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EuroVis 2016 18th EG/VGTC Conference on Visualization 6-10 June 2016, Groningen, the Netherlands Hierarchical Stochastic Neighbor Embedding Nicola Pezzotti 1 , Thomas Höllt 1 , Boudewijn P.F. Lelieveldt 2 , Elmar Eisemann 1 , Anna Vilanova 1 1. Computer Graphics & Visualization, Delft University of Technology, Delft, The Netherlands 2. Division of Image Processing, Leiden Medical Center, Leiden, The Netherlands

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Hierarchical Stochastic Neighbor EmbeddingNicola Pezzotti1, Thomas Hllt1, Boudewijn P.F. Lelieveldt2, Elmar Eisemann1,Anna Vilanova1Computer Graphics & Visualization, Delft University of Technology, Delft, The NetherlandsDivision of Image Processing, Leiden Medical Center, Leiden, The Netherlands

EuroVis 201618th EG/VGTC Conference on Visualization6-10 June 2016, Groningen, the Netherlands

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Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //

1

Hierarchical organization of data

Image Collection

Nature

Man-made

Ships

Vehicles

2

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Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //Images, they can be organized hierarchically based on the objects that they represent.And we can do that for different data

This kind of hierarchies arise when we

Visualizing relationships between data pointsParallel-Coordinate Plots do not scaleDimensionality Reduction (DR)3Embedding

High-DimensionalFeature Vectors

DimensionalityReduction

Dim-1Dim-2

DataFeatureExtraction

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Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //Non-linear Dimensionality ReductionData often lay on a non-linear manifold in the high-dimensional spaceWidely used on real-world dataComputationally intensive4

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Non-Linear DR with Landmarks5

[Landmark-SNE, Landmark-ISOMAP][LSP, P-LSP, LAMP, LoCH, Pekalska]

Hybrid techniques

Non linear

Dim-1Dim-2Emb-Dim-1Emb-Dim-1

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Multiscale Dimensionality Reduction Non-linear DRLandmark basedHierachical exploration of the dataOverview-first & Details-on-DemandFilter & Drill-inProabilistic framework

Hierarchical Stochastic Neighbor Embedding6

Hierarchical SNEEmb-Dim-1

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Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //Algorithm

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Hierarchical SNE - Algorithm8

SimilarityBased Embedding tSNE1

1: Van der Maaten et al. - Visualizing data using t-SNE - Journal of Machine Learning Research - 2008.Localized SimilaritiesLow memory footprint

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Hierarchical SNE - Algorithm9

Dim-1Dim-2

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Hierarchical SNE - Algorithm10

Dim-1Dim-2

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Hierarchical SNE - Algorithm11

Dim-1Dim-2

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Hierarchical SNE - Algorithm12

Dim-1Dim-2

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Hierarchical SNE - Algorithm13

Dim-1Dim-2

LowHighDistribution

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Hierarchical SNE - Algorithm14

Dim-1Dim-2

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Hierarchical SNE - Algorithm15

Dim-1Dim-2

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Hierarchical SNE - Algorithm16

Dim-1Dim-2

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Hierarchical SNE - Algorithm17

Dim-1Dim-2

66%33%Localized Area of InfluenceLow memory footprint

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Hierarchical SNE - Algorithm18

SimilarityBased Embedding tSNE

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Hierarchical SNE - Algorithm19

SimilarityBased Embedding tSNE

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Hierarchical SNE - Algorithm20

Random walksMore than 1k per ms

Hierarchical AnalysisTop-downLink between scale given by the area of influence

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Use Case 1Deep Learning

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Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //Use case I: Deep Learning22

Feature vector 4096 DimensionsAre the images processed by AlexNet [1] organized hierarchically by the network?1: Krizhevsky et al. - ImageNet Classification with Deep Convolutional Neural Networks - Advances in neural information processing systems - 2012.

Label+Image

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Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //Use case I: Deep Learning

Test set

NatureMan-made100k Images92s23

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Use case I: Deep Learning

Nature

VehiclesAppliancesShipsMan-made

24

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Use case I: Deep Learning

AppliancesShipsVehicles

TrainsCarsBusesSport cars

25

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Use Case 2Hyperspectral Images

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Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //Use case II: Hyperspectral images27

EuroVis 2016

Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //Use case II: Hyperspectral images28

Pixels 1M Data points (1024x1024)Images 12 DimensionsClusters in the EmbeddingGroup of pixels that correspond to the same phenomenon

EuroVis 2016

Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //Use case II: Hyperspectral images29

Surface

Space

LowHighInfluence

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Use case II: Hyperspectral images30

Outer space

Corona

LowHighInfluence

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Use case II: Hyperspectral images31

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Use case II: Hyperspectral images32

LowHighInfluence

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Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //Conclusion

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Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //Hierarchical Stochastic Neighbor EmbeddingNovel hierarchical analysis of non-linear dataOutperforms existing techniquesComputation timeSize of the data to be computedK-Nearest Neighbor PreservationStability of the embeddings

34Conclusions

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Questions?

This project is founded by STW through the V.An.P.I.Re project

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