Murphy, Bro, and Stedmon
368
discriminant analysis (LDA) and discriminant analysis based upon partial least squares
regression (PLS-DA).
In Figure 10.14, PLS-DA on the unfolded EEMs (normalized and mean-centered) is
used to predict membership of three classes representing estuarine, stream or WTP sites for
each of the samples from the Horsens catchment data set. Cross-validation of the PLS-DA
model using random subsets of the data indicated that a three component model was appropriate. Unlike in PLS regression, where models are desired to have minimum RMSE cv , in
PLS-DA models are selected in order to have the lowest possible cross-validated classification error rates (Kjeldahla and Bro, 2010). In the current example, cross-validated classification error rates are 2.2%, 0.2%, and 1.6% for estuary, stream, and WTP sites respectively.
In Figure 10.14, the vertical axis shows the predicted class membership (cross-validated)
for each sample, plotted in relation to a calculated threshold (dotted line) that distinguishes
samples that are assessed as belonging to a particular class (above the line) from samples
that are not (below the line). Ideally, a good classification model also shows tight clustering
of sites around 1 (class members) or zero (non-class members); in the current example, the
absence of tight clustering is presumably a reflection of the continuity between sites in the
data set, and the somewhat arbitrary designation of the three classes. In Figure 10.14a, all
but four samples from stations E1–E5 are correctly assigned to the estuary class, while a
small number of river (n = 3) and WTP (n = 3) samples cannot be distinguished from the
estuary class. In Figure 10.14b showing predicted membership of the stream class, similar success rates for classification are observed. In Figure 10.14c, all samples from site
16 are correctly assigned to the WTP class, along with one misclassified sample from the
estuary.
In previous studies of DOM fluorescence, a limited range of classification techniques
have been applied. Bilal et al. (2010) used classification and regression trees (CART) of
DOM fluorescence characteristics to investigate the persistence of farm waste contamination during a biodegradation experiment. Hall and Kenny (2007) used SIMCA coupled to a
PARAFAC model to classify port samples according to their harbor of origin along the US
east coast, while Hall et al. (2005) used multilinear N-PLS-DA to classify samples by port
and river of origin. Overall, however, discrimination techniques have been underutilized
in the interpretation of DOM fluorescence data sets, and could play a much larger role in
understanding and predicting the behavior of natural organic matter fluorescence in the
future.
10.11 Summary
In this chapter, a range of chemometric models for exploring and visualizing CDOM fluorescence data sets and for predicting the relationship between fluorescence and other variables have been introduced. It is apparent that exploratory methods, particularly PARAFAC
and PCA, have already been widely implemented. Conversely, calibration models and discriminant analyses have been attempted relatively rarely, yet have considerable potential
368
discriminant analysis (LDA) and discriminant analysis based upon partial least squares
regression (PLS-DA).
In Figure 10.14, PLS-DA on the unfolded EEMs (normalized and mean-centered) is
used to predict membership of three classes representing estuarine, stream or WTP sites for
each of the samples from the Horsens catchment data set. Cross-validation of the PLS-DA
model using random subsets of the data indicated that a three component model was appropriate. Unlike in PLS regression, where models are desired to have minimum RMSE cv , in
PLS-DA models are selected in order to have the lowest possible cross-validated classification error rates (Kjeldahla and Bro, 2010). In the current example, cross-validated classification error rates are 2.2%, 0.2%, and 1.6% for estuary, stream, and WTP sites respectively.
In Figure 10.14, the vertical axis shows the predicted class membership (cross-validated)
for each sample, plotted in relation to a calculated threshold (dotted line) that distinguishes
samples that are assessed as belonging to a particular class (above the line) from samples
that are not (below the line). Ideally, a good classification model also shows tight clustering
of sites around 1 (class members) or zero (non-class members); in the current example, the
absence of tight clustering is presumably a reflection of the continuity between sites in the
data set, and the somewhat arbitrary designation of the three classes. In Figure 10.14a, all
but four samples from stations E1–E5 are correctly assigned to the estuary class, while a
small number of river (n = 3) and WTP (n = 3) samples cannot be distinguished from the
estuary class. In Figure 10.14b showing predicted membership of the stream class, similar success rates for classification are observed. In Figure 10.14c, all samples from site
16 are correctly assigned to the WTP class, along with one misclassified sample from the
estuary.
In previous studies of DOM fluorescence, a limited range of classification techniques
have been applied. Bilal et al. (2010) used classification and regression trees (CART) of
DOM fluorescence characteristics to investigate the persistence of farm waste contamination during a biodegradation experiment. Hall and Kenny (2007) used SIMCA coupled to a
PARAFAC model to classify port samples according to their harbor of origin along the US
east coast, while Hall et al. (2005) used multilinear N-PLS-DA to classify samples by port
and river of origin. Overall, however, discrimination techniques have been underutilized
in the interpretation of DOM fluorescence data sets, and could play a much larger role in
understanding and predicting the behavior of natural organic matter fluorescence in the
future.
10.11 Summary
In this chapter, a range of chemometric models for exploring and visualizing CDOM fluorescence data sets and for predicting the relationship between fluorescence and other variables have been introduced. It is apparent that exploratory methods, particularly PARAFAC
and PCA, have already been widely implemented. Conversely, calibration models and discriminant analyses have been attempted relatively rarely, yet have considerable potential