Semi-supervised LIBS quantitative analysis method based on co-training regression model with selection of effective unlabeled samples

Theaccuracyoflaser-inducedbreakdownspectroscopy(LIBS)quantitativemethodisgreatlydependentontheamountofcertifiedstandardsamplesusedfortraining.However,inpracticalapplications,onlylimitedstandardsampleswithlabeledcertifiedconcentrationsareavailable.Anovelsemi-supervisedLIBSquantitativeanalysismethodisproposed,basedonco-trainingregressionmodelwithselectionofeffectiveunlabeledsamples.Themainideaoftheproposedmethodistoobtainbetterregressionperformancebyaddingeffectiveunlabeledsamplesinsemi-supervisedlearning.First,effectiveunlabeledsamplesareselectedaccordingtothetestingsamplesbyEuclideanmetric.Twooriginalregressionmodelsbasedonleastsquaressupportvectormachinewithdifferentparametersaretrainedbythelabeledsamplesseparately,andthentheeffectiveunlabeledsamplespredictedbythetwomodelsareusedtoenlargethetrainingdatasetbasedonlabelingconfidenceestimation.Thefinalpredictionsoftheproposedmethodonthetestingsampleswillbedeterminedbyweightedcombinationsofthepredictionsoftwoupdatedregressionmodels.Chromiumconcentrationanalysisexperimentsof23certifiedstandardhigh-alloysteelsampleswerecarriedout,inwhich5sampleswithlabeledconcentrationsand11unlabeledsampleswereusedtotraintheregressionmodelsandtheremaining7sampleswereusedfortesting.Withthenumbersofeffectiveunlabeledsamplesincreasing,therootmeansquareerroroftheproposedmethodwentdownfrom1.80%to0.84%andtherelativepredictionerrorwasreducedfrom9.15%to4.04%.