The Spectral Prediction of Original Primary Pigment Based on Constrained Non-Negative Matrix Factorization

With direct prediction in the spectral reflectance space with principal component analysis, the numbers of eigenvectors will surpass the numbers of real primary pigments while the eigenvectors and the corresponding coefficients have negative value, which can not directly presented original primary pigment spectral characteristics and corresponding concentration. We proposed an innovative spectral prediction method in which a complete linear spectral space was created according to optical properties of originals pigment. A constrained non-negative matrix factorization algorithm to predict the numbers and spectral curve shapes of real primary pigments was used in the space. So, this paper designed an overall research plan and implementation process about spectral prediction method firstly, and studied how to select and establish a spectral linear space which was conformed to optical properties of originals; taking transparent pigments as example, and spectra constrained non-negative matrix factorization (SCNMF) algorithm was established to predict primary pigment spectra based on basic non-negative matrix factorization algorithm (BNMF). Aiming at realizing multiple optimal solution of BNMF and improving the prediction accuracy as well as make the matrix decomposition results to be clearly physically meaningful; the proposed SCNMF needs to satisfy four constraints: non negative constraint, additive constraint, smoothness constraint and sparseness constraint. The objective function and iterative algorithm to meet four constraints were set up. The prediction results show that the proposed method can realize accurate prediction of original primary pigments’ numbers and spectra effectively.