Abstract
Many real world applications are of time-varying nature and an online learning algorithm is preferred in tracking the real-time changes of the time-varying system. Online sequential extreme learning machine (OSELM) is an excellent online learning algorithm, and some improved OSELM algorithms incorporating forgetting mechanism have been developed to model and predict the time-varying system. But the existing algorithms suffer from a potential risk of instability due to the intrinsic ill-posed problem; besides, the adaptive tracking ability of these algorithms for complex time-varying system is still very weak. In order to overcome the above two problems, this paper proposes a novel OSELM algorithm with generalized regularization and adaptive forgetting factor (AFGR-OSELM). In the AFGR-OSELM, a new generalized regularization approach is employed to replace the traditional exponential forgetting regularization to make the algorithm have a constant regularization effect; consequently the potential ill-posed problem of the algorithm can be completely avoided and a persistent stability can be guaranteed. Moreover, the AFGR-OSELM adopts an adaptive scheme to adjust the forgetting factor dynamically and automatically in the online learning process so as to better track the dynamic changes of the time-varying system and reduce the adverse effects of the outdated data in time; thus it tends to provide desirable prediction results in time-varying environment. Detailed performance comparisons of AFGR-OSELM with other representative algorithms are carried out using artificial and real world data sets. The experimental results show that the proposed AFGR-OSELM has higher prediction accuracy with better stability than its counterparts for predicting time-varying system.
Highlights
In many real world applications such as financial data analysis, industrial process monitoring, weather forecast, and customer behavior prediction, the samples arrive successively in the form of a data stream [1]
In the sequential learning process of the AFGR-online sequential extreme learning machine (OSELM), the forgetting factor (FF) can be adaptively tuned in a recursive way to timely suit the dynamic changes of the timevarying system; a desirable prediction performance of the algorithm can be anticipated. (iii) The effectiveness and practicability of the AFGR-OSELM algorithm are evaluated with both artificial and real world data sets, and the results show that the proposed algorithm can obtain more superior prediction accuracy with better stability compared with other representative models
With the help of the adaptive forgetting factor, the AFGR-OSELM can well track the dynamic changes of the time-varying system and timely reduce the adverse effects of the outdated samples; it is capable of producing desirable prediction results in time-varying environment
Summary
In many real world applications such as financial data analysis, industrial process monitoring, weather forecast, and customer behavior prediction, the samples arrive successively in the form of a data stream [1]. The R-OSELM successfully overcomes the potential ill-posed problem and tends to provide good generalization performance and stability, and it has become a practical online modeling method in real applications. In [23], the authors presented a new variable forgetting factor OSELM using the directional FF method (DFF-OSELM), which achieved superior prediction performance in industrial applications when compared to the OSELM algorithm In both LAFF-OSELM and DFF-OSELM, the intrinsic ill-posed problem is not considered, so they may encounter a potential instability. The built-in generalized regularization approach makes the AFGR-OSELM have a constant regularization effect without fading in the whole learning process; as a result the potential ill-posed problem of the algorithm can be completely overcome and a persistent stability can be maintained in all online learning stages.
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