Enhancement of online sequential extreme learning machine based on the householder block exact inverse QRD recursive least squares

The online sequential extreme learning machine (OS-ELM) has been used for training without retraining the ELM when a chunk of data is received. However, OS-ELM may be affected by an improper number of hidden nodes settings which reduces the generalization of OS-ELM. This paper addresses this problem in OS-ELM. A new structural tolerance OS-ELM (STOS-ELM), based on the Householder block exact inverse QRD recursive least squares algorithm having numerical robustness is proposed. Experimental results conducted on four regressions and five classification problems showed that STOS-ELM can handle the situation when the network is constructed with an improper number of hidden nodes. Accordingly, the proposed STOS-ELM can be easily applied; the size of the hidden layer of ELM can be roughly approximated. If a chunk of data is received, it can be updated in the existing network without having to worry about the proper number of given hidden nodes. Furthermore, the accuracy of the network trained by STOS-ELM is comparable to that of the batch ELM when the networks have the same configurations. STOS-ELM can also be applied in ensemble version (ESTOS-ELM). We found that the stability of STOS-ELM can be further improved using the ensemble technique. The results show that ESTOS-ELM is also more stable and accurate than both of the original OS-ELM and EOS-ELM, especially in the classification problems.