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I'm an engineer with an interest in statistics, and my company sent me to a 1 week training in PCA/PCR (principal component analysis/regression) using The Unscrambler. I'm starting to apply these analyses to data sets in my work, but I'm the most experienced person my company has in this analysis.

I understand that most data requires some amount of pre-processing, and what the different methods and types are, but how do I know if I've done a good job of preprocessing? Are there diagnostics for preprocessing? How do I tell an over-processed data set versus an under-processed set?

The pre-processing I was taught includes things like transformations, mean centering, variable scaling, normalization, derivatives, MSC/eMSC that are performed on the data set before the PCA or PCR is performed.

The first data set I'm working on is continuous process data for a PCR (how can we predict the outcome variable based on these (correlated) input variables). The second data set will be classification of different spectra (if the type of problem matters).

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One thing is that the data entering into the PCA should typically be standardized (zero mean, unit standard deviation) or else different scaling among variables might greatly influence your results.

And you should make sure that your data are reliable, as in any type of analysis. This seems obvious, but is too often overlooked. (It's not unusual to spend as much or more time doing quality control on data as on the analyses per se.)

Beyond that, think about what any linear modeling is trying to accomplish: fit a reasonable first-order approximation to the relation of your dependent variable to your independent variables. Any pre-PCA data transformation (or before any linear model) should be done with that in mind. As an example, for necessarily positive data with skew, a log transform prior to analysis often will provide a better model. Such transformations and other pre-processing should be done with that goal in mind, informed by your understanding of the subject matter. For the purposes you have in mind, don't be afraid to try different pre-processing approaches.

Ultimately, the test will be whether your prediction/classification models work adequately.

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