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Ǜ is assumed to have a linear relationship with the abundance of composition
(Li 2006 ; Yen et al. 1998 ; Whiting et al. 2004 ; Milliken and Mustard 2005 ):
ln R D ln .1 Ǜ/
(1.4)
1.4
PLS Modeling
1.4.1
Iron Modeling
In our PLS model, modeling data points including 47 lunar sampling sites from
Wilcox et al. ( 2005 ) and 6 added data from lunar farside highlands and fresh areas,
so there are 53 modeling sites in total, and X is a 53 5 matrix, and Y is a 53 1
matrix. After transforming reflectance into absorbance, we standardized both X and
Y in order to get a more stable model. While modeling, the most important thing
is to derive reasonable iron content as well as suppress the space weathering effect
at the same time. All of the five bands are included in the dependent variables to
keep the maximum potential, and they are expressed by A 1 A 5 , respectively. Band
ratios are helpful especially when extracting chemical abundances, and they are also
indications of maturity degree. Our model takes account of the typical NIR/VIS ratio
(950 nm/750 nm), which is used in Lucey's algorithm. Pieters et al. ( 2002 )have
tested the correlations between composition and spectral ratios, and experiments
showed that the highest correlation for iron is 1,000/400 nm. Hence, we also bring
it into our model, expressed by 1,000/415 nm. Finally, all the variables chosen to
build model are listed in Eq. 1.5 , c 0 c 7 are regression coefficients, and A 1 A 5
represent five absorption bands of Clementine data:
A 4
A 2
c 6 C
A 5
A 1
c 7
5
X
Iron D c 0 C
A i c i C
(1.5)
iD1
After inputting all the data into PLS toolbox, leave-one-out cross-validation is
executed during modeling. The cross-validation means modeling with one variable
left out until all the variables have been left out once; thus we would derive a
regression model in each cross-validation and compute the root mean square error
of cross-validation (RMSECV) for every leave-one-out model by Eq. 1.6 ; k is the
number of variable that is left out. Usually, the one with minimum RMSECV will
be chosen as the best LV number. After the number of components is determined,
the total root mean square (RMSE) can be calculated by Eq. 1.7 .
Figure 1.2 is the plot of RMSE and RMSECV values, the minimum RMSECV
is 1.51 wt%, and the corresponding LV number is 1. Measured abundances of iron
and those derived from the PLS model are plotted in Fig. 1.3 . Correlation coefficient
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