title: Long-term time series prediction using OP-ELM.
abstract: In this paper, an Optimally Pruned Extreme Learning Machine (OP-ELM) is applied to the problem of long-term time series prediction. Three known strategies for the long-term time series prediction i.e. Recursive, Direct and DirRec are considered in combination with OP-ELM and compared with a baseline linear least squares model and Least-Squares Support Vector Machines (LS-SVM). Among these three strategies DirRec is the most time consuming and its usage with nonlinear models like LS-SVM, where several hyperparameters need to be adjusted, leads to relatively heavy computations. It is shown that OP-ELM, being also a nonlinear model, allows reasonable computational time for the DirRec strategy. In all our experiments, except one, OP-ELM with DirRec strategy outperforms the linear model with any strategy. In contrast to the proposed algorithm, LS-SVM behaves unstably without variable selection. It is also shown that there is no superior strategy for OP-ELM: any of three can be the best. In addition, the prediction accuracy of an ensemble of OP-ELM is studied and it is shown that averaging predictions of the ensemble can improve the accuracy (Mean Square Error) dramatically.
authors.affiliation: Department of Information and Computer Science, Aalto University School of Science, FI-00076 Aalto, Finland. Electronic address: alexander.grigorevskiy@aalto.fi.
authors.forename: Alexander
authors.initials: A
authors.lastname: Grigorievskiy
authors.affiliation: Department of Information and Computer Science, Aalto University School of Science, FI-00076 Aalto, Finland.
authors.forename: Yoan
authors.initials: Y
authors.lastname: Miche
authors.affiliation: Pyhäjärvi Institute, Sepäntie 7, FI-27500, Kauttua, Finland.
authors.forename: Anne-Mari
authors.initials: AM
authors.lastname: Ventelä
authors.affiliation: University of Lille 1, IAE, 104 avenue du peuple Belge, 59043 Lille cedex, France.
authors.forename: Eric
authors.initials: E
authors.lastname: Séverin
authors.affiliation: Department of Information and Computer Science, Aalto University School of Science, FI-00076 Aalto, Finland; IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain; Computational Intelligence Group, Computer Science Faculty, University of the Basque Country, Paseo Manuel Lardizabal 1, Donostia-San Sebastián, Spain.
authors.forename: Amaury
authors.initials: A
authors.lastname: Lendasse
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D007259:Infrared Rays; D007834:Lasers; D016018:Least-Squares Analysis; D016014:Linear Models; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D009792:Oceans and Seas; D012623:Seawater; D016082:Solar System; D060388:Support Vector Machine; D013696:Temperature; D013995:Time
keywords: DirRec strategy; Direct strategy; ELM; LS-SVM; OP-ELM; Ordinary least squares; Recursive strategy; Time series prediction