Restricted Boltzmann machine: a non-linear substitute for PCA in spectral processing^⋆

¹ Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, 100012 Beijing, PR China
e-mail: buyude001@163.com
² School of Mathematics and Statistics, Shandong University, Weihai, 264209, Shandong, PR China
³ School of Mechanical, Electrical & Information Engineering, Shandong University, Weihai, 264209, Shandong, PR China

Received: 13 May 2014
Accepted: 17 February 2015

Abstract

Context. Principal component analysis (PCA) is widely used to repair incomplete spectra, to perform spectral denoising, and to reduce dimensionality. Presently, no method has been found to be comparable to PCA on these three problems. New methods have been proposed, but are often specific to one problem. For example, locally linear embedding outperforms PCA in dimensionality reduction. However, it cannot be used in spectral denoising and spectral reparing. Wavelet transform can be used to denoise spectra; however, it cannot be used in dimensionality reduction.

Aims. We provide a new method that can substitute PCA in incomplete spectra repairing, spectral denoising and spectral dimensionality reduction.

Methods. A new method, restricted Boltzmann machine (RBM), is introduced in spectral processing. RBM is a particular type of Markov random field with two-layer architecture, and use Gibbs sampling method to train the algorithm. It can be used in spectral denoising, dimensionality reduction and spectral repairing.

Results. The performance of RBM is comparable to PCA in spectral processing. It can repair the incomplete spectra better: the difference between the RBM repaired spectra and the original spectra is smaller than that between the PCA repaired spectra and the original spectra. The denoised spectra given by RBM is similar to those given by PCA. In dimensionality reduction, RBM performs better than PCA: the classification results of RBM+ELM (i.e. the extreme learning machine) is higher than those of PCA+ELM. This shows that RBM can extract the spectral features more efficiently than PCA. Thus, RBM is a good alternative method for PCA in spectral processing.