Comparison of clustering techniques for determining compositional units on Mercury from MESSENGER spectral observations.

Kurzfassung

The Mercury Atmospheric and Surface Composition Spectrometer (MASCS) obtained spectra of much of the surface of Mercury during the rst two MESSENGER ybys of the planet. The resulting dataset is composed of several hundred re ectance spectra that have not yet been corrected for any eect due to observing geometry or to surface material phase curves. Our hypothesis is that the separation of surface signal from other contributions can be eciently performed by the use of statistical techniques. We adopt principal component and clustering analyses to identify and characterize spectral units along the MASCS ground tracks. In order to extract the spectral shapes of the primary surface components exposed in the surface area an- alyzed, we applied an R-mode factor analysis, aiming to nd an eigenvector set that minimizes data covariance. Identication of the dierent components and their abundances is accom- plished by principal component analysis together with an evaluation of the eigenvectors and eigenvalues of the covariance matrix (also called covariance matrix decomposition). A compar- ison of the results using only the near-infrared (NIR) and visible (VIS) portions of the spectra indicates that the NIR spectral range is carrying less information than the VIS portion. We also nd that the eigenvectors are essentially unchanged if the full wavelength range is selected (VIS+NIR) rather than limiting observations to the VIS range. The full-range analysis shows that seven eigenvectors are needed to reconstruct the original spectrum to within the level of variability associated with the observational data. Each spectral eigenvector can be regarded as a representative of a distinct spectral class that varies in spatial abundance along the track. The rst eigenvector always displays a strong positive or \red" slope, probably strongly linked to uncorrected eects associated with viewing geometry variations, and all eigenvectors show distinctive spectral signatures. Concentration coecients, or eigenvector abundances, indicate that spectral units show marked geographical variation and a strong correlation with surface units mapped by MESSENGER's Mercury Dual Imaging System (MDIS). Because we do not photometrically correct the data, we apply a decorrelation technique (Mahalanobis transforma- tion) to remove dependence on observation angle in the retrieved concentration coecients. We obtain a set of transformed variables that no longer are eigenvector concentration coecients or abundances. These variables therefore cannot be used to linearly reconstruct the original dataset via inversion of the covariance matrix decomposition transformation. The Mahalanobis decorrelation removes the variation directly linked to viewing geometry variations, but it re- tains the eigenvector abundance variation along each track that can be used to classify the measurements and to identify spectral units. Those coecients are analyzed through three dierent clustering techniques: hierarchical, K-means and self-organizing maps. We evaluate the optimal partition of our set by means of dierent validation criteria, and we compare the output from the dierent algorithms. At the same time, we make use of newly available high- temperature spectra from our Planetary Emissivity Laboratory to assist in the identication of the components of each unit. Application to data from the rst yby provides us with condence in the ability of these techniques to extract physical properties of surface materials.