On Combining Fuzzy C-Regression Models and Fuzzy C-Means with Automated Weighting of the Explanatory Variables
Ricardo A. M. da Silva, Francisco de A.T. de Carvalho · 2018
This paper presents a fuzzy clusterwise regression method aiming to provide linear regression models that are based on homogeneous clusters of observations with respect to the explanatory variables and that are well fitted with respect to the response variable. To achieve this aim, this method combines Fuzzy C-Regression Models and Fuzzy C-Means with automatic computation of relevance weights to the explanatory variables. Because it learns simultaneously a prototype and a linear regression model for each cluster it is able to provide an appropriated regression model for unknown observations based on their description by the explanatory variables. We also discussed both, a heuristic procedure to automatically tune one of the hyperparameters of the proposed method in order to obtain more useful (explanation) models in a prediction task, and a way of making a fuzzy combination of each intra-cluster fitted model as a more natural and appropriate response to the problem of choosing the best regression model for a prediction task. Experiments with synthetic and real datasets corroborate the usefulness of the proposed method.