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

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.