[OPTICAL REVIEW Vol. 19, No. 5 (2012) 294-305]
© 2012 The Japan Society of Applied Physics

Initialization of Nonnegative Matrix Factorization by Gaussian Primaries for Reconstruction of Spectral Data

Syamak FARAJIKHAH and Seyed Hossein AMIRSHAHI*

Department of Textile Engineering, Amirkabir University of Technology (Tehran Polytechnic), No. 424 Hafez Avenue, Tehran 15914, Iran

(Received May 11, 2012; Accepted July 23, 2012)

The Gaussian and Gaussian-sigmoidal primaries are introduced as initialization functions in the nonnegative matrix factorization (NNMF) method to achieve more consistent error statistics. The proposed NNMF method with multiplicative update algorithm is employed for reconstruction of spectral data of Munsell and Colorchecker DC datasets from the corresponding CIEXYZ tristimulus values and the resultant achievements are compared with those obtained from PCA and the classical NNMF techniques. Both colorimetric and spectrophotometric errors between the original and the reconstructed spectra are used for the evaluation of reconstruction methods. While run to run variability of the classical NNMF method with multiplicative update algorithm is significantly remarkable, the stability of the suggested technique is fairly high, similar to the PCA method. The ensuing findings show that the embedding of Gaussian initializing vectors in NNMF method provide the all positive bases that enhance both the accuracy of Gaussian method and the reliability of NNMF technique.

Key words: spectral recovery, nonnegative matrix factorization, Gaussian and sigmoidal primaries, principal component analysis

*E-mail address: hamirsha@aut.ac.ir