Approximate-Nearest-Subspace：最近的子空間近似教學(xué)課件2

36、“不可能”這個(gè)字(法語是一個(gè)字)，只在愚人的字典中找得到。--拿破侖。37、不要生氣要爭(zhēng)氣，不要看破要突破，不要嫉妒要欣賞，不要托延要積極，不要心動(dòng)要行動(dòng)。38、勤奮，機(jī)會(huì)，樂觀是成功的三要素。(注意：傳統(tǒng)觀念認(rèn)為勤奮和機(jī)會(huì)是成功的要素，但是經(jīng)過統(tǒng)計(jì)學(xué)和成功人士的分析得出，樂觀是成功的第三要素。39、沒有不老的誓言，沒有不變的承諾，踏上旅途，義無反顧。40、對(duì)時(shí)間的價(jià)值沒有沒有深切認(rèn)識(shí)的人，決不會(huì)堅(jiān)韌勤勉。ApproximateNearestSubspace：最近的子空間近似ApproximateNearestSubspace：最近的子空間近似36、“不可能”這個(gè)字(法語是一個(gè)字)，只在愚人的字典中找得到。--拿破侖。37、不要生氣要爭(zhēng)氣，不要看破要突破，不要嫉妒要欣賞，不要托延要積極，不要心動(dòng)要行動(dòng)。38、勤奮，機(jī)會(huì)，樂觀是成功的三要素。(注意：傳統(tǒng)觀念認(rèn)為勤奮和機(jī)會(huì)是成功的要素，但是經(jīng)過統(tǒng)計(jì)學(xué)和成功人士的分析得出，樂觀是成功的第三要素。39、沒有不老的誓言，沒有不變的承諾，踏上旅途，義無反顧。40、對(duì)時(shí)間的價(jià)值沒有沒有深切認(rèn)識(shí)的人，決不會(huì)堅(jiān)韌勤勉。ApproximateNearestSubspace：最近的子空間近似ApproximateNearestSubspaceSearch

withapplicationstopatternrecognitionRonenBasriTalHassnerLihiZelnik-ManorWeizmannInstituteCaltechSubspacesinComputerVisionZelnik-Manor&Irani,PAMI’06IlluminationFacesObjectsViewpoint,MotionDynamictextures…ApproximateNearestSubspaceSearch

withapplicationstopatternrecognitionRonenBasriTalHassnerLihiZelnik-ManorWeizmannInstituteCaltechSubspacesinComputerVisionZelnik-Manor&Irani,PAMI’06Basri&Jacobs,PAMI’03Nayaretal.,IUW’96IlluminationFacesObjectsViewpoint,MotionDynamictextures…QueryNearestSubspaceSearchWhichistheNearestSubspace?SequentialSearchSequentialsearch:

O(ndk)Tooslow!!Isthereasublinearsolution?Databased

dimensionsn

subspacesk

subspacedimensionARelatedProblem:

NearestNeighborSearchd

dimensionsn

pointsSequentialsearch:

O(nd)Thereisasublinearsolution!DatabaseApproximateNN(1+)rTreesearch(KD-trees)LocalitySensitiveHashingFast!!Query:Logarithmic

Preprocessing:O(dn)rIsitpossibletospeed-up

NearestSubspaceSearch?Existingpoint-basedmethodscannotbeappliedTreesearchLSHOurSuggestedApproachReductiontopointsWorksforboth

linearandaffinespacesRuntimeSequentialOurDatabasesizeProblemDefinitionFindMappingApplystandardpointANNtou,vAlinearfunctionoforiginaldistanceMonotonicindistanceIndependentmappingsFindingaReductionConstants?DependsonqueryFeelinglucky?Wearelucky!!BasicReductionWant:minimize/GeometryofBasicReductionDatabaseLiesonasphereandonahyper-planeQueryLiesonaconeImprovingtheReductionFinalReduction=constantsCanWeDoBetter?If=0TrivialmappingAdditiveConstantisInherentFinalMappingGeometryANSComplexitiesPreprocessing:

O(nkd2)LinearinnLoginnQuery:

O(d2)+TANN(n,d2)DimensionalityMaybeLargeEmbeddingind2Mightneedtousesmall

εCurrentsolution:Userandomprojections(useJohnson-LindenstraussLemma)RepeatseveraltimesandselectthenearestSyntheticDataVaryingdatabasesized=60,k=4RuntimeSequentialOurDatabasesizeVaryingdimensionn=5000,k=4RuntimeSequentialOurdimensionFaceRecognition(YaleB)Database64illuminationsk=9subspacesQuery:NewilluminationFaceRecognitionResultWrongMatchWrongPersonTrueNSApproxNSRetilingwithPatchesPatchdatabaseQueryApproxImageWantedRetilingwithSubspacesSubspacedatabaseQueryApproxImageWantedPatches+ANN~0.6secSubspaces+ANS~1.2secPatches+ANN~0.6secSubspaces+ANS~1.2secSummaryFast,approximatenearestsubspacesearchReductiontopointANNUsefulapplicationsincomputervisionDisadvantages:Embeddingind2AdditiveconstantOthermethods?Additionalapplications?Alotmoretobedone…..THANKYOU謝謝你的閱讀知識(shí)就是財(cái)富豐富你的人生41