Pagecontent:
Using non-negative matrix factorization in the unmixing of diffuse reflectance spectra.
NEW: Download the DRS-Unmixer 1.0 Software
DRS-Unmixer is a stand-alone application which will help you to produce a linear mixture model for your own DRS data sets. Please download the Zip-file, which also contains a manual discussing the ideas behind DRS-Unmixer and a detailed explaination of how to use the software.
Diffuse reflectance spectroscopy (DRS) determines the “colour” of sediment across a given range of wavelengths. A Minolta 2002C instrument is used routinely on research cruises to measure percentage reflectance at 10 nm increments across the visible wavelength band (400 and 700 nm). The visible light wavelength range can provide information on a number of process indicative materials such as iron oxides, clay minerals, carbonates and organic matter. Characteristic spectral peaks in their first derivative reflectance curves help to identify these materials.
Hematite and goethite both have characteristic peaks in the first derivatives of the reflectance spectra. This helps in their identification in sediment samples.
The DRS spectra of natural sediments do however represent a composite signal of the different constituent minerals; therefore it is necessary to “unmix” the data to obtain information on specific materials. Certain conditions must be met if we are to unmix a collection of DRS spectra in a meaningful way and we attempt to characterise two factors:
End-members: represent the reflectance spectra of the constituent materials. The end-member spectra must have the same units as the measured DRS data [% reflectance in the range 0-100]
Fractional abundances: give the proportion of each end-member present in the measured spectra. The abundances must 0 or greater (in other words negative abundances are not allowed) and for each measured spectrum the abundances of the end-members must add to 1 (so-called full additivity).
To obtain such an unmixed representation of a DRS data set we take the matrix of measured data and try to reduce it into the discussed factors (fractional abundances and end-members) that meet the mixing constraints of non-negativity and full additivity. To produce factors that only contain positive values may seem trivial, but in fact it places some tricky non-linear constraints on the unmixing. An analytical solution to the problem is not possible, so instead we must proceed numerically. Starting with a first guess of the solution (in practise just random numbers) the non-negative matrix factorisation algorithm of Lee and Seung (1999) is applied to gradually push the model towards the correct solution.
Unmixed DRS data from ODP Site 967 in the eastern Mediterranean. A four end-member solution provides a good model of the data and an be interpreted in terms of environmental change.
Shown above is an example taken from Mediterranean sediments (ODP Site 967) spanning the period between 900 and 1500 thousand years ago. Four end-members are identified which correspond to organic matter which increases in more humid climates, aeolian dust from Africa transported by the strong winds that form during drier periods, grey ooze that consists of microfossil shells and fluvial material which is predominantly composed of clays transported by the Nile. The unmixing of the DRS data set therefore gives us detailed information concerning climate change and variations in the importance of the different transport mechanisms that fed sediment into the eastern Mediterranean.