J/A+A/576/A96       New code for PCA in spectral analysis    (Bu+, 2015)
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Restricted Boltzmann machine: a non-linear substitute for PCA in spectral
processing.
    Bu Y., Zhao G., Luo A-l., Pan J., Chen Y.
   <Astron. Astrophys. 576, A96 (2015)>
   =2015A&A...576A..96B
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ADC_Keywords: Models ; Spectroscopy
Keywords: methods: statistical - methods: data analysis - methods: numerical

Abstract:
    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.

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

    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.

Description:
    Source code of RBM algorithm which can be executed in MATLAB 2013.
    This code is based on the more general code by Hinton and coauthors
    (Hinton & Salakhutdinov 2006).

    The supplementary material contains two files. We only need to run
    file rbm_dimreduction to reduce the dimension of the data. The other
    file is the function file that will be called when running
    rbm_dimreduction.

    Data format. The format of data should be MAT-file format. Each row of
    the data matrix X=[x_1_^T^,x_2_^T^,...,x_n_^T^]^T^ represents a
    spectrum vector.

    Variables in the script file rbm_dimreduction. It needs two inputs to
    run rbm_dimreduction: variable h, the dimension of the hidden vector;
    and variable T1, the spectra data. After running rbm_dimreduction, we
    can get the output variable rbm. Variable rbm.hiddata is the data set
    of RBM components. Each row of rbm.hiddata represents the low
    dimensional projection of a spectrum vector. Variable rbm.rec is the
    data set of the reconstructed spectra (denosied or repaired spectra).

File Summary:
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 FileName    Lrecl  Records    Explanations
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ReadMe          80        .    This file
rbm_train.m     86      134    Function file calling by rbm_dimreduction.m
rbm_dim.m      140       17    File used to reduce the dimension of the data
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Acknowledgements:
     Yude Bu, 123974934(at)qq.com

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(End)                                      Patricia Vannier [CDS]    08-Apr-2015