Multiple regression with fuzzy data

  • Authors:

  • Andrzej Bargiela;Witold Pedrycz;Tomoharu Nakashima

  • Affiliations:

  • School of Computer Science, The University of Nottingham, Nottingham NG8 1BB, UK;Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alta., Canada T6G 2G6;College of Engineering, Osaka Prefecture University, Gakuen-cho 1-1, Sakai, Osaka 599-8531, Japan

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2007

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Abstract

In this paper, we propose an iterative algorithm for multiple regression with fuzzy variables. While using the standard least-squares criterion as a performance index, we pose the regression problem as a gradient-descent optimisation. The separation of the evaluation of the gradient and the update of the regression variables makes it possible to avoid undue complication of analytical formulae for multiple regression with fuzzy data. The origins of fuzzy input data are traced back to the fundamental concept of information granulation and an example FCM-based granulation method is proposed and illustrated by some numerical examples. The proposed multiple regression algorithm is applied to one-, three- and nine-dimensional synthetic data sets as well as the 13-dimensional Boston Housing dataset from the machine learning repository. The algorithm's performance is illustrated by the corresponding plots of convergence of regression parameters and the values of the prediction error of the resulting regression model. General comments on the numerical complexity of the proposed algorithm are also provided.