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The extreme learning machine (ELM) is an efficient way to build single-hidden-layer feedforward networks (SLFNs). However, its fault tolerant ability is very weak. When node noise or node failure exist in a network trained by the ELM concept, the performance of the network is greatly degraded if a countermeasure is not taken. However, this kind of countermeasure for the ELM or incremental learning is seldom reported. This paper considers the situation that a trained SLFN suffers from the coexistence of node fault and node noise. We develop two fault tolerant incremental ELM algorithms for the regression problem, namely node fault tolerant incremental ELM (NFTI-ELM) and node fault tolerant convex incremental ELM (NFTCI-ELM). The NFTI-ELM determines the output weight of the newly inserted node only. We prove that in terms of the training set mean squared error (MSE) of faulty SLFNs, the NFTI-ELM converges. Our numerical results show that the NFTI-ELM is superior to the conventional ELM and incremental ELM algorithms under faulty situations. To further improve the performance, we propose the NFTCI-ELM algorithm. It not only determines the output weight of the newly inserted node, but also updates all previously trained output weights. In terms of training set MSE of faulty SLFNs, the NFTCI-ELM converges, and it is superior to the NFTI-ELM.

Fault and Noise Tolerance in the Incremental Extreme Learning Machine