Abstract: Performing multivariate spectral analysis to determine relationships between chemical species in a sample, includes: providing intensity measurement data as plural measured spectra from the sample, each spectrum having unique identifier and intensity values for bins of a binned spectral range; expressing the intensity measurement data as an m×n matrix V, m and n respectively represents number of bins of the spectral range and number of unique identifiers; performing non-negative factorisation of the matrix V to obtain an m×p derived spectra matrix W and a p×n spectral weightings matrix H minimizing an error function |V?WH|, p representing a number of derived spectra and is selected such that the non-negative factorisation over-fits WH to V; identifying correlations between the p derived spectra of the derived spectra matrix W which explain variance in the intensity measurement data; and determining chemical relationships between chemical species in the sample.

Abstract: Performing multivariate spectral analysis to determine relationships between chemical species in a sample, includes: providing intensity measurement data as plural measured spectra from the sample, each spectrum having unique identifier and intensity values for bins of a binned spectral range; expressing the intensity measurement data as an m×n matrix V, m and n respectively represents number of bins of the spectral range and number of unique identifiers; performing non-negative factorisation of the matrix V to obtain an m×p derived spectra matrix W and a p×n spectral weightings matrix H minimizing an error function ?V-WH?, p representing a number of derived spectra and is selected such that the non-negative factorisation over-fits WH to V; identifying correlations between the p derived spectra of the derived spectra matrix W which explain variance in the intensity measurement data; and determining chemical relationships between chemical species in the sample.