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