The prediction error in CLS and PLS: the importance of feature selection prior to multivariate calibration
Nadler B, Coifman R. The prediction error in CLS and PLS: the importance of feature selection prior to multivariate calibration. Journal Of Chemometrics 2005, 19: 107-118. DOI: 10.1002/cem.915.Peer-Reviewed Original ResearchClassical least squaresMultivariate regression algorithmExact mathematical analysisNet analyte signal vectorLeast squaresRegression algorithmSquared errorAdditional error termPartial least squaresFinite trainingMathematical analysisAsymptotic errorDimensional reductionLinear mixture modelMean squared errorInput dataError termMixture modelSignal vectorOverall prediction errorTheoretical justificationP dimensionN samplesLarge calibrationPrediction errorPartial least squares, Beer's law and the net analyte signal: statistical modeling and analysis
Nadler B, Coifman R. Partial least squares, Beer's law and the net analyte signal: statistical modeling and analysis. Journal Of Chemometrics 2005, 19: 45-54. DOI: 10.1002/cem.906.Peer-Reviewed Original ResearchRegression vectorFinite training setNet analyte signal vectorInput-output samplesJoint probability distributionPartial least squaresCommon regression algorithmsNoise-free caseNoise-free samplesRandom variablesRandom realizationsLinear multivariate modelProbability distributionAsymptotic optimalityInfinite numberK iterationLinear mixture modelMean squared errorSpecific probabilistic modelMixture modelSignal vectorUnstructured noiseLeast squaresPLS algorithmProbabilistic model