Inverse partitioned matrix-based semi-random incremental ELM for regression

  • Guoqiang ZengEmail author
  • Fenxi Yao
  • Baihai Zhang
Extreme Learning Machine and Deep Learning Networks


Incremental extreme learning machine has been verified that it has the universal approximation capability. However, there are two major issues lowering its efficiency: one is that some “random” hidden nodes are inefficient which decrease the convergence rate and increase the structural complexity, the other is that the final output weight vector is not the minimum norm least-squares solution which decreases the generalization capability. To settle these issues, this paper proposes a simple and efficient algorithm in which the parameters of even hidden nodes are calculated by fitting the residual error vector in the previous phase, and then, all existing output weights are recursively updated based on inverse partitioned matrix. The algorithm can reduce the inefficient hidden nodes and obtain a preferable output weight vector which is always the minimum norm least-squares solution. Theoretical analyses and experimental results show that the proposed algorithm has better performance on convergence rate, generalization capability and structural complexity than other incremental extreme learning machine algorithms.


Extreme learning machine The minimum norm least-squares solution Inefficient nodes Convergence rate Inverse partitioned matrix 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of AutomationBeijing Institute of TechnologyBeijingPeople’s Republic of China

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