Letter: On non-iterative learning algorithms with closed-form solution

This letter discusses non-iterative learning methods with closed-form solution such as the kernel ridge regression and randomization based single hidden layer feedforward neural networks like random vector functional link (RVFL). Similarities and differences between these methods are also discussed. Irrelevance of kernel-trick for randomized neural networks is explained. The need for dual formulation or constrained optimization formulation for kernel methods and RVFL is distinguished. Finally, the articles in this special issue focusing on non-iterative learning methods with closed-form solution are summarized. A common conclusion in these articles is that the RVFL developed in the early 1990s outperforms the extreme learning machines (ELM). This conclusion is consistent with the earlier findings [1], [2], [3] that the direct links enhance the performance of the RVFL.