The stupid question is the question not asked  
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Re: Re:{4} Maintainable code is the best code  principal componentsby Masem (Monsignor) 
on Oct 03, 2001 at 17:37 UTC ( #116443=note: print w/replies, xml )  Need Help?? 
Without going into too many specifics given the nature of my work, I'm using it to try to break down chemical spectra into identifiable components. When/if I get to publish this, I'll try to let folks know, though time in the peerreviewed journal world is only an illusion... :)
For those that are curious, principle component analysis or factor analysis or a number of other different names descibes a method for breaking down sets of data in key basis sets. It assumes that all experimental data is a linear combination of collected data, and thus, if your collected data is N units long with M total sets, you can use singular value decomposition to get M basis sets N units long, and a square M x M weight matrix. This is an 'exact' specification. However, we typically want only C components, with C << M. Because during singular value decomposition, we generate M eigenvalues, we can use empirical, statistical, or other methods to determine what C is, and which of those M basis sets are the most important. Note that these basis sets may have any actual meaning; as jeroenes indicates, the method breaks out these basis sets as to attempt to minimize the variation of the data along one Cdimensional vector. However, there are ways to transform the data from the PCA basis set to a set of vectors that have some meaning. In my case, it's going from a basis set of spectra that represent no real substance to spectra of real substances; I can then get an idea of the composition of all the other nonbasis set data that I started with. As jeroenes also indicated, you can use the basis sets and weights to find out where clusters of data exist, and use those to guide the selection of basis sets and transformations to understand the data better. It's a very elegant method for largescale data analysis and very easy to do with help from computers (there's enough empirical analysis that has to be done that a human needs to guide the end decisions).

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