The Logistic Regression from the Viewpoint of the Factor Space Theory
Keywords:
logistic regression, factor space theory, fuzzy sets, logistic membership functionAbstract
Logistic regression plays an important role in machine learning. People excitingly use it in conceptual matching yet with some details to be understood further. This paper aims to present a reasonable statement on logistic regression based on fuzzy sets and the factor space theory. An example about breast cancer diagnosis is displayed to show how the factor space theory can be incorporated into the understanding and use of logistic regression.
References
Bao Y.K (2011); Data Analysis, Tsinghua University Press, 2011.
Bruzzi B.P, Sylvan B.G, David P.B, Louise A.B, Catherine S. (1985); Estimating the Population Attributable Risk for Multiple Risk Factors Using Case-Control Data, American Journal of Epidemiology, 122(5), 904-914, 1985. https://doi.org/10.1093/oxfordjournals.aje.a114174
Dayton C.M. (1992); Logistic Regression Analysis, University of Maryland, 1992.
Guo S.C, Chen G. (2001); Method of Soft Computing in Information Science, Northeastern University Press, 2001.
Li H.X, Wang P.Z. (1994); A Mathematical Theory on Knowledge Representation, Tianjin Scientific and Technical Press, 1994.
Liu Z.L, Liu Y.C. (1992); Theory of Factorial Neural Networks, Beijing Normal University Press, 1992.
Liu H.T, Wang P.Z; Background distribution and fuzzy background relationship (to be published).
Mood C. (2010); Logistic Regression: Why We Cannot Do What We Think We Can Do, and What We Can Do About It, European Sociological Review, 26(1), 67-82, 2010. https://doi.org/10.1093/esr/jcp006
Peduzzi P., Concato J., Kemper K. (1996); A simulation study of the number of events per variable in logistic regression analysis, Journal of clinical epidemiology, 49(12), 1373-1379, 1996. https://doi.org/10.1016/S0895-4356(96)00236-3
Prette Z. A. P. D, Prette A.D, Oliveira L.A.D, Gresham F.M, Vance M.J. (2012); Role of social performance in predicting learning problems: Prediction of risk using logistic regression analysis, School Psychology International, 33(6), 615-630, 2012. https://doi.org/10.1177/0020715211430373
Russell S.J, Norvig P. (2011); Artificial Intelligence A modern Approach (Third Edition), Tsinghua University Press, 2011.
Steyerberga E.W, Jrb F. E. H, Borsbooma G. J. J. M. (2001); Internal validation of predictive models: Efficiency of some procedures for logistic regression analysis, Journal of Clinical Epidemiology, 54, 774-781, 2001. https://doi.org/10.1016/S0895-4356(01)00341-9
Wang P.Z. (2013); Factor space and factor data bases, Journal of Liaoning Engineering and Technology University, 32(10), 1-8, 2013.
Wang P.Z, Guo S.C, Bao Y.K, Liu H.T. (2014); Causality analysis in factor spaces, Journal of Liaoning Engineering and Technology University, 33(7), 1-6, 2014.
Wang P.Z. (2015); Factor space and data science, Journal of Liaoning Engineering and Technology University, 34(2), 273-280, 2015.
Wang P.Z. (1981); In: Hao BL et al (eds) Advance of statistical physics.Science, Beijing, 1981.
Wang P.Z. (1985); Fuzzy Sets and Falling Shadow of Random Sets, Beijing Normal University Press, 1985.
Wang P.Z, Sugeno M. (1982); The factors field and background structure for fuzzy subsets, Fuzzy Mathematics, (2), 45-54, 1982.
Wang P.Z, Zhang H.M, Ma X.W, Xu W. (1991); Fuzzy set-operations represented by falling shadow theory, in: Fuzzy Engineering toward Human Friendly Systems, Proceedings of the International Fuzzy Engineering Symposium '91, Yokohama, Japan, 1, 82-90, 1991.
Wang P.Z, Liu H.C, Zhang X.H. (1993); Win-win strategy for probability and fuzzy mathematics, The Journal of Fuzzy Mathematics, 1(1), 223-231, 1993.
Wang P.Z. (2013); Fuzzy Mathematics and Optimization,Beijing Normal University Press, 2013.
Wang P.Z, Liu Z.L, Shi Y, Guo S.C. (2014); Factor Space, the Theoretical Base of Data Science, Annals of Data Science, 1(2), 233-251, 2014. https://doi.org/10.1007/s40745-014-0017-5
Zadeh L.A. (1965); Fuzzy Subsets, Information and Control, 8, 338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X
Published
Issue
Section
License
ONLINE OPEN ACCES: Acces to full text of each article and each issue are allowed for free in respect of Attribution-NonCommercial 4.0 International (CC BY-NC 4.0.
You are free to:
-Share: copy and redistribute the material in any medium or format;
-Adapt: remix, transform, and build upon the material.
The licensor cannot revoke these freedoms as long as you follow the license terms.
DISCLAIMER: The author(s) of each article appearing in International Journal of Computers Communications & Control is/are solely responsible for the content thereof; the publication of an article shall not constitute or be deemed to constitute any representation by the Editors or Agora University Press that the data presented therein are original, correct or sufficient to support the conclusions reached or that the experiment design or methodology is adequate.
