Hessian unsupervised extreme learning machine

Extreme learning machines (ELMs) are shown to be efficient and effective learning algorithms for regression and classification tasks. ELMs, however, are typically utilized to solve supervised learning problems. Only a handful of research on ELMs focuses on exploring unlabeled data. One representative work is the unsupervised extreme learning machine (US-ELM), where the standard ELM is expanded for unsupervised learning based on Laplacian regularization. However, Laplacian regularization has poor extrapolation power since it tends to bias the solution towards a constant function. In this paper, we propose a new framework termed Hessian unsupervised ELM (HUS-ELM) to enhance the unsupervised learning of ELM. In particular, Hessian regularization can properly exploit the intrinsic local geometry of the data manifold compared to Laplacian regularization. This leverages the performance of HUS-ELM in unsupervised learning problems since the Hessian regularization can correctly reflect the positional relationship between the unlabeled samples. Six publicly available datasets are used to evaluate the proposed algorithm. The experimental results indicate that the proposed method performs better than other unsupervised learning methods in terms of clustering accuracy.