A comparative analysis of support vector machines and extreme learning machines.

The theory of extreme learning machines (ELMs) has recently become increasingly popular. As a new learning algorithm for single-hidden-layer feed-forward neural networks, an ELM offers the advantages of low computational cost, good generalization ability, and ease of implementation. Hence the comparison and model selection between ELMs and other kinds of state-of-the-art machine learning approaches has become significant and has attracted many research efforts. This paper performs a comparative analysis of the basic ELMs and support vector machines (SVMs) from two viewpoints that are different from previous works: one is the Vapnik-Chervonenkis (VC) dimension, and the other is their performance under different training sample sizes. It is shown that the VC dimension of an ELM is equal to the number of hidden nodes of the ELM with probability one. Additionally, their generalization ability and computational complexity are exhibited with changing training sample size. ELMs have weaker generalization ability than SVMs for small sample but can generalize as well as SVMs for large sample. Remarkably, great superiority in computational speed especially for large-scale sample problems is found in ELMs. The results obtained can provide insight into the essential relationship between them, and can also serve as complementary knowledge for their past experimental and theoretical comparisons.