## 3 Materials and Methods
### Classification for Multianalyzer Data Fusion  
Frequently, the terms data fusion and information fusion are employed as synonyms, but data fusion should apply to the raw data acquired directly from sensors, whilst the term information fusion should denote data that have been processed in some way. As noted by [PERSON] et al. [52], who used data acquired from an integrated micro-RS/XRFS system for the classification and discrimination of ochre pigments, fusion can be undertaken directly on raw spectra after background removal or on the features extracted from the pre-processed spectra. We have utilized the latter approach in this study. In order to combine data from the multiple analyzers, a hierarchical classification approach was used (Figure 1). For each sample, a set of \(\rm N_{s}\times D_{s}\) spectra were collected for each instrument, where \(\rm N_{s}\) refers to the number of spectra for analyzer s and \(\rm D_{s}\) refers to the dimensions of a spectrum collected by s. Multiple locations on each soil sample pellet were interrogated as described in Section 3.2 to adequately model the within-sample variability, given the potential heterogeneity of the soil samples. This resulted in a different number of spectra collected per instrument. The dimensions of the spectra are also specific to each analyzer, with \(\rm D_{s}\) = 14,823 data points, 8194 data points, and 2152 data points for the LIBS, XRFS, and Raman analyzers respectively. The analyzer-specific classifiers were applied to the spectra generating \(\rm N_{s}\times C\) classifier confidences that the sample's spectra belong to each of C classes, where the number of classes range from 2 to 6 depending on the classification schema (see Section 4, Table 1). In order to generate an input vector for the fusion classifier, the classifier confidences for each analyzer were averaged to produce a single \(1\times C\) vector. These vectors were then concatenated to create a single vector that is \(1\times 3C\) for the sample as an input to the final classifier. This feature input vector was classified by the fusion classifier and a class label assigned to the sample based on the class that generated the highest fusion-classifier confidence. Classification accuracy was estimated using leave-one-sample-out cross-validation. Each sample was  
Figure 1: Flow chart of the process used for analyzer data fusion. The three instruments collected spectra (Figure 2) from multiple locations on each soil pellet. These spectra are first classified using analyzer-specific classifiers, that output a set of confidence values that each spectrum belongs to each class. Then, the confidences from each analyzer-specific classifier are averaged and concatenated to generate a single vector for the sample. Finally, this vector is used as the input to the final data fusion classifier and a class label for the sample is generated. in turn held out as a test sample and the remaining samples were used to train both the analyzer-specific and fusion classifiers. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Soil Suite** & **Class** & **Samples/Class** \\ \hline \multirow{8}{*}{**New Mexico**} & Rio Salada & 14 \\  & Sedillo Hill & 8 \\  & Lower Socorro Canyon & 4 \\  & Upper Socorro Canyon & 6 \\  & White Sands & 6 \\  & Willard & 6 \\ \hline \multirow{8}{*}{**Military Installations**} & MMR Joint Base Cape Cod (MA) & 11 \\  & Ft. Eustis (VA) & 10 \\ \cline{1-1}  & Ft. Benning (GA) & 11 \\ \cline{1-1}  & ING Camp Kinama (ID) & 10 \\ \cline{1-1}  & Ft. Lewis (WA) & 10 \\ \cline{1-1}  & Ft. Wainwright (AK) & 9 \\ \hline \multirow{2}{*}{**New Hampshire**} & Lebanon & 6 \\ \cline{1-1}  & Belmont & 6 \\ \hline \multirow{2}{*}{**New Hampshire (Belmont)**} & Pit \#1 & 6 \\ \cline{1-1}  & Pit \#2 & 6 \\ \cline{1-1}  & Pit \#3 & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Definition of the soil classification schemas and number of samples per class. Figure 2: Example of the XRFS, RS, and LIBS spectra used in this study for data fusion, in this case for the White Sands, NM soil.