Adaptive forgetting factor OS-ELM and bootstrap for time series prediction

Abstract

Online sequential extreme learning machine (OS-ELM) for single-hidden layer feedforward networks (SLFNs) is an effective machine learning algorithm. But OS-ELM has some underlying weaknesses of neglecting time series timeliness and being incapable to provide quantitative uncertainty for prediction. To overcome these shortcomings, a time series prediction method is presented based on the combination of OS-ELM with adaptive forgetting factor (AFF-OS-ELM) and bootstrap (B-AFF-OS-ELM). Firstly, adaptive forgetting factor is added into OS-ELM for adjusting the effective window length of training data during OS-ELM sequential learning phase. Secondly, the current bootstrap is developed to fit time series prediction online. Then associated with improved bootstrap, the proposed method can compute prediction interval as uncertainty information, meanwhile the improved bootstrap enhances prediction accuracy and stability of AFF-OS-ELM. Performances of B-AFF-OS-ELM are benchmarked with other traditional and improved OS-ELM on simulation and practical time series data. Results indicate the significant performances achieved by B-AFF-OS-ELM.