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The inverse-free extreme learning machine (ELM) algorithm proposed in [4] wasbased on an inverse-free algorithm to compute the regularized pseudo-inverse,which was deduced from an inverse-free recursive algorithm to update theinverse of a Hermitian matrix. Before that recursive algorithm was applied in[4], its improved version had been utilized in previous literatures [9], [10].Accordingly from the improved recursive algorithm [9], [10], several efficientinverse-free algorithms for ELM were proposed in [13] to reduce thecomputational complexity. In this paper, we propose two inverse-free algorithmsfor ELM with Tikhonov regularization, which can increase multiple hidden nodesin an iteration. On the other hand, we also propose two efficient decrementallearning algorithms for ELM with Tikhonov regularization, which can removemultiple redundant nodes in an iteration.

Efficient Inverse-Free Incremental and Decremental Algorithms for Multiple Hidden Nodes in Extreme Learning Machine