Design of Reinforced Fuzzy Model Driven to Feature Selection Through Univariable-Based Correlation and Multivariable-Based Determination Coefficient Analysis

Abstract

In this article, we introduce a design methodology of reinforced fuzzy models based both on univariate analysis and multivariable analysis to cope with high-dimensional problems. This approach is aimed at reducing the design process and curbing computing overhead inherently associated with the increasing volume of data in terms of both their number and the dimensionality of the feature space. The critical features of the proposed fuzzy models are highlighted as follows: First, the essential input variables of the model are selected by running the univariable and multivariable analyses. In univariate analysis, input variables with a strong linear relationship with the output variable are selected through correlation analysis completed for each input space and output space. On the contrary, in multivariable analysis, input variables are chosen by comparing the determination coefficients obtained from the subsets of input variables. Second, according to the analysis of the input variable, we construct two different kinds of fuzzy models. The first fuzzy model comprises the design of the univariable-based fuzzy model (UFM) and its aggregation. The UFMs are made by the individual input variables selected from the univariable analysis using a correlation coefficient. The subspaces formed by correlation analysis are applied for determining the centers of the membership function (MF). The results produced by individual fuzzy models are aggregated through some <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> -conorms. The second fuzzy model is with the fuzzy clustering for improving the form of fuzzy space in the premise part of a fuzzy rule. To curb the dramatic increase in size of fuzzy rule in high-dimensional problems, the clustering space is employed as the fuzzy space, and the partition matrix produced by fuzzy provided the required degrees of the MF. Experimental studies include a suite of synthetic and publicly available data. The superiority of the proposed design methodology was demonstrated by using 34 publicly available datasets and also compared with the conventional models associated with the fuzzy rule-based models as well as the state-of-the-art models reported in the literature.