Monotonic classification extreme learning machine

Monotonic classification problems mean that both feature values and class labels are ordered and monotonicity relationships exist between some features and the decision label. Extreme Learning Machine (ELM) is a single-hidden layer feedforward neural network with fast training rate and good generalization capability, but due to the existence of training error, ELM cannot be directly used to handle monotonic classification problems. This work proposes a generalization of ELM for processing the monotonic classification, named as Monotonic Classification Extreme Learning Machine (MCELM) in which the monotonicity constraints are imposed to the original ELM model. Mathematically, MCELM is a quadratic programming problem in which the monotonicity relationships are considered as constraints and the training error is the objective to be minimized. The mathematical model of MCELM not only can make the generated classifier monotonic but also can minimize the classification error. MCELM does not need to tune parameters iteratively, and therefore, keeps the advantage of extremely fast training which is the essential characteristic of ELM. MCELM does not require that the monotonic relationships existing between features and the output are consistent, which essentially relaxes the assumption of consistent monotonicity used in most existing approaches to handling monotonic classification problems. In comparison with exiting approaches to handling monotonic classification, MCELM can indeed generate a monotonicity-reserving classifier which experimentally shows a much better generalization capability on both artificial and real world datasets.