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Re: Re:{4} Maintainable code is the best code -- principal components

by 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 peer-reviewed 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 C-dimensional 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 non-basis 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 large-scale 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).

-----------------------------------------------------
Dr. Michael K. Neylon - mneylon-pm@masemware.com || "You've left the lens cap of your mind on again, Pinky" - The Brain
It's not what you know, but knowing how to find it if you don't know that's important

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 [Corion]: marto: I believe nowadays, at least window.opener should not be set anymore (except maybe within the same domain) [Corion]: But I wouldn't really know as I don't use iexplore much (except at \$work) and mostly surf with JS disabled (except at \$work :) ) [marto]: yeah, this is at work, where some intranet app launches links via window.open. When users close the intranet page so that only the new JS opened windows exist, clicking URLs in an email (or whatever) don't open [Corion]: marto: It somewhat makes sense that the reduced popup window doesn't get new URLs, but it makes less sense that no new browser window opens :)

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