Independent Component Analysis and Nonnegative Linear Model Analysis of Illuminant and Reflectance Spectra

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Xiong, W. and Funt, B., "Independent Component Analysis and Nonnegative Linear Model Analysis of Illuminant and Reflectance Spectrae",
AIC'2005 Proc. 10th Congress of the International Color Association, Granada, May 2005

## Abstract:

Principal Component Analysis (PCA), Independent Component Analysis (ICA), Non-Negative Matrix
Factorization (NNMF) and Non-Negative Independent Component Analysis (NNICA) are all techniques that
can be used to compute basis vectors for finite-dimensional models of spectra. The two non-negative
techniques turn out to be especially interesting because the pseudo-inverse of their basis vectors is also close
to being non-negative. This means that after truncating any negative components of the pseudo-inverse
vectors to zero, the resulting vectors become physically realizable sensors functions whose outputs map
directly to the appropriate finite-dimensional weighting coefficients in terms of the associated (NNMF or
NNICA) basis. Experiments show that truncating the negative values incurs only a very slight performance
penalty in terms of the accuracy with which the input spectrum can be approximated using a finitedimensional
model.

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Keywords:
Colour vision, independent component analysis, modeling spectra, finite dimensional models, sensor design

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