Selection of classification boundaries using the logistic regression

We propose the method for selecting classification boundaries for the logistic regression model, by applying the sparse regularization. We can investigate which combination of classification boundaries are truly necessary for the multinomial logistic model by encouraging some of coefficient parameters themselves or their differences toward exactly zeros. The model is estimated by the maximum penalized likelihood method with the fused lasso type penalty. We also introduce some model selection criteria for evaluating models estimated by the penalized likelihood method. Simulation and real data analysis show insights that the proposed method goes well.