## 4 Results and Discussion
### Multianalyzer Data Fusion Results  
The classification accuracy with each individual analyzer is compared to the accuracy achieved with data fusion for the New Mexico and military installation soil suites in Figure 7A. For the  
Figure 6: Plot of loading vectors versus wavelength (nm) for the LIBS analysis of the New Mexico (**A**) and military installation (**B**) soil samples. The loading values that have the largest impact on the PLSDA model are labeled with the element associated with that emission line. New Mexico soils, the classification accuracy for the individual analyzers ranges from 79. to 91% correct. Data fusion increases classification accuracy to 94% correct. For the military installation soils, classification relying on the RS spectra performs poorly with a classification accuracy of 64% correct. In contrast, classification using either the XRFS or LIBS spectra results in classification accuracy of >93% correct. Data fusion increases the classification accuracy to >98% correct. For both data sets, fusion increases classification accuracy over any of the individual instruments suggesting the benefit for assessing soils with multiple analyzers. Classification accuracy for the two New Hampshire soil schemas is shown in Figure 7B. As is expected from the principal component score plots (Figure 4), samples are perfectly discriminated in terms of the Lebanon and Belmont locations. This is true for each of the individual analyzers, thus their data fusion provides no additional benefit. For the within-location discrimination for the soil pits at the Belmont site, no benefit is observed for data fusion; however, this may be a result of the extremely poor classification accuracy with the RS spectra. This suggests that for multianalyzer data fusion to be beneficial, some minimum level of accuracy need be achieved by each instrument. The potential for multianalyzer data fusion to correct classification errors is demonstrated in Figure 8 for the New Mexico soils. Four classification matrices are shown where the rows indicate the true class of the samples and the columns indicate the class label selected by the classification algorithm. The entries in the matrix, \(m_{ij}\), are the percent of samples with the true label from row \(i\) and the classifier-selected label from column \(j\). Thus, the diagonal entries are the percent of samples that were correctly classified, and off-diagonal entries demonstrate assignment errors made by the classifier. As expected from the visualization in Figure 3, most classification errors for each analyzer occur between the Lower and Upper Socorro Canyon classes, where the geological similarity is high between soils at the two sites. None of the individual analyzers correctly classify the Socorro Canyon samples with greater than 60% accuracy. With data fusion, the classification accuracy of the Socorro Canyon  
Figure 7: Classification accuracy for the individual XRFS, RS, and LIBS analyzers and for three-instrument data fusion for (**A**) the New Mexico (left) and military installation soils (right) and (**B**) the New Hampshire Lebanon and Belmont and Lebanon locations (left) and the three Belmont location soil pits (right) described in Table 1.  
samples is increased to 70% correct and other off-diagonal errors committed by single analyzer classification are eliminated. For example, for the military installation soils, classification accuracy with data collected with the Raman analyzer is poor. In order to estimate the relative importance of each analyzer to the fusion classification, we considered the regression weights applied to each instrument's data. In a trained PLSDA classifier, the regression weights are the values applied to the feature vector to estimate the confidence that a sample belongs to each class [60]. For each instrument, the magnitudes of the regression weights for the analyzer-specific features were pooled across the classes, and the probability density function (pdf) was estimated using kernel density estimation [59].