Large-scale kernel extreme learning machine

Kernel Extreme Learning Machine (KELM) generalizes basic Extreme Learning Machine (ELM) to the kernel-based framework, and produces better generalization than ELM. But its time O(n²m+n³+ns)≈O(n³) (where n is the number of training sets, m is the number of dimensions and s is the number of output nodes) increases polynomial with respect to the data size, and thus unsuitable for large-scale problems (n ≥20000). Here we will propose an accelerated framework for KELM, and then implement an effective algorithm named Nyström Kernel Extreme Learning Machine (NKELM) based on Nyström low-rank decomposition under the framework. The time cost of NKELM O(nmL+mL²+L³+nLs)≈O(n) (L is the number of hidden nodes, and L≪n in common cases) is significantly lower than KELM, and very suitable for large-scale problems. The experimental results on large-scale datasets show that NKELM can produce good generalization performance with fast learning speed.