GENERALIZED SIMULATED ANNEALING FOR CALIBRATION SAMPLE SELECTION FROM AN EXISTING SET AND ORTHOGONALIZATION OF UNDESIGNED EXPERIMENTS

ealibrared.The diseussion in this PaPer foeuses on near一infrared(NIR)sPeetroseoPy as the examPle instrument.However,the Proeedures Presented are aPPlieable tomost methods of instrumental analysis.Essentially,ealibration eonsists of assembling a seriesof samPles eontaining the analyte or analytes at     

VARIANCE-DECOMPOSITION OF PURE-COMPONENT SPECTRA AS A MEASURE OF SELECTIVITY

Care is required for multicomponent analysis if misleading results are to be avoided. The problem ofill-conditioned calibration matrices is of primary concern. This type of numerical instability isrepresented as spectral overlap of calibration spectra. Depending on the degree of spectral overlap, thesample concentration estimates can be severely affected. A practical statistical procedure is discussedwhich tests for the presence of spectral overlap among the pure-component spectra and simultaneouslyassesses the degree that concentration estimates may be degraded. Guidelines are developed to ascertainhow much departure from spectral orthogonality is acceptable.     

CONDITION NUMBERS, ITERATIVE REFINEMENT AND ERROR BOUNDS

Concentration estimates of components present in a sample mixture can be obtained using matrixmathematics. In the past, the condition number of the calibration matrix has been used to give anamplification factor by which uncertainties in data can work through to errors in the concentrationestimates. This paper explores an additional interpretation of condition numbers with regards tosignificant figures and rounding errors. A procedure is suggested which will always give the most accurateconcentration estimates provided the calibration matrix is not too ill-conditioned. Condition numbershave also been used by analytical chemists to discuss the error bounds for concentration estimates.Unfortunately, only one representative error bound can be approximated for all the components. Thispaper will show how to compute bounds for individual concentration estimates obtained as solutions to asystem of m equations and n unknowns. The procedure is appropriate when calibration data and sampleresponses are inaccurate.     

COMPUTER-GENERATED MULTICOMPONENT CALIBRATION DESIGNS FOR OPTIMAL ANALYSIS SAMPLE PREDICTIONS

This paper utilizes variable step size generalized simulated annealing(VSGSA)to design multicomponentcalibration samples for spectroscopic data.VSGSA is an optimization procedure which is capable ofconverging to exact positions of global optima located on multidimensional continuous functions.On thebasis of analysis sample response vectors,optimally designed calibration concentration matrices areobtained assuming knowledge of components present.The complexity of response surfaces establishedby the optimization criteria is described.     

WHICH PRINCIPAL COMPONENTS TO UTILIZE FOR PRINCIPAL COMPONENT REGRESSION

Principal components(PCs)for principal component regression(PCR)have historically been selectedfrom the top down for a reliable predictive model.That is,the PCs are arranged in a list starting withthe most informative(PC associated with the largest singular value)and proceeding to the leastinformative(PC associated with the smallest singular value).PCs are then chosen starting at the top ofthis list.This paper discusses an alternative procedure of treating PC selection as an optimization prob-lem.Specifically,without any regard to the ordering,the optimal subset of PCs for an acceptablepredictive model is desired.Five data sets are analyzed using the conventional and alternative approaches.Two data sets are spectroscopic in nature,two data sets deal with quantitative structure-activityrelationships(QSARs)and one data set is concerned with modeling.All five data sets confirm thatselection of a subset without consideration to order secures the best results with PCR.One data set isalso compared using partial least squares 1.