Ordinal extreme learning machine

Recently, a new fast learning algorithm called Extreme Learning Machine (ELM) has been developed for Single-Hidden Layer Feedforward Networks (SLFNs) in G.-B. Huang, Q.-Y. Zhu and C.-K. Siew "[Extreme learning machine: theory and applications," Neurocomputing 70 (2006) 489-501]. And, ELM has been successfully applied to many classification and regression problems. In this paper, the ELM algorithm is further studied for ordinal regression problems (named ORELM). We firstly proposed an encoding-based framework for ordinal regression which includes three encoding schemes: single multi-output classifier, multiple binary-classifications with one-against-all (OAA) decomposition method and one-against-one (OAO) method. Then, the SLFN was redesigned for ordinal regression problems based on the proposed framework and the algorithms are trained by the extreme learning machine in which input weights are assigned randomly and output weights can be decided analytically. Lastly widely experiments on three kinds of datasets were carried to test the proposed algorithm. The comparative results with such traditional methods as Gaussian Process for Ordinal Regression (ORGP) and Support Vector for Ordinal Regression (ORSVM) show that ORELM can obtain extremely rapid training speed and good generalization ability. Especially when the data set's scalability increases, the advantage of ORELM will become more apparent. Additionally, ORELM has the following advantages, including the capabilities of learning in both online and batch modes and handling non-linear data.