%\VignetteIndexEntry{An R Package for Chemometric Analysis of Spectra (NMR, IR etc)}
%\VignetteDepends{chemometrics, robustbase, RColorBrewer, plyr, pcaPP, mvtnorm, mvoutlier, pls, lattice, grid, rgl, R.utils, mclust, mvbutils, sna, knitr}
%\VignetteKeywords{multivariate}
%\VignettePackage{ChemoSpec}
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\documentclass[10pt]{article}
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\usepackage[square, comma, numbers, sort&compress]{natbib} % allows grouping of references [1-4, 8]

\usepackage{ccaption} % Stuff to change the format of a figure caption
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% run a few things in the background for use later
<< SetUp, echo = FALSE, eval = TRUE, results = "hide" >>=

# You must knit this file with getwd() set to the directory it is in!

# R options & configuration:

rm(list = ls())
options(width =  50, show.signif.stars = FALSE)

suppressMessages(library("knitr"))
suppressMessages(library("ChemoSpec"))
suppressMessages(library("RColorBrewer"))
suppressMessages(library("mvbutils"))
suppressMessages(library("sna"))

desc <- packageDescription("ChemoSpec")
vers <- paste("(Package Version ", desc$Version, ")", sep = "")
#vers <- paste("R package version", meta$Version)

# Stuff specifically for knitr:

opts_chunk$set(out.width = "0.8\\textwidth", fig.align = "center", fig.width = 7, fig.height = 7, cache = FALSE)

# Note: defaults are eval = TRUE, echo = TRUE
@


\title{ChemoSpec: An R Package for Chemometric\\
Analysis of Spectroscopic Data\\
\Sexpr{vers}}
\author{Bryan A. Hanson\footnote{The development of ChemoSpec has been generously supported by DePauw University in the form of sabbatical funding and a Fisher Fellowship. Thanks!}\\
e-mail: \href{mailto:hanson@depauw.edu}{hanson@depauw.edu}\\
\\
with contributions from Matt J. Keinsley\\
\\
DePauw University\\
Department of Chemistry \& Biochemistry\\
Greencastle Indiana USA\\
\\
\href{http://github.com/bryanhanson/ChemoSpec}{github.com/bryanhanson/ChemoSpec}\\
\href{http://CRAN.R-project.org/package=ChemoSpec}{CRAN.R-project.org/package=ChemoSpec}\\
}
\date{\today}

%%%%%     Now we start the document     %%%%%

\begin{document}

\maketitle

\begin{abstract}
\texttt{ChemoSpec}\cite{ChemoSpec-pkg} is a collection of functions for plotting spectra (NMR, IR etc, as well as chromatograms) and carrying out various forms of top-down exploratory data analysis, such as hierarchical cluster analysis (HCA), principal components analysis (PCA) and model-based clustering. Robust methods appropriate for this type of high-dimensional data are employed. \texttt{ChemoSpec} is designed to facilitate comparison of  samples from treatment and control groups.   It is designed to be user friendly and suitable for people with limited background in \texttt{R}.  This vignette gives some background on \texttt{ChemoSpec} and takes the reader through a typical workflow.
\end{abstract}
\newpage
\tableofcontents
\setcounter{tocdepth}{2}
\section{Introduction} %%%%%%%%%%%%%%%
Chemometrics, as defined by Varmuza and Filzmoser\cite{Filz}, is

\begin{quote}
"\ldots the extraction of relevant information from chemical data by mathematical and statistical tools."
\end{quote}

This is an appropriately broad definition, considering the wealth of questions and tasks that can be treated by chemometric approaches.  In our case, the focus is on spectral data sets, which typically have many variables (frequencies) and relatively few samples.  Such multivariate, \emph{high p, low n} data sets present some algorithmic challenges, but these have been addressed by knowledgeable folks.  In particular, for both the practical and theoretical background to multivariate chemometric analysis, I strongly recommend the Varmuza/Filzmoser book.\cite{Filz}  Some of the functions described here are not much more than wrappers for the functions they and others have made available to the \texttt{R} community in their packages.  Another excellent text is the one by Ron Wehrens.\cite{Wehrens}

\texttt{ChemoSpec} was developed for the chemometric analysis of spectroscopic data, such as UV-Vis, NMR or IR data (it also works with chromatographic data, see below).\footnote{\texttt{ChemoSpec} was not developed for and has not been tested with mass spectral data sets (MS), as there are other dedicated packages for this purpose.  See the \href{http://cran.at.r-project.org/web/views/ChemPhys.html}{Chemometrics and Computational Physics Task View} for an overview.}  The approach is entirely exploratory and unsupervised, in other words, "top-down"\cite{Prog-Metabolomics}.  I developed it while beginning a new research focus on plant metabolomics, and I needed software to analyze the data I was collecting.  My research involves ecological experiments on plant stress, so \texttt{ChemoSpec} was designed to accommodate samples that have different histories, i.e., they fall into different classes, categories or groups.  Examples would be treatment and control groups, or simply different specimens (red flowers vs. blue flowers).  Since my research is done with undergraduates, who are true novices with \texttt{R}, \texttt{ChemoSpec} is designed to be as user friendly as possible, with plenty of error checking, helpful warnings and a consistent interface.  It also produces graphics that are consistent in style and annotation, and are suitable for use in publications and posters.  Careful attention was given to writing the documentation for the functions, but this vignette serves as the best starting point for learning data analysis with \texttt{ChemoSpec}.

The centerpiece of \texttt{ChemoSpec} is the \texttt{Spectra} object.  This is the place where your data is stored and made available to \texttt{R}.  Once your data in stored this way and checked, all analyses are easily carried out.  \texttt{ChemoSpec} currently ships with several built-in data sets; we'll use one called \texttt{SrE.IR} for our demonstrations.  You will see in just a moment how to access it and inspect it.

I assume you have at least a bare-bones knowledge of \texttt{R} as you begin to learn \texttt{ChemoSpec}, and have a good workflow set up.  For detailed help on any function discussed here, type \texttt{?function\_name} at the console.

Finally, some conventions for this document:  names of \texttt{R} "objects" such as packages, functions, function arguments, and data sets are in \texttt{typewriter} font.  The commands you issue at the console and the output are shown with a light grey background, and are colored according to use and purpose, courtesy of the excellent \texttt{knitr} package.\cite{knitr-pkg}

By the way, if you try \texttt{ChemoSpec} and find it useful, have questions, have opinions, or have suggestions, please do let me know.  The version you are using already incorporates a great deal of user input, why not add yours?  Possible bugs and feature requests should be documented using the Github issues system at \href{http://github.com/bryanhanson/ChemoSpec/issues}{github.com/bryanhanson/ChemoSpec/issues}

\section{A Sample Workflow} %%%%%%%%%%%%%%%%
This sample exploration is designed to illustrate a typical \texttt{ChemoSpec} workflow.  The point is to illustrate how to carry out the commands, what options are available and typically used, and the order in which one might do the analysis.  The \texttt{SrE.IR} data set will be used for illustration only -- we are not trying to reach useful conclusions.  You may wish to put your versions of these commands into a script file that you can source as you go along.  This way you can easily make changes, and it will all be reproducible.  To do this, open a blank \texttt{R} document, and type in your commands.  Save it as something like \textcolor{blue}{My\_First\_ChemoSpec.R}.  Then you can either cut and paste portions of it to the console for execution, or you can source the entire thing:

<< Chunk1,  results = "hide", eval = FALSE>>=
source("My_First_ChemoSpec.R")
@

\subsection{Getting Data into ChemoSpec} %%%%%%%%%%%%%%%
Currently, there is only one means of moving raw data sets into \texttt{ChemoSpec}, and that is the function \texttt{files2SpectraObject} (it is relatively easy to write analogous functions for other formats).  This function assumes that your raw data files are formatted as .csv files, and contain only the data itself, in two columns.\footnote{Users in the EU have different standards for a .csv file: they are delimited by semi-colons, and a comma is used where a decimal point is used in the United States.  For these files, use the argument \texttt{format = "csv2"} to read the files properly.}  The first column should be the frequency values, and this column must be the same for all files (as it will be if these are data sets from the same instrument and experimental parameters).  The second column should contain the intensity values.  There should not be a header row.  If your data set contains treatment and control groups, or any analogous class/group information, this information should be encoded in the file names.  \texttt{files2SpectraObject} argument \texttt{gr.crit} will be the basis for a grep process on the file names, and from there, each file, representing a sample, will be assigned to a group and be assigned a color as well.  If your samples don't fall into groups, that's fine too, but you still have to give \texttt{gr.crit} something to go on---just give it one string that is common to all the file names.  Obviously, this approach encourages one to name the files as they come off the instrument with forethought as to how they will be analyzed, which in turn depends upon your experimental design.  Nothing wrong with having a plan!  Remember that \texttt{files2SpectraObject} acts on all .csv files it finds in a directory, so don't have any extra .csv files hanging around.  The output of \texttt{files2SpectraObject} is a \texttt{Spectra} object, which is \texttt{R}-speak for an object that contains not only your data, but other information about the experiment, as provided by you via the arguments to \texttt{files2SpectraObject}.

Here's a typical example (we have to talk hypothetically because I don't have your data).  Let's say you had a folder containing 30 NMR files of flower essential oils.  Imagine that 18 of these were from one hypothetical subspecies, and 12 from another.  Further, let's pretend that the question under investigation has something to do with the taxonomy of these two supposed subspecies, in other words, an investigation into whether or not they should be considered subspecies at all.  If the files were named like this:

\textcolor{blue}{sspA1.csv} \ldots \textcolor{blue}{sspA18.csv} and \textcolor{blue}{sspB1.csv} \ldots \textcolor{blue}{sspB12.csv}

Then the following command should process the files and create the desired \texttt{Spectra} object:

<< Chunk2,  results = "hide", eval = FALSE>>=
files2SpectraObject(gr.crit = c("sspA", "sspB"), gr.cols = c("red3", "dodgerblue4"),
freq.unit = "ppm", int.unit = "peak intensity", descrip = "Subspecies Study",
out.file = "subspecies")
@
	
This causes \texttt{files2SpectraObject} to inspect the file names for the strings \texttt{sspA} and \texttt{sspB} and use these to assign the samples into groups.  Samples in \textcolor{blue}{sspA*.csv} files will be assigned the color \texttt{red3} and \textcolor{blue}{sspB*.csv} will be assigned \texttt{dodgerblue4} (see Section~\ref{ColSym} for some suggestions about planning ahead on color choices, as well as \texttt{?colorSymbol}).   After running this command, a new file called \textcolor{blue}{subspecies.RData} will be in your directory, and you can access the data set and give it whatever name you like as follows (function \texttt{loadObject} is from package \texttt{R.utils}):

<< Chunk3,  results = "hide", eval = FALSE>>=
SubspeciesNMR <- loadObject("subspecies.RData")
@

Now it is ready to use.

\subsection*{Working with Chromatograms}

While all the language in this vignette and in the package are geared toward analysis of spectra, \texttt{ChemoSpec} can also work with chromatograms as the raw data.  In this case, time replaces frequency of course, but other than that the analysis is virtually the same.  So the only real difference is when you issue the command \texttt{files2SpectraObject}, you will give the frequency unit along these lines: \texttt{freq.unit = "time (minutes)"}.

\subsection*{Built-in Data Sets}

\texttt{ChemoSpec} ships with several built-in data sets. \texttt{SrE.IR} is the set used for this vignette.  It is composed of a collection of 14 IR spectra of essential oil extracted from the palm \emph{Serenoa repens} or Saw Palmetto, which is commonly used to treat BPH in men.  The 14 spectra are of different retail samples, and are divided into two categories based upon the label description: adSrE, adulterated extract, and pSrE, pure extract.  The adulterated samples typically have olive oil added to them, which has no effect on BPH.  There are two additional spectra included as references/outliers: evening primrose oil, labeled EPO in the data set, and olive oil, labeled OO.  These latter two oils are mixtures of triglycerides for the most part, while the SrE samples are largely fatty acids.  As a result, the spectra of these two groups differ: the glycerides have ester carbonyl stretches and no O--H stretch, while the fatty acids have acid carbonyl stretches and an O--H stretch consistent with a carboxylic acid OH.

Also included is \texttt{SrE.NMR} which is the corresponding set of NMR spectra, and \texttt{CuticleIR}.  The latter is a series of IR spectra of the cuticle (leaf surface) of the plant \emph{Portulaca oleracea}.  The data were taken by gently pinning the leaf against an ATR sampling device.  The plants were grown at two different temperatures, and two different genotypes (varieties) were used (a classic G x E, genotype by environment, experiment). 

The \texttt{SrE.IR} data set is used as the example in this vignette as the sample spectra are fairly different and give good separation by most chemometric methods.  The \texttt{CuticleIR} spectra differ in much more subtle ways and as as result are more of a challenge to analyze.  For more details about these data sets, type \texttt{?data\_set\_name} at the console.


\subsection{Preliminary Inspection of Data} %%%%%%%%%%%%%%%
\label{sec-prelim}

\emph{The} first thing you should do, and this is very important, is to make sure your data are in good shape.  First, you can summarize the data set you created, and verify that the data ranges and other details look like you expect them to:

<< Chunk5, echo = TRUE >>=
data(SrE.IR) # makes the data available
sumSpectra(SrE.IR)
@

\texttt{sumSpectra} provides several pieces of information, and we'll discuss some of them as we go along.

\subsubsection{Plotting the Spectra} %%%%%%%%%%%%%%%

Assuming that everything looks good so far, it's time to plot the spectra and inspect them.  A good practice would be to check every spectrum for artifacts and other potential problems.  The function \texttt{LoopThruSpectra} takes the pain out of inspecting quite a few spectra.  See the help page for details.  However, for plotting just a few spectra, you should use \texttt{plotSpectra}.   A basic plot is shown in Figure~\ref{plot}.  In this case we have chosen to plot one spectrum from each category.  Note that the carbonyl and $\rm C_{sp2}-H$ regions are clearly different in these samples.

<< Chunk8, fig.cap = "\\label{plot}Plotting Spectra" >>=
# We'll make a fancy title here and re-use in other plots
myt <- expression(bolditalic(Serenoa)~bolditalic(repens)~bold(Extract~IR~Spectra))
plotSpectra(SrE.IR, main = myt,
which = c(1, 2, 14, 16),
yrange = c(0, 1.6), offset = 0.4, lab.pos = 2200)
@

Depending upon the intensity range of your data set, and the number of spectra to be plotted, you have to manually adjust the arguments \texttt{yrange}, \texttt{offset} and \texttt{amplify}, but this usually only takes a few iterations.  Keep in mind that  \texttt{offset}, and \texttt{amplify} are multiplied in the function, so if you increase one, you may need to decrease the other.  Suppose that you wanted to focus just on the carbonyl region of these spectra; you can add the argument  \texttt{xlim}.  To demonstrate, let's look at fewer spectra, and at higher amplitude, so we can see details, as shown in Figure~\ref{subplot}.


<< Chunk10, fig.cap = "\\label{subplot}Zooming in on a Spectral Region" >>=
plotSpectra(SrE.IR, main = myt,
which = c(1, 2, 14, 16), xlim = c(1650, 1800),
yrange = c(0, 0.6), offset = 0.1, lab.pos = 1775)
@

These sample plots display the IR spectra in two ways that may be upsetting to some readers: First, the x-axis is "backwards", because the underlying spectra were originally saved with an ascending frequency axis (which is not always the case).  This is readily fixed by supplying the \texttt{xlim}  argument in the desired order, e.g. \texttt{xlim = c(1800, 1650)} in the previous example.  Second, the vertical scale in these examples is absorbance.  When using IR for structural elucidation, the vertical axis is typically \%T, with the peaks pointing downward.  You don't have that choice in \texttt{ChemoSpec} because the absorbance mode is the appropriate one for chemometrics.  Record your original spectra that way and get used to it.

The argument \texttt{which} in \texttt{plotSpectra} takes a numerical list of the spectra you wish to plot--- you can think of this as the row number if you imagine each spectra to be a row in a matrix, with intensities in the columns (with each column corresponding to a particular frequency value).  You may be wondering how to determine which particular sample is in each row.  This is best accomplished with a grep command.  For instance, if you wanted to know what row/sample the olive oil was in, the following methods would locate it for you:

<< Chunk9 >>=
SrE.IR$names # suitable if there are not many spectra
grep("OO", SrE.IR$names) # use if there are more spectra
@

\subsection{Data Pre-Processing Options} %%%%%%%%%%%%%%%

There are a number of data pre-processing options available for your consideration.  The main choices are whether to normalize the data, whether to bin the data, and whether to scale the data.  Data scaling is handled by the PCA routines, see Section~\ref{sec-pca}.

\subsubsection{Normalization} %%%%%%%%%%%%%%%

Normalization is handled by the \texttt{normSpectra} function.  Usually one normalizes data in which the sample preparation procedure may lead to differences in concentration, such as body fluids that might have been diluted during handling, or that vary due to the physiological state of the organism studied.  The \texttt{SrE.IR} data set is taken by placing the oil extract directly on an ATR device and no dilution is possible, so normalization probably isn't really appropriate.  Currently, there are two normalization options.  The default option is probabalistic quotient normalization (need ref).  The alternative is to divide each point (frequency) in a spectrum by the sum of all points in that spectrum, which is known as normalizing to total intensity.  Normalization is accomplished by the following code (which we won't actually run):

<< Chunk17, eval = FALSE, echo = TRUE >>=
not_wanted <- normSpectra(SrE.IR)
@

But remember, this doesn't make sense for this data set.  The literature contains a number of useful discussions about normalization issues.\cite{Scale-Norm-Nicholson, NMR-Norm, Cent-Scale-Norm, Filz, Raftery-Signal-Processing}

\subsubsection{Bucketing or Binning} %%%%%%%%%%%%%%%

Another type of pre-processing that you may wish to consider is binning or bucketing, in which groups of frequencies are collapsed into one frequency value, and the corresponding intensities are summed.  There are two reasons for doing this.  One is to compact the data, but the algorithms in \texttt{R} are quite fast, and data sets of the size of \texttt{SrE.IR} or even the much larger \texttt{SrE.NMR} don't slow it down much.  The other reason is to compensate for shifts in very narrow peaks from sample to sample.  This is typically done with aqueous $\rm ^{1}H $ NMR samples because changes in dilution, ionic strength, or pH can cause signficant shifts for some types of protons. Spectra with broad, rolling peaks won't have this problem (UV-Vis for example).  The function \texttt{binBuck} is your friend.  This example illustrates the process but is not really necessary with IR data:

<< Chunk18 >>=
tmp <- binBuck(SrE.IR, bin.ratio = 4)
sumSpectra(tmp)
@

Compare the results here with the \texttt{sumSpectra} of the full data set (Section~\ref{sec-prelim}). In particular note that the frequency resolution has gone down due to the binning process.  \texttt{ChemoSpec} uses the simplest of binning algorithms: after perhaps dropping a few points (with a warning) to make your data set divisible by the specified \texttt{bin.ratio}, data points are replaced by the average frequency and the sum of the grouped intensities.  Depending upon the fine structure in your data and the \texttt{bin.ratio} this might cause important peaks to be split between different bins.  There are more sophisticated binning algorithms in the literature that try to address this, but none are currently implemented in \texttt{ChemoSpec}.\cite{Gaussian-binning, Adaptive-binning}

\subsubsection{Correcting Baseline Drift} %%%%%%%%%%%%%%%

\texttt{ChemoSpec} uses the functions in the package \texttt{baseline} to correct wandering baselines.  The function, \texttt{baselineSpec}, can operate interactively or not.  Figure~\ref{baseline} shows a typical usage.  Method \texttt{rfbaseline} works well for IR spectra; \texttt{retC = TRUE} puts the corrected spectra into the new \texttt{Spectra} object so we can use it going forward (and we will).


<< Chunk10b, fig.cap = "\\label{baseline}Correcting baseline drift"  >>=
SrE2.IR <- baselineSpec(SrE.IR, int = FALSE, method = "rfbaseline", retC = TRUE)
@

\subsection{Identifying \& Removing Problematic Samples} %%%%%%%%%%%%%%%

In the process of plotting and inspecting your spectra, you may find some spectra/samples that have problems.  Perhaps they have instrumental artifacts.  Or maybe you have decided to eliminate one subgroup of samples from your data set to see how the results differ.  To  remove a particular sample, or samples meeting a certain criteria, you use the \texttt{removeSample} function.  This function uses a grepping process based on its \texttt{rem.sam} argument, so you must be careful due to the greediness of grep.  Let's imagine that sample TD\_adSrE has artifacts and needs to be removed.  The command would be:

<<  Chunk11 >>=
noTD <- removeSample(SrE2.IR, rem.sam = c("TD_adSrE"))
sumSpectra(noTD)
grep("TD_adSrE", noTD$names)
@

The \texttt{sumSpectra} command confirms that there are now one fewer spectra in the set.  As shown, you could also re-grep for the sample name to verify that it is not found.  The first argument in \texttt{grep} is the pattern you are searching for; if that pattern matches more than one name they will all be "caught."  For example if you used "SrE" as your pattern you would remove all the samples except the two reference samples, since "SrE" occurs in "adSrE" and "pSrE".  You can check this in advance with the grep function itself:

<< Chunk12 >>=
SrE <- grep("SrE", SrE2.IR$names)
SrE2.IR$names[SrE] # gives the name(s) that contain "SrE"
SrE # gives the corresponding indicies
@

This is what is meant by "grep is greedy".  In this situation, you have three choices:
\begin{enumerate}

\item You could manually remove the problem samples (\texttt{str(SrE2.IR)}) would give you an idea of how to do that; see also below under Hierarchical Cluster Analysis).

\item \texttt{removeSample} also accepts indices of samples, so you could grep as above, note the index of the sample you actually want to remove, and use that in \texttt{rem.sam}.

\item If you know a bit about grep and regex, you can pass a more sophisticated search pattern to \texttt{rem.sam}. 

\end{enumerate}

\subsubsection{Removing Groups} %%%%%%%%%%%%%%%

\texttt{removeSample} uses the names of the samples (in \texttt{Spectra\$names}) to identify and remove individual samples from the \texttt{Spectra} object.  There is also a function \texttt{removeGroup} which will remove samples belonging to a particular group in \texttt{Spectra\$groups}.

\subsubsection{Identifying \& Removing Regions of No Interest} %%%%%%%%%%%%%%%

Many spectra will have regions that should be removed before analysis.  It may be an uninformative, interfering peak like the water peak in $\rm ^{1}H$ NMR, or the $\rm CO_2$ peak in IR.  Or, there may be regions of the spectra that simply don't have much information -- they contribute a noisy baseline and not much else.  An example would be the region from about 1,800 or 1,900 $\rm cm^{-1} $ to about 2,500 $\rm cm^{-1} $ in IR, a region where there are typically no peaks except for the atomospheric $\rm CO_2$ stretch, and rarely (be careful!) alkyne stretches.

Finding these regions might be pretty simple, a matter of inspection coupled with your knowledge of spectroscopy.  Another approach is to use the function \texttt{specSurvey} to examine the entire set of spectra.  This function computes a summary statistic (your choice) of the intensities at a particular frequency across the data set, as well as the mean or median.  In regions with little variation, the mean/median and upper/lower summary lines will be close together.  Figure~\ref{surv} demonstrates the process.


<< Chunk14,  fig.width = 8, fig.height = 5, fig.cap = "\\label{surv}Checking for Regions of No Interest" >>=
specSurvey(SrE2.IR, method = "iqr", main = "S. repens Extract IR Spectra", by.gr = FALSE)
@

In Figure~\ref{surv} we kept all the groups together by using argument \texttt{by.gr = FALSE}.  We also looked at the entire spectral range.  In Figure~\ref{survA} we can look just at the carbonyl region.  The black line is the median value of intensity across the entire set of spectra.  The red lines are the upper and lower interquartile ranges which makes it pretty clear that the carbonyl region of this data set varies a lot.


<< Chunk14a, fig.cap = "\\label{survA}Detail of Carbonyl Region"  >>=
specSurvey(SrE2.IR, method = "iqr", main = "S. repens Detail of Carbonyl Region",
by.gr = FALSE, xlim = c(1650, 1800))
@


Finally, \texttt{specSurvey} allows us to view the data set by group, which is really more useful.  Let's look at the carbonyl region by group (Figure~\ref{survB}). Note that we get warnings because two of the groups have too few members to compute the interquartile range, and these are not shown.  As a result, some panels are empty.


<< Chunk14b, fig.cap = "\\label{survB}Detail of Carbonyl Region by Group"  >>=
specSurvey(SrE2.IR, method = "iqr", main = "S. repens Detail of Carbonyl Region",
by.gr = TRUE, xlim = c(1650, 1800))
@

For reasons that will become evident in a moment, let's look at the region between 1800 and 2500 $\rm cm^{-1} $ (Figure~\ref{survC}).

<< Chunk14c, fig.cap = "\\label{survC}Inspection of an Uninteresting Spectral Region"  >>=
specSurvey(SrE2.IR, method = "iqr", main = "S. repens Detail of Empty Region",
by.gr = FALSE, xlim = c(1800, 2500), ylim = c(0.0, 0.05))
@

From a theoretical perspective, we expect this region to be devoid of interesting peaks.  In fact, even when pooling the groups the signal in this region is very weak, and the only peak present is due to atomospheric $\rm CO_2 $.  We can remove this region, since it is primarily noise and artifact, with the function \texttt{removeFreq} as follows. Note that there are fewer frequency points now.

<< Chunk15 >>=
SrE3.IR <- removeFreq(SrE2.IR, rem.freq = SrE2.IR$freq > 1800 & SrE2.IR$freq < 2500)
sumSpectra(SrE3.IR)
@

Notice that \texttt{sumSpectra} has identified a gap in the data set.  You can see this gap in the data as shown in Figure~\ref{gaps} (\texttt{sumSpectra}  checks for gaps, but doesn't produce the plot); both the numerical results and a figure are provided.


<< Chunk7, fig.cap = "\\label{gaps}Procedure to Find Gaps in a Data Set" , tidy = FALSE >>=
check4Gaps(SrE3.IR$freq, SrE3.IR$data[1,], plot = TRUE)
@


\subsection{Hierarchical Cluster Analysis} %%%%%%%%%%%%%%%
\label{sec-hca}

Hierarchical cluster analysis (HCA from  now on) is a clustering method (no surprise!) in which "distances" between samples are calculated and displayed in a dendrogram (a tree-like structure; these are also used in evolution and systematics where they are called cladograms).  The details behind HCA can be readily found elsewhere (Chapter 6 of \cite{Filz} is a good choice).  With \texttt{ChemoSpec} you have access to any of the methods available for computing distances between samples and any of the methods for identifying clusters.  A typical example is shown in Figure~\ref{hca}.


<< Chunk19, fig.cap = "\\label{hca}Hierarchical Cluster Analysis" >>=
HCA <- hcaSpectra(SrE3.IR, main = "S. repens IR Spectra")
@

The result is a dendrogram.  The vertical scale represents the numerical distance between samples.  Not unexpectedly, the two reference samples which are known to be chemically different cluster together separately from all other samples.  Perhaps surprisingly, the various pure and adulterated oil extracts do not group together precisely.  The function \texttt{hcaScores} does the same kind of analysis using the results of PCA, rather than the raw spectra.  It is discussed in the next section.

\subsection{Principal Components Analysis} %%%%%%%%%%%%%%%
\label{sec-pca}

Principal components analysis (PCA from now on) is the real workhorse of exploratory data analysis.  It makes no assumptions about group membership, but clustering (possibly in high dimensions) of the resulting sample scores can be very helpful in understanding your data.  The theory and practice of PCA is covered well elsewhere (Chapter 3 of \cite{Filz} is an excellent choice).  Here, we'll concentrate on using the PCA methods in \texttt{ChemoSpec}.  Briefly however, you can think of PCA as determining the minimum number of components necessary to describe a data set, in effect, removing noise.  Think of a typical spectrum:  some regions are clearly just noise.  Further, a typical spectroscopic peak spans quite a few frequency units as the peak goes up, tops out, and then returns to baseline.  Any one of the points in a particular peak describe much the same thing, namely the intensity of the peak.  Plus, each frequency within a given peak envelope is correlated to every other frequency in the envelope (they rise and fall in unison as the peak changes size from sample to sample).  PCA can look "past" all the noise and underlying correlation in the data set, and boil the entire data set down to essentials.  Unfortunately, the principal components that are uncovered in the process don't correspond to anything concrete, usually.  Again, you may wish to consult a more detailed treatment!

Table~\ref{opt} gives an overview of the options available in \texttt{ChemoSpec}, and the relevant functions.

\begin{table}
\caption{Principal Components Analysis Options \& Functions}
\label{opt}
\begin{center}
\begin{tabular}{|ll|l|}
\hline
\textbf{PCA options} & scaling options & function\\
\hline
classical PCA &  no scaling, autoscaling, Pareto scaling & \texttt{classPCA} \\
robust PCA & no scaling, median absolute deviation & \texttt{robPCA} \\
&&\\
\textbf{Diagnostics} &  & \\
\hline
OD plots & & \texttt{pcaDiag} \\
SD plots & & \texttt{pcaDiag}\\
&&\\
\textbf{Choosing the correct no. of PCs} & & \\
\hline
scree plot & & \texttt{plotScree}\\
alternate style scree plot & & \texttt{plotScree2}\\
bootstrap analysis (classical PCA only) & & \texttt{pcaBoot} \\
&&\\

\textbf{Score plots} & plotting options &  \\
\hline
2D plots & robust or classical confidence ellipses & \texttt{plotScores} \\
3D plots && \\
---static 3D plots & & \texttt{plotScores3D}\\
---interactive 3D plots & & \texttt{plotScoresRGL}\\
&&\\
\textbf{Loading plots} & & \\
\hline
loadings vs frequencies & & \texttt{plotLoadings} \\
loadings vs other loadings & & \texttt{plot2Loadings} \\
s-plot (correlation vs covariance) & & \texttt{sPlotSpectra} \\
&&\\
\hline
\textbf{Other} &&\\
HCA of PCA scores & & \texttt{hcaScores} \\
ANOVA-PCA & & \texttt{aovPCA} \\
\hline
\end{tabular}
\end{center}
\end{table}


There's quite a bit of choice here; let's work through an example and illustrate, or at least mention, the options as we go.  Keep in mind that it's up to you to decide how to analyze your data.  Most people try various options, and follow the ones that lead to the most insight.  But the decision is yours!

The first step is to carry out the PCA.  You have two main options, either classical methods, or robust methods.  Classical methods use all the data you provide to compute the scores and loadings.  Robust methods focus on the core or heart of the data, which means that some samples may be downweighted.  This difference is important, and the results from the two methods may be quite different, depending upon your the nature of your data.  The differences arise because PCA methods (both classical and robust) attempt to find the components that explain as much of the variance in the data set as possible.  If you have a sample that is genuinely corrupted, for instance due to sample handling, its spectral profile may be very different from all other samples, and it can legitimately be called an outlier.  In classical PCA, this one sample will contribute strongly to the variance of the entire data set, and the PCA scores will reflect that (it is sometimes said that scores and loadings follow the outliers).  With robust PCA, samples with rather different characteristics do not have as great an influence, because robust measures of variance, such as the median absolute deviation, are used.

Note that neither \texttt{classPCA} nor \texttt{robPCA} carry out any normalization by samples.  You need to decide if you want to normalize the samples, and if so, use \texttt{normSpectra}.

Besides choosing to use classical or robust methods, you also need to choose a scaling method.  For classical PCA, your choices are no scaling, autoscaling, or Pareto scaling.  In classical analysis, if you don't scale the data, large peaks contribute more strongly to the results.  If you autoscale, then each peak contributes equally to the results (including noise "peaks").  Pareto scaling is a compromise between these two.  For robust PCA, you can choose not to scale, or you can scale according to the median absolute deviation.  Median absolute deviation is a means of downweighting more extreme peaks.  The literature has plenty of recommendations about scaling options appropriate for the type of measurement (instrument) as well as the nature of the biological data set.\cite{Raftery-Signal-Processing, Scale-Norm-Nicholson, NMR-Norm, Cent-Scale-Norm, Filz, Error-Struc-NMR}

There is not enough space here to illustrate all possible combinations of options; Figure~\ref{classPCA} and FIgure~\ref{robPCA} show the use and results of classical and robust PCA without scaling, followed by plotting of the first two PCs (we'll discuss plotting options momentarily).  You can see from these plots that the robust and classical methods have produced rather different results, not only in the overall appearance of the plots, but in the amount of variance explained by each PC.

Since we've plotted the scores to see the results, let's mention a few features of \texttt{plotScores} which produces a 2D plot of the results (we'll deal with 3D options later).  Note that an annotation is provided in the upper left corner of the plot that describes the history of this analysis, so you don't lose track of what you are viewing.  The \texttt{tol} argument controls what fraction of points are labeled with the sample name.  This is a means of identifying potential outliers.  The \texttt{ellipse} argument determines if and how the ellipses are drawn (the 95\% confidence interval is used).

You can choose \texttt{"none"} for no ellipses, \texttt{"cls"} for classically computed confidence ellipses, \texttt{"rob"} for robustly computed ellipses, or \texttt{"both"} if you want to directly compare the two.  Note that the use of classical and robust here has nothing to do with the PCA algorithm --- it's the same idea however, but applied to the 2D array of scores produced by PCA.  Points outside the ellipses are more likely candidates for outlier status.


<< Chunk10a, fig.cap = "\\label{classPCA}Classical PCA" >>=
class <- classPCA(SrE3.IR, choice = "noscale")
plotScores(SrE3.IR, main = "S. repens IR Spectra", class,
pcs = c(1,2), ellipse = "rob", tol = 0.01)
@

<< Chunk21, fig.cap = "\\label{robPCA}Robust PCA" >>=
robust <- robPCA(SrE3.IR, choice = "noscale")
plotScores(SrE3.IR, main = "S. repens IR Spectra", robust,
pcs = c(1,2), ellipse = "rob", tol = 0.01)
@

Plots such as shown in Figures~\ref{classPCA} and \ref{robPCA} can give you an idea of potential outliers, but \texttt{ChemoSpec} includes more sophisticated approaches.  The function \texttt{pcaDiag} can produce two types of plots that can be helpful (Figures~\ref{OD} and \ref{SD}).  The meaning and interpretation of these plots is discussed in more detail in Varmuza and Filzmoser, Chapter 3.\cite{Filz}


<< Chunk22, fig.cap = "\\label{OD}Diagnostics: Orthogonal Distances"  >>=
diagnostics <- pcaDiag(SrE3.IR, class, pcs = 2, plot = "OD")
@

<< Chunk23, fig.cap = "\\label{SD}Diagnostics: Score Distances" >>=
diagnostics <- pcaDiag(SrE3.IR, class, pcs = 2, plot = "SD")
@

Depending upon your data, and your interpretation of the results, you may decide that some samples should be discarded, in which case you can use \texttt{removeSample} as previously described, then repeat the PCA analysis.  The next step for most people is to determine the number of PCs needed to describe the data.  This is usually done with a scree plot as shown in Figure~\ref{scree}.  \texttt{ChemoSpec} has an alternate style scree plot which I actually think is much more informative (Figure~\ref{scree2}).

If you are using classical PCA, you can also get a sense of the number of PCs needed via a bootstrap method, as shown in Figure~\ref{boot}. Note that this method is iterative and takes a bit of time.  Comparing these results to the scree plots, you'll see that the bootstrap method suggests that 4 or 5 PCs would not always be enough to reach the 95\% level, while the scree plots suggest that 2 PC are sufficient.


<< Chunk24, fig.cap = "\\label{scree}Scree Plot" >>=
plotScree(class, main = "S. repens IR Spectra")
@

<< Chunk24a, fig.cap = "\\label{scree2}Alternate Style Scree Plot"  >>=
plotScree2(class, main = "S. repens IR Spectra")
@

<< Chunk25, fig.cap = "\\label{boot}Bootstrap Analysis for No. of PCs"  >>=
out <- pcaBoot(SrE3.IR, pcs = 5, choice = "noscale")
@

Now let's turn to viewing scores in 3D.  There are currently two options in \texttt{ChemoSpec}: plotting using \texttt{lattice} graphics, which produces a static plot that you have to adjust manually, and an interactive plot based on package \texttt{rgl}.  Probably the best place to start is with \texttt{plotScoresRGL}.  It it well suited to exploring data, and can be printed out in high quality.  However, the nature of the open GL graphics device means that the title and the legend move with the data, so this may not give a hardcopy suitable for publications.  This interactive plot cannot be invoked in this document, but here are the necessary commands:

<< Chunk26,  results = "hide", eval = FALSE >>=
plotScoresRGL(SrE3.IR, class, main = "S. repens IR Spectra",
leg.pos = "A", t.pos = "B") # not run - it's interactive!
@

For full details, of course take a look at the manual page, \texttt{?plotScoresRGL}.  If you want a similar and probably more publication-worthy plot, you can use \texttt{plotScores3D} as shown in Figure~\ref{s3D}.  In this example we've set \texttt{ellipse = FALSE} because the "adSrE" data points form a very elongated ellipse which forces the plotting limits in such a way that other points become very hard to see.


<< Chunk27, fig.cap = "\\label{s3D}Plotting Scores in 3D using plotScores3D"   >>=
plotScores3D(SrE3.IR, class, main = "S. repens IR Spectra", ellipse = FALSE)
@

In addition to the scores, PCA also produces loadings which tell you how each variable (frequencies in spectral applications) affect the scores.  Examining these loadings can be critical to interpreting your results.  Figure~\ref{load} gives an example.  You can see that the different carbonyl peaks have a large and opposing effect on PC 1.  PC 2 on the other hand is driven by a number of peaks, with some interesting opposing peaks in the hydrocarbon region.  While the actual analysis of the data is not our goal here, it would appear that PC 1 is sensitive to the ester vs. acid carbonyl group, and PC 2 is detecting the saturated vs. unsaturated fatty acid chains (the latter having $\rm C_{sp2}-H $ peaks).


<< Chunk29, fig.cap = "\\label{load}Loading Plot"  >>=
plotLoadings(SrE3.IR, class, main = "S. repens IR Spectra",
loads = c(1, 2), ref = 1)
@

You can also plot one loading against another, using function \texttt{plot2Loadings} (Figure~\ref{load2}).  This is typically not too useful for spectroscopic data, since many of the variables are correlated (as they are parts of the same peak, hence the serpentine lines in the figure).  The most extreme points on the plot, however, can give you an idea of which peaks (frequencies) serve to differentiate a pair of PCs, and hence, drive your data clustering.


<< Chunk30, fig.cap = "\\label{load2}Plotting One Loading vs. Another"   >>=
plot2Loadings(SrE3.IR, class, main = "S. repens IR Spectra",
loads = c(1, 2), tol = 0.002)
@

However, a potentially more useful approach is to use an s-plot to determine which variables have the greatest influence.  A standard loadings plot (\texttt{plotLoadings}) shows you which frequency ranges contribute to which principal components, but the plot allows the vertical axis to be free.  Unless you look at the y axis scale, you get the impression that the loadings for principal component 1 etc. all contribute equally.  The function \texttt{sPlotSpectra} plots the correlation of each frequency variable with a particular score against the covariance of that frequency variable with the same score.  The result is an s-shaped plot with the most influential frequency variables in the upper right hand and lower left quadrants.  An example is shown in Figures~\ref{splot} and \ref{splot2}.  In the latter figure you can clearly see the influence of the carbonyl peaks.  This method was reported in Wiklund \emph{et. al.}\cite{Wiklund2008}


<< Chunk30a,  fig.cap = "\\label{splot}s-Plot to Identify Influential Frequencies"  >>=
spt <- sPlotSpectra(SrE3.IR, class, main = "S. repens IR Spectra", pc = 1, tol = 0.001)
@

<< Chunk30b,  fig.cap = "\\label{splot2}s-Plot Detail"  >>=
spt <- sPlotSpectra(SrE3.IR, class, main = "Detail of S. repens IR Spectra", pc = 1, tol = 0.05, xlim = c(-0.04, -0.01), ylim = c(-1.05, -0.9))
@

Finally, you can blend the ideas of PCA and HCA.  Since PCA eliminates the noise in a data set (after you have selected the important PCs), you can carry out HCA on the PCA scores, since the scores represent the cleaned up data.  The result using the \texttt{SrE.IR} data set are not different than doing HCA on the raw spectra, so we won't illustrate it, but the command would be:

<< Chunk31,  results = "hide", eval = FALSE >>=
hcaScores(SrE3.IR,  class, scores = c(1:5), main = "S. repens IR Spectra")
@

\subsection{ANOVA-PCA}  %%%%%%%%%%%%%%%

Harrington \emph{et. al.}\cite{Harrington2005} (and a few others\cite{Pinto2008}) have demonstrated a method which combines traditional ANOVA with PCA.  Standard PCA is blind to class membership, though one generally colors the points in a score plot using the known class membership.  ANOVA-PCA uses the class membership to divide the original centered data matrix into submatrices.  Each submatrix corresponds to a particular factor, and the rows of the submatrix have been replaced by the average spectrum of each level of the factor.  The original data set is thought of as a sum of these submatrices plus residual error.  The residual error is added back to each submatrix and then PCA is performed.  This is conceptually illustrated in Figures~\ref{aovPCA2} and \ref{aovPCA1}.

\begin{figure}
\begin{center}
\scalebox{0.75}{\includegraphics{aovPCA2}}
\caption{\label{aovPCA2}aovPCA breaks the data into a series of submatrices}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\scalebox{0.75}{\includegraphics{aovPCA1}}
\caption{\label{aovPCA1}Submatrices are composed of rows which are averages of each factor level}
\end{center}
\end{figure}

ANOVA-PCA has been implemented in \texttt{ChemoSpec} via the functions \texttt{aovPCA}, \texttt{aovPCAscores} and \texttt{aovPCAloadings}.   The idea here is that if a factor is significant, there will be separation along PC1 in a plot of PC1 vs PC2.  Unfortunately, there are not enough groups and levels within the \texttt{SrE.IR} data set to carry out ANOVA-PCA.  However, the help page for \texttt{aovPCA} contains an example using the \texttt{CuticleIR} data set which illustrates how to carry out the analysis.  It also demonstrates another useful function, \texttt{splitSpectraGroups} which allows you to take an existing group designation and split into new designations.  See \texttt{\textsl{?aovPCA}}.

\subsection{Model-Based Clustering Using mclust}  %%%%%%%%%%%%%%%

PCA and HCA are techniques which are unsupervised and assume no underlying model.  HCA computes distances between pairs of spectra and groups these in an iterative fashion until the dendrogram is complete.  PCA seeks out components that maximize the variance.  While in PCA one often (and \texttt{ChemoSpec} does) displays the samples coded by their group membership, this information is not actually used in PCA; any apparent correspondence between the sample group classification and the clusters found is accidental in terms of the computation, but of course, this is what one hopes to find!

\texttt{mclust} is a model-based clustering package that takes a different approach.\cite{mclust-pkg, mclust-art}.  \texttt{mclust} assumes that there are groups within your data set, and that those groups are multivariate normally distributed.  Using an iterative approach, \texttt{mclust} samples various possible groupings within your data set, and uses a Bayesian Information Criterion (BIC) to determine which of the various groupings it finds best fits the data distribution. \texttt{mclust} looks for groups that follow certain constraints, for instance, one constraint is that all the groups found must have a spherical distribution of data points, while another allows for ellipsoidal distributions.  See the paper by Fraley and Raftery\cite{mclust-art} for more details.  The basic idea however is that \texttt{mclust} goes looking for groups in your data set, and then you can compare the groupings it finds with the groupings you know to be true.

\texttt{ChemoSpec} contains several functions that interface with and extend \texttt{mclust} functions.  \texttt{mclust} first uses the BIC to determine which model best fits your data; these results are shown in Figure~\ref{mclust1}.  Next, Figure~\ref{mclust2} shows the 5 groups that \texttt{mclust} finds in the data which actually is composed of 4 groups (though admittedly, two of those groups are composed of one member each; these are labeled "e").  It's of some interest to visually compare the score plot in Figure~\ref{classPCA} with the \texttt{mclust} results in Figure~\ref{mclust2}.  Next, \texttt{mclust} will map the true groups onto the groups it has found.  Points in error are X-ed out.  These results can be seen in Figure~\ref{mclust3}.  From this plot, you can see that \texttt{mclust} finds 4 groups among the two true groups "adSrE" and "pSrE".  In general, you have to be very careful about using \texttt{mclust}'s notion of an error:  it is very hard to map the found groups onto the "truth" in an algorithmic way.  I lean toward not using the "truth" option in \texttt{mclust} more and more.


<<  Chunk35, fig.cap = "\\label{mclust1}mclust Chooses an Optimal Model" >>=
model <- mclustSpectra(SrE3.IR, class, plot = "BIC",
main = "S. repens IR Spectra")
@

<< Chunk36, fig.cap = "\\label{mclust2}mclust's Thoughts on the Matter"  >>=
model <- mclustSpectra(SrE3.IR, class, plot = "proj",
main = "S. repens IR Spectra")
@

<< Chunk37, fig.cap = "\\label{mclust3}Comparing mclust Results to the TRUTH"  >>=
model <- mclustSpectra(SrE3.IR, class, plot = "errors",
main = "S. repens IR Spectra", truth = SrE3.IR$groups)
@

You can also do a similar analysis in 3D, using \texttt{mclust3dSpectra}.  This function uses \texttt{mclust} to find the groups, but then uses non-\texttt{mclust} functions to draw confidence ellipses.  This function uses \texttt{rgl} graphics so it cannot demonstrated here, but the commands would be:

<< Chunk33,  results = "hide", eval = FALSE >>=
mclust3dSpectra(SrE3.IR, class) # not run - it's interactive!
@

You have all the options here that you do with \texttt{plotScoresRGL}, namely, classical, robust or no ellipses, control of the ellipse details, and labeling of extreme points.

I hope you have enjoyed this tour of the features of \texttt{ChemoSpec}!

\section{Functions That Are Not Discussed Here} %%%%%%%%%%%%%%%

See the help files of course  \ldots

\begin{enumerate}
  \item \texttt{splitSpectraGroups}  A good example of its use can be found in \texttt{\textsl{?aovPCA}}.
  \item \texttt{hypTestScores}
  \item \texttt{hmapSpectra}
  \item \texttt{evalClusters}
  \item \texttt{clupaSpectra}
\end{enumerate}

\section{Colors and Symbol Options}  %%%%%%%%%%%%%%%
\label{ColSym}

In \texttt{ChemoSpec}, the user may use any color name/format known to R.  For ease of comparison, it would be nice to plan ahead and use the same color scheme for all your plots.  However, if you are just doing preliminary work, \texttt{ChemoSpec} will choose colors for you automatically.

In addition to colors, \texttt{"Spectra"} objects also contain a list of symbols, and alternative symbols.  These are useful for plotting in black and white, or when color-blind individuals will be viewing the plots.  The alternative symbols are simply lower-case letters, as these are needed for \texttt{plotScoresRGL}, and other \texttt{rgl}-graphics driven functions which cannot plot traditional symbols. 

Two recommended color schemes are shown in Figure~\ref{colors}.  By name, these are:

\begin{quote}
primary scheme: c("red3", "dodgerblue4", "forestgreen", "purple4", "orangered", "yellow", "orangered4", "violetred2")

pastel scheme: c("seagreen", "brown2", "skyblue2", "hotpink3", "chartreuse3", "darkgoldenrod2", "lightsalmon3", "gray48")
\end{quote}

Finally, the current color scheme of a \texttt{Spectra} object may be determined using \texttt{sumSpectra} or changed using \texttt{conColScheme}.


<<  Chunk4,  echo = FALSE, fig.width = 6, fig.height = 4, fig.cap = "\\label{colors}Recommended Color Sets in ChemoSpec" >>=
par(mfrow = c(2,1), mar = c(3, 1, 2, 1))
display.brewer.pal(8, "Set1")
title(main = "ChemoSpec Primary Scheme")
display.brewer.pal(8, "Set2")
title(main = "ChemoSpec Pastel Scheme")
par(mfrow = c(1,1))
@

\section{Technical Background} %%%%%%%%%%%%%%%

\texttt{ChemoSpec} is written entirely in \texttt{R}, there is no compiled code.  Hence, it should be platform independent (please let me know if you discover otherwise).  \texttt{ChemoSpec} uses \texttt{S3} classes under the hood because frankly they were much faster to write.  For the pros and cons of classes and object-oriented programming in \texttt{R}, see the help archives (search my name for one thread and some really interesting replies from the big dogs).  \texttt{ChemoSpec} employs several different graphics packages - the choice was one of practicality.  In general, I tried to make all the graphics output look similar for consistency.

In understanding the operation of a package, it is useful to know how the functions relate to each other, i.e., which functions call each other.  These relationships are readily visualized with a diagram like Figure~\ref{food}.  This was generated by first using the \texttt{foodweb} function in package \texttt{mvbutils}\cite{mvb-pkg}, then removing the links to function \texttt{chkSpectra} which generates a lot of clutter since nearly all functions in \texttt{ChemoSpec} call it.  Finally, the resulting adjacency matrix was converted into a graph by \texttt{gplot} in package \texttt{sna}\cite{Butts2010}.


<< Chunk38,  echo = FALSE, fig.cap = "\\label{food}Map of Functions in ChemoSpec", fig.width = 10, fig.height = 10  >>=
CS <- foodweb(where = "package:ChemoSpec", plotting = FALSE)
CS$funmat <- CS$funmat[-9, -9] # removes chkSpectra
set.seed(7) # 7, 9, 19 decent
tst <- gplot(CS$funmat, displaylabels = TRUE, label.cex = 0.6,
	arrowhead.cex = 0.5, label.pos = 6, pad = 1.5)
@

\section{Acknowledgements} %%%%%%%%%%%%%%%

The development of \texttt{ChemoSpec} began while I was on sabbatical in 2007-2008, and was aided greatly by an award of a Fisher Fellowship.  These programs are coordinated by the Faculty Development Committee at DePauw, and I am very grateful to them as well as the individuals who originally created these programs.  One of my student researchers, Kelly Summers, took the data included in \texttt{CuticleIR} in the summer of 2009 as part of a preliminary study.  I am also grateful to Prof. Peter Filzmoser who answered a number of my questions related to the algorithms in his \texttt{chemometrics} package.  Finally, Roberto Canteri of the Fundazione Bruno Kessler (Italy) brought some small bugs to my attention, and made some good suggestions for improving the underlying code.  I am grateful to Roberto for assistance!  For additional contributors, please see the NEWS file and the Github issues tracker.

\section{Related Packages} %%%%%%%%%%%%%%%

Several other packages exist which do some of the same tasks as \texttt{ChemoSpec}, and do other things as well.  The package closest in functionality to \texttt{ChemoSpec} is  \texttt{hyperSpec} written by my friend and collaborator Claudia Belietes (these packages were developed independently around the same time).\cite{hyperSpec-pkg}  There is also a package designed to interconvert \texttt{Spectra} objects and \texttt{hyperSpec} objects, which allows one to  move data between the packages more easily.\cite{hCB-pkg}  Package \texttt{TIMP} is geared toward sophisticated modeling of time-dependent spectral data sets.\cite{TIMP-art}   New packages may appear at any time. A good place to check these things out is the \href{http://cran.at.r-project.org/web/views/ChemPhys.html}{Chemometrics and Computational Physics Task View}.



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