降维与回归思路概述

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1、降维与回归思路概述提纲目标概述降维回归降维与回归研究目标3D不变性特征与图像不变性特征间的回归模型需要研究特征的简约或者说稀疏表示问题。回归映射模型提纲目标概述降维回归降维与回归降维的隐含假设不同变化下的图像（表象）具有特定的低维几何结构(Science’00;MM’09)DimensionalityreductionDiscovertheintrinsicgeometryembeddedinhighdimensionaldataApproachesLinearmethods:PCA,MDS-Nonlinear

2、ones:LLE,ISOMAP,Laplacianeigenmap,LPP,OLPP(x,y,z)=[x,sin(x),cos(x)]Asetofrulesthatdescribestherelationshipbetweenthepoints(objects)inadataset.Theserulesaresufficienttodescribeorgeneratethehigh-dimensionalpoints.ManifoldlearningtechniquesTheintrinsicgeometryi

3、softensmoothandapproximatelylinearinalocalregion.LLE(Science’00)——PreservelocalrelationshipsFacemanifoldobtainedbyLLEImagesoffaces(11)mappedintotheembeddingspacedescribedbythe1sttwocoordinatesofLLE.Representativefacesareshownnexttocircledpointsindifferentpar

4、tsofthespace.Thebottomimagescorrespondtopointsalongthetop-rightpath(linkedbysolidline),illustratingoneparticularmodeofvariabilityinposeandexpression.ManifoldlearningtechniquesISOMAP(Science’00)——preservegeodesicdistanceFacemanifoldbyISOMAPTargetrecognitionus

5、ingMLMotivation-Silhouettesofawalkerfromdifferentviewshavedifferentembeddings-Inferviewsand3DposefromtheembeddingsDifferenttargetswithappearance(silhouette)variationshavedifferentembeddings?Infertargettypes(classification)andaspects(tracking)fromembeddings?E

6、mbeddingsofdifferenttargetEmbeddingsofdifferenttargetexhibitdifferentshapes.ManifoldrepresentationoftargetswithaspectvariationsRotatingTigerSilhouettesReconstructedSilhouettesAppearancevariationsofatargetw.r.t.aspects3Dpointsalongtheembedding.Evolutionofth

7、e3DpointsreflectstheaspectvariationsofthetargetEmbeddingmatchingProbe:ChallengerProbe:M60Probe:T28Probe:TigerEmb:ChallengerEmb:M60Emb:T28Emb:TigerEmbeddingmatchingchallengerm60t28tigerchallenger:0.1571.8222.9331.644m60:0.9150.6313.2931.456t28:3.6725.4460.173

8、1.654tiger:1.4477.6210.7370.105HausdorrfdistancetomeasurethesimilaritybetweencurvesClassifytargetsfromvideoswithaspectvariationsbymatchingtheembeddings.FourFactorsinGaitAnalysis16POSEGAITVIEWSHA