Fig. 5
From: Comprehensive modeling of bloodstain aging by multivariate Raman spectral resolution with kinetics
Kinetic optimization for spectral deconvolution of bloodstains. a Schematics of the kinetic P-ALS. The Raman spectral dataset depicted as the matrix D was decomposed into the score matrix C and the loading profile matrix S. The first (magenta) and fourth (turquoise) scores in the matrix C were subsequently fitted to the respective kinetic equations (fo and fd), which yielded the rate constants (ko and kd). The rate constants were updated by fitting to the Arrhenius equation. The corresponding new kinetic equations (fo,new and fd,new) were subsequently obtained. The penalty ALS was implemented by incorporating the fitted kinetic curves and the label-vectors (Ho = [1, 0, 0, 0, 0] and Hd = [0, 0, 0, 1, 0]) with the weighting factor λ into the least-squares calculation. Then, the updated matrix C was used to estimate the matrix S for the next iterative calculation. b–e The kinetic fitting to the scores of the first (b, c) and fourth (d, e) spectral components decomposed by the kinetic P-ALS. b, d represent the fitted curves (solid lines) of the kinetic equations to the scores (circles) at 30 °C (dark magenta and dark turquoise), 24 °C (magenta and turquoise), and 16 °C (light magenta and light turquoise), respectively. The circles only show the scores obtained from one of the three donors, corresponding to Fig. 4. c, e Show the fitting of the Arrhenius equation (dashed lines) to the yielded rate constants (diamonds)
