Dual-manifold regularized regression models for feature selection based on hesitant fuzzy correlation - Mokhtia, Mahla; Eftekhari, Mahdi; Saberi-Movahed, Farid (Knowledge-based systems, 2021)
In this paper, three novel frameworks based on the widespread regression methods Ridge, LASSO and Elastic Net are established to perform the task of feature selection. The suggested frameworks, which benefit from the joint advantages of the dual-manifold learning and the hesitant fuzzy correlation (HFC), utilize the concept of the hesitant fuzzy correlation matrix (HFCM) of the features and samples. In order to compute the HFCM, a fuzzy clustering algorithm is applied to samples (or features), and a hesitant fuzzy set on each sample (or each feature) is obtained after projecting the cluster membership functions on different samples (or features). Then, two kinds of HFCMs are calculated for samples of each class and the whole of features, respectively. In specific, a feature manifold regularization term based on the HFCM among features is added to the objective function in order to preserve the similarity between the features and the feature weights. Furthermore, a sample manifold regularization term is also considered for the purpose of preserving the local correlation among the samples of each class. Eventually, a set of experiments are conducted on twenty-four datasets in order to validate the performance of each method. The results confirm that the proposed approaches are effective to select suitable features in terms of both the number of selected features and the classification accuracy. •Three novel frameworks based on Ridge, LASSO and Elastic Net are established.•The hesitant fuzzy correlation (HFC) is used in the data and feature manifold.•Ridge, LASSO and Elastic Net are regularized by the HFC-based manifold terms.