PRML03.pdf - Feature Embedding(Cont\u2019d Tetsuji Ogawa Dept of Communications Computer Engineering [email protected]

PRML03.pdf - Feature Embedding(Cont’d Tetsuji Ogawa Dept...

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FeatureEmbedding Tetsuji Ogawa Dept.ofCommunications&ComputerEngineering [email protected] (Cont’d)
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LectureOutline 1. Orthogonalexpansion 2. PrincipalComponentAnalysis( PCA ) 3. LinearDiscriminantAnalysis( LDA ) 4. LocallyPreservingProjection( LPP ) 5. LocalFisherDiscriminantAnalysis( LFDA ) 6. Introductionofourwork(e.g., CDDA ) DISCUSSION 2
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LPP L ocality P reserving P rojection Preservinggeometricalstructureofneighborhood samplesbeforeandafterprojection. 3 x W y
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ManifoldEmbedding 4 Dimensionalityreductionfortwo‐dimensionaldataembeddedina nonlinearmanifoldspacewithrelativepositioninformation preserved. EuclideandistancemeasuredbetweenAandDismuchdifferent thandistancemeasuredwithinmanifoldspace; thesepointsare neighboringinEuclideandistancebutwidelyseparatedonmanifold .
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6 Locality: Preserved!
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7 Locality: Preserved! Locality: NOTpreserved!
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8 𝑦 െ 𝑦 ⋅ 𝐴 ௜௝ ௜,௝ 𝐖𝐱 െ 𝐖𝐱 𝐴 ௜௝ ௜,௝ Locality: Preserved! Locality: NOTpreserved! Objectivefunctionwithweights 𝐴 ௜௝ incursheavypenaltyifneighboringpoints 𝐱 and 𝐱 aremappedfarapart.
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