Murphy, Bro, and Stedmon
340
A principal objective when analyzing complex data sets is to reduce the dimensionality
of the data set in order to separate important features from redundant information and noise.
The reduced data set is then simpler to interpret. Thus, an excitation–emission matrix (EEM)
data set consisting of many thousands of individual data points (samples × excitation ×
emission) may be reduced to a fraction of its original size (e.g., samples × intensity at a few
wavelength pairs), with greatly increased interpretability and opportunities for visualizing
the data graphically, while retaining all of the essential information contained in the original data set. A second principal objective is to detect patterns in the relationships between
variables, in order to develop prediction/calibration models for other important parameters
that are harder to measure.
This chapter is not intended as a statistics tutorial as much as a broad overview of the
available chemometric techniques likely to be of greatest assistance for interpreting fluorescence data. The list is by no means exhaustive – there are literally thousands of different
techniques and variations to be discovered, and describing all of them would require many
textbooks. Similarly, the algorithms underpinning the chemometric methods discussed here
are presented elsewhere (Désiré-Luc Massart et al., 1988; Martens and Næs, 1989; Smilde
et al., 2004) and many useful tutorials for understanding and applying various techniques
are published (e.g., Geladi and Kowalski, 1986; Thomas, 1994; Bro, 1997; Stedmon and
Bro, 2008) or available online (see, e.g., http://www.models.life.ku.dk/). The focus here
is on describing how chemometric methods can and have already been put to use for the
interpretation of natural organic matter fluorescence.
An example data set is used to demonstrate some of the chemometric techniques discussed in this chapter. The data set is derived from the Horsens catchment, Denmark and
consists of fluorescence EEMs and absorbance measured at 375 nm (a375), together with
dissolved organic carbon (DOC), and the nutrients total dissolved phosphorus (TDP), total
dissolved nitrogen (TDN), dissolved organic phosphorus (DOP = TDP – dissolved inorganic P), dissolved organic nitrogen (DON = TDN – dissolved inorganic N). The locations
of sampling sites are illustrated in Figure 10.1. Detailed information about the data set (20
sites, n = 543 samples) is presented in Stedmon et al. (2006). Previously, an eight-component model was obtained using PARAllel FACtor analysis (PARAFAC; see later) on a
data set consisting of these samples together with more than 600 samples generated during
a series of degradation experiments (Stedmon and Markager, 2005a). Analyses presented
herein were performed using PLS_toolbox (v. 6.0.1) operated with MATLAB (R2010a).
10.2 Multivariate and Multiway Data Sets
The distinction between multivariate and multiway data is best illustrated by example
(Figure 10.2). A simple multivariate data set consists of I samples for which fluorescence
intensities at five emission wavelengths (x 1 – x 5 ) at a fixed excitation wavelength have
been measured; these data are arranged in a table (Figure 10.2a). Now assume that the
experiment had been conducted under four increasing temperatures (t 1 – t 4 ). There are
now two possible ways to arrange the new data set, either as a two-way (multivariate)
340
A principal objective when analyzing complex data sets is to reduce the dimensionality
of the data set in order to separate important features from redundant information and noise.
The reduced data set is then simpler to interpret. Thus, an excitation–emission matrix (EEM)
data set consisting of many thousands of individual data points (samples × excitation ×
emission) may be reduced to a fraction of its original size (e.g., samples × intensity at a few
wavelength pairs), with greatly increased interpretability and opportunities for visualizing
the data graphically, while retaining all of the essential information contained in the original data set. A second principal objective is to detect patterns in the relationships between
variables, in order to develop prediction/calibration models for other important parameters
that are harder to measure.
This chapter is not intended as a statistics tutorial as much as a broad overview of the
available chemometric techniques likely to be of greatest assistance for interpreting fluorescence data. The list is by no means exhaustive – there are literally thousands of different
techniques and variations to be discovered, and describing all of them would require many
textbooks. Similarly, the algorithms underpinning the chemometric methods discussed here
are presented elsewhere (Désiré-Luc Massart et al., 1988; Martens and Næs, 1989; Smilde
et al., 2004) and many useful tutorials for understanding and applying various techniques
are published (e.g., Geladi and Kowalski, 1986; Thomas, 1994; Bro, 1997; Stedmon and
Bro, 2008) or available online (see, e.g., http://www.models.life.ku.dk/). The focus here
is on describing how chemometric methods can and have already been put to use for the
interpretation of natural organic matter fluorescence.
An example data set is used to demonstrate some of the chemometric techniques discussed in this chapter. The data set is derived from the Horsens catchment, Denmark and
consists of fluorescence EEMs and absorbance measured at 375 nm (a375), together with
dissolved organic carbon (DOC), and the nutrients total dissolved phosphorus (TDP), total
dissolved nitrogen (TDN), dissolved organic phosphorus (DOP = TDP – dissolved inorganic P), dissolved organic nitrogen (DON = TDN – dissolved inorganic N). The locations
of sampling sites are illustrated in Figure 10.1. Detailed information about the data set (20
sites, n = 543 samples) is presented in Stedmon et al. (2006). Previously, an eight-component model was obtained using PARAllel FACtor analysis (PARAFAC; see later) on a
data set consisting of these samples together with more than 600 samples generated during
a series of degradation experiments (Stedmon and Markager, 2005a). Analyses presented
herein were performed using PLS_toolbox (v. 6.0.1) operated with MATLAB (R2010a).
10.2 Multivariate and Multiway Data Sets
The distinction between multivariate and multiway data is best illustrated by example
(Figure 10.2). A simple multivariate data set consists of I samples for which fluorescence
intensities at five emission wavelengths (x 1 – x 5 ) at a fixed excitation wavelength have
been measured; these data are arranged in a table (Figure 10.2a). Now assume that the
experiment had been conducted under four increasing temperatures (t 1 – t 4 ). There are
now two possible ways to arrange the new data set, either as a two-way (multivariate)