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 finite-dimensional model.
Presented at the AIC2005 10th Congress of the International Color Association, May 2005.
Xiong, W., and Funt, B., "Independent Component Analysis and Nonnegative Linear Model Analysis of Illuminant and Reflectance Spectra," Proc. AIC2005 10th Congress of the International Color Association, Granada, May 2005.
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