To optimize root mean square error (RMSE) between given spectra data and re-created spectra data (minimizing the distance between them), the derivative of the spectra plugged into the LMM_FAE function (both endmember and mixed spectra), was taken.
Additionally, to check the best initial guess of abundances in RMSE, using the derivative of all spectra again, LMM_FAE was edited to iterate through different initial guesses. A plot of initial guesses and RMSE was provided to visualize the data.
Report:
Derivative_Optimizing_RMSE.pdf
Code:
Derivatibe_RMSE_Optimization.py
It was found that taking the derivative of all spectra did reduce RMSE significantly when run through LMM_FAE.
It was found that there was a global minimum at/around a1=a2=a3=0.33 for RMSE.
Taking the derivative of spectra in LMM_FAE should be explored further in modeling the unmixing of end members and finding optimized abundances.
The best initial guess for minimizing RMSE, specifically using the derivative of all spectra, is a1=a2=a3=0.33.