Spectral Mixture Decomposition by Least Dependent Component Analysis
  A recently proposed mutual information based algorithm for decomposing data into least dependent components (MILCA) is applied to spectral analysis, namely to blind recovery of concentrations and pure spectra from their linear mixtures. The algorithm is based on precise estimates of mutual information between measured spectra, which allows to assess and make use of actual statistical dependencies between them. We show that linear filtering performed by taking second derivatives effectively reduces the dependencies caused by overlapping spectral bands and, thereby, assists resolving pure spectra. In combination with second derivative preprocessing and alternating least squares postprocessing, MILCA shows decomposition performance comparable with or superior to specialized chemometrics algorithms. The results are illustrated on a number of simulated and experimental (infrared and Raman) mixture problems, including spectroscopy of complex biological materials.   MILCA is available online at http://www.fz-juelich.de/nic/cs/software 
Sergey A. Astakhov, Harald St\"ogbauer, Alexander Kraskov, Peter   Grassberger