Linear-Algebra-Methods-for-data-mining

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1、LinearAlgebraMethodsforDataMiningSaaraHyv¨onen,Saara.Hyvonen@cs.helsinki.fiSpring2007OverviewofsometopicscoveredandsometopicsnotcoveredonthiscourseLinearAlgebraMethodsforDataMining,Spring2007,UniversityofHelsinkiLinearalgebratoolkit•QRiteration•eigenvalues,eigenvaluedecomposition,general

2、izedeigenvalueproblem•singularvaluedecompositionSVD•NMF•powermethod(forfindingeigenvaluesand-vectors)LinearAlgebraMethodsforDataMining,Spring2007,UniversityofHelsinki1Dataminingtasksencountered•regression•classification•clustering•findinglatentvariables•visualizingandexploration•rankingLin

3、earAlgebraMethodsforDataMining,Spring2007,UniversityofHelsinki2QRwasusedfor...•orthogonalizingasetof(basis)vectorsX=QR.•solvingtheleast-squaresproblem:22TR222krk=kb−Axk=kQb−xk=kb1−Rxk+kb2k.0•leastsquaresproblemswereencounterede.g.whenwewishtoexpressamatrixA∈Rm×nintermsofasetofbasisvec

4、torsX∈Rm×k,k

5、ing,Spring2007,UniversityofHelsinki5•Lineardiscriminantanalysis:lineardiscriminants=eigenvectorscorrespondingtothelargesteigen-valuesofthegeneralizedeigenvalueproblemSbw=λSww.LinearAlgebraMethodsforDataMining,Spring2007,UniversityofHelsinki6•Spectralclustering:basedonrunningk-meansclust

6、eringonthematrixobtainedfromtheeigenvectorscorrespondingtothelargesteigenvaluesofthegraphlaplacianmatrixL=D−1/2AD−1/2.LinearAlgebraMethodsforDataMining,Spring2007,UniversityofHelsinki72.521.510.50−0.5−1−1.5−2−2.5−2−1.5−1−0.500.511.522.5LinearAlgebraMethodsforDataMining,Spring2007,Univer

7、sityofHelsinki8SpectralclusteringUsemethodsfromspectralgraphpartitioningtodoclustering.Needed:pairwisedistancesbetweendatapoints.Thesecanbethoughtofasweightsoflinksinagraph:clusteringproblembecomesagraphpartitioningproblem.Unlikek-means,clustersneednotbeconvex.LinearAlgebraMeth