Generalized extreme learning machine acting on a metric space

Abstract

Functional data learning is an extension of traditional data learning, that is, learning the data chosen from the Euclidean space $${\mathbb{R}^{n}}$$ to a metric space. This paper focuses on the functional data learning with generalized single-hidden layer feedforward neural networks (GSLFNs) acting on some metric spaces. In addition, three learning algorithms, named Hilbert parallel overrelaxation backpropagation (H-PORBP) algorithm, ν-generalized support vector regression (ν-GSVR) and generalized extreme learning machine (G-ELM) are proposed to train the GSLFNs acting on some metric spaces. The experimental results on some metric spaces indicate that GELM with additive/RBF hidden-nodes has a faster learning speed, a better accuracy, and a better stability than HPORBP algorithm and ν-GSVR for training the functional data. The idea of GELM can be used to extend those improved extreme learning machines (ELMs) that act on the Euclidean space $${\mathbb{R}^{n}, }$$ such as online sequential ELM, incremental ELM, pruning ELM and so on, to some metric spaces.