Variable selection methods for multi-class classification using signomial function

We develop several variable selection methods using signomial function to select relevant variables for multi-class classification by taking all classes into consideration. We introduce a $$\ell _{1}$$ ℓ 1 -norm regularization function to measure the number of selected variables and two adaptive parameters to apply different importance weights for different variables according to their relative importance. The proposed methods select variables suitable for predicting the output and automatically determine the number of variables to be selected. Then, with the selected variables, they naturally obtain the resulting classifiers without an additional classification process. The classifiers obtained by the proposed methods yield competitive or better classification accuracy levels than those by the existing methods.