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MathGroup Archive 1998

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Deconvolution of Experimental Observations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13482] Deconvolution of Experimental Observations
  • From: jrowney at Arco.COM (John D. Rowney)
  • Date: Sun, 26 Jul 1998 02:33:41 -0400
  • Organization: ARCO Oil % Gas Company
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

I have a suite of ~30 experimentally observed gas compositions.  Each
composition is expressed in terms of the mole fractions of 12
identified species.  The mole fractions sum to one.

I suspect that each of these gases is actually a mixture of a small
number (2-4) of "reference" gases.

1)  How do I test the hypothesis? (Principal Component Analysis? - see
below)

and

2) How might I determine the "best-fit" compositions of each of the
"reference" gases so that the experimentally observed gas compositions
can be deconvolved into mixtures of them.

Principal Component Analysis?

Using Mathematica, I have calculated the CovarianceMatrix of the data. 
I then calculated the Eigenvalues of the matrix and there are three
which are much larger than the others.  Am I right in extrapolating
this observation to an assumption that three "reference" gases should
be enough to explain the variations in the data?  I then calculated the
PrincipalComponents - but unfortunately don't know what to do next!

I know that this may be more of a multivariate statistics question, but
I am trying to do all the analysis in Mathematica - hence I have
posited it here.

Any help would be appreciated.

John

jrowney at arco.com



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