prentice – Hall. Englewood Cliffs, New York (1966)
Bobrowski, L., Bołdak, C.: Stepwise inversion of large matrices with the Gauss-Jordan vector transformation. J. Adv. Math. Comput. Sci. (2022)
Bobrowski, L., Łukaszuk, T.: Relaxed Linear Separability (RLS) Approach to Feature (Gene) Subset Selection, p. 103 – 118 in: Selected Works in Bioinformatics, Edited by: Xuhua Xia, INTECH OPEN 2011
Bobrowski, L., et al.: Separating gene clustering in the rare mucopolysaccharidosis disease. J. Appl. Genet. 63(2), 361–368 (2022). https://doi.org/10.1007/s13353-022-00691-2
Acknowledgments
The presented study was supported by the grant WZ/WI-IIT/3/2020 from the Bialystok University of Technology and funded from the resources for research by the Polish Ministry of Science and Higher Education.
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Bobrowski, L. (2022). Collinear Data Structures and Interaction Models. In: Nguyen, N.T., Manolopoulos, Y., Chbeir, R., Kozierkiewicz, A., Trawiński, B. (eds) Computational Collective Intelligence. ICCCI 2022. Lecture Notes in Computer Science(), vol 13501. Springer, Cham. https://doi.org/10.1007/978-3-031-16014-1_30
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