# Overview of multivariate statistics for chemometrics (e.g., Raman spectra)

I am looking for an overview of multivariate statistics for chemometrics. I'm reviewing a number of articles that for the most part are analyzing a large number (300+) of various spectra (IR, UV-Vis, Raman, etc.) with varying levels of multivariate data (some have hundreds of data points, some thousands per spectra). These papers are using techniques like:

• PCA—principal components analysis, for data exploration and reduction;
• HCA—hierarchical cluster analysis;
• PLS-DA—partial least squares discriminant analysis;
• SVM—support vector machines,
• SIMCA—soft independent modeling by class analogy;
• LDA / QDA—linear / quadratic discriminant analysis (and various algorithms too, such as LDA genetic algorithm vs LDA successive projections algorithm),
• or some combination of them.

The goal of the majority of the articles is to distinguish the samples from which the spectra came from, and to predict (classify) an unknown sample based on its spectra. In general the samples are spectra from ink samples to distinguish them from one another (as in a forensic application). So in most cases some amount of ink samples are examined, a model is made (using any number of techniques), and sometimes blind ink samples are tested against the model. It just seems like every author does something very different from the others with no real clear indication of why.

Are there any resources that specifically comment on this sort of decision making and how to go about selecting one or more multivariate techniques that are not aimed at statisticians?

• @ gung In general the samples are spectra from ink samples to distinguish them from one another (as in a forensic application). So in most cases some amount of ink samples are examined, a model is made (using any number of techniques), and sometimes blind ink samples are tested against the model. It just seems like every author does something very different from the others with no real clear indication of why.
– Tim
Dec 14 '15 at 20:35
• @gung Understood, thanks. And yes, they are all chemometric.
– Tim
Dec 14 '15 at 20:43
• I edited your question to keep it open. (If you just want a guide to how to choose... it will be considered too broad; but asking for a book / reference is on topic.) Ultimately, the only way to be able to choose which to use is to learn about all the techniques & what they do / how they work. Do you use R? Dec 14 '15 at 21:22
• @gung I do not use R, and while I'm learning about all of the techniques it seems quite overwhelming at times. I have a general idea of what they are, but I was hoping to find additional references that might address the topic directly. Thank you for the formatting and all of your help!
– Tim
Dec 14 '15 at 22:34
• I asked because there are some R-based books on multivariate statistics for chemometrics that would let you learn about the techniques & try them out. There may be similar books for other software. What do you use? MATLAB? Something else? Dec 14 '15 at 22:45

Gathering from the question that this is about classification rather than regression (in chemometrics aka calibration).

• You may be interested in reading Richard Brereton's Chemometrics for Pattern Recognition, it contains loads of useful information though it may be a bit overwhelming as a beginning.

• There are some general principles/rules of thumb/questions to guide the decision, e.g.

• one-class classifiers address so-called one-class problems where one well defined class should be separated from "everything else" (everything else is ill-defined), e.g. SIMCA, one-class SVM
• Are all classes well-defined? How much spread within the class do you expect? Do you expect the classes to have similar shape and size? Do you need "unknown" and/or "uncertain" as possible output?
• Is only class boundary of interest? E.g. presence/absence of analyte asks for different methods (logistic regression, PLS-DA) than identity proof in loading dock analysis (one-class classifiers, or e.g. LDA, QDA).
• if from a physico-chemical point of view you can expect your data to follow a bilinear relationship (mixture spectra are linear combination of pure component spectra weighted by concentrations), then bilinear models should be appropriate
• if the application suggests that the class boundaries are highly irregular, a non-linear classifier is needed
• the lower your samples : variates ratio, the more regularizaton or aggregation you need
• How important is spectroscopic interpretation of what the model does? Bilinear models offer much easier interpretation possibilities than e.g. random forests or artificial neural networks.
• What is the signal-to-noise ratio of your single data points (spectrum)? Low SNR -> SVM not appropriate

Nevertheless, it is a well-known professional secret that the quality of the model depends very much on the experience of the chemometrician with the chosen type of model (but then, professional experience guides the choice as well...).

(Otherwise, I'm one of the resources who comment on and teach this sort of decision making ;-) )