Sparse Discriminant Analysis

Abstract

tionanddimensionreductionareofgreatimportanceiscommonin Classi cationinhigh-dimensionalfeaturespaceswhereinterpreta-biologicalandmedicalapplications. methodsasmicroarrays,1DNMR,andspectroscopyhavebecomeev- Fortheseapplicationsstandard erydaytoolsformeasuringthousandsoffeaturesinsamplesofinterest. Furthermore,thesamplesareoftencostlyandthereforemanysuch problemshavefewobservationsinrelationtothenumberoffeatures. Traditionallysuchdataareanalyzedby lectionbeforeclassi cation. Weproposeamethodwhichperforms rstperformingafeaturese-lineardiscriminantanalysiswithasparsenesscriterionimposedsuch thattheclassi mergedintooneanalysis. cation, featureselectionanddimensionreductionis thantraditionalfeatureselectionmethodsbasedoncomputationally Thesparsediscriminantanalysisisfaster heavycriteriasuchasWilk'slambda,andtheresultsarebetterwith regardstoclassi tomixturesofGaussianswhichisusefulwhene.g.biologicalclusters cationratesandsparseness.Themethodisextended arepresentwithineachclass. low-dimensionalviewsofthediscriminativedirections. Finally,themethodsproposedprovide 1