My presentation of the "Hierarchical Stochastic Neighbor Embedding" algorithm at EuroVIS 2016. HSNE is a non-linear dimensionlity reduction technique for the exploration of large high-dimensional datasets.

1. EuroVis 2016
18th EG/VGTC Conference on Visualization
6-10 June 2016, Groningen, the Netherlands
Hierarchical Stochastic Neighbor Embedding
Nicola Pezzotti1, Thomas Höllt1, Boudewijn P.F. Lelieveldt2,
Elmar Eisemann1, Anna Vilanova1
1. Computer Graphics & Visualization, Delft University of Technology, Delft, The Netherlands
2. Division of Image Processing, Leiden Medical Center, Leiden, The Netherlands

2. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //EuroVis 2016
Hierarchical organization of data
Image Collection
Nature
Man-made
Ships
Vehicles
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3. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
• Visualizing relationships between data points
• Parallel-Coordinate Plots do not scale
Dimensionality Reduction (DR)
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EmbeddingHigh-Dimensional
Feature Vectors
Dimensionality
Reduction
Dim-1
Dim-2
Data
Feature
Extraction

4. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //EuroVis 2016
Non-linear Dimensionality Reduction
• Data often lay on a non-linear manifold in the high-dimensional space
• Widely used on real-world data
• Computationally intensive
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5. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
Non-Linear DR with Landmarks
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[Landmark-SNE, Landmark-ISOMAP]
[LSP, P-LSP, LAMP, LoCH, Pekalska]
Hybrid techniques
Non linear
Dim-1
Dim-2
Emb-Dim-1
Emb-Dim-1

6. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
•Multiscale Dimensionality Reduction
• Non-linear DR
• Landmark based
• Hierachical exploration of the data
• Overview-first & Details-on-Demand
• Filter & Drill-in
• Proabilistic framework
Hierarchical Stochastic Neighbor Embedding
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Hierarchical SNE
Emb-Dim-1

7. EuroVis 2016
Algorithm

8. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
Hierarchical SNE - Algorithm
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Similarity
Based
Embedding
tSNE1
1: Van der Maaten et al. - Visualizing data using t-SNE -
Journal of Machine Learning Research - 2008.
• Localized Similarities
• Low memory footprint

9. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
Hierarchical SNE - Algorithm
9
Dim-1
Dim-2

10. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
Hierarchical SNE - Algorithm
10
Dim-1
Dim-2

11. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
Hierarchical SNE - Algorithm
11
Dim-1
Dim-2

12. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
Hierarchical SNE - Algorithm
12
Dim-1
Dim-2

13. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
Hierarchical SNE - Algorithm
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Dim-1
Dim-2
Low High
Distribution

14. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
Hierarchical SNE - Algorithm
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Dim-1
Dim-2

15. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
Hierarchical SNE - Algorithm
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Dim-1
Dim-2

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Hierarchical SNE - Algorithm
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Dim-1
Dim-2

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Hierarchical SNE - Algorithm
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Dim-1
Dim-2
66%
33%
• Localized Area of Influence
• Low memory footprint

18. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
Hierarchical SNE - Algorithm
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Similarity
Based
Embedding
tSNE

19. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
Hierarchical SNE - Algorithm
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Similarity
Based
Embedding
tSNE

20. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
Hierarchical SNE - Algorithm
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•Random walks
• More than 1k per ms
•Hierarchical Analysis
• Top-down
• Link between scale given by the area
of influence

21. EuroVis 2016
Use Case 1
Deep Learning

22. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
Use case I: Deep Learning
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Feature vector
4096 Dimensions
Are 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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Use case I: Deep Learning
Test set
Nature
Man-made
100k Images
92s
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24. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //EuroVis 2016
Use case I: Deep Learning
Nature
Vehicles
Appliances
Ships
Man-made
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25. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //EuroVis 2016
Use case I: Deep Learning
Appliances
Ships
Vehicles Trains
Cars
Buses
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26. EuroVis 2016
Use Case 2
Hyperspectral Images

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Use case II: Hyperspectral images
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Use case II: Hyperspectral images
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• Pixels
• 1M Data points (1024x1024)
• Images
• 12 Dimensions
• Clusters in the Embedding
• Group of pixels that
correspond to the same
phenomenon

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Use case II: Hyperspectral images
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Surface
Space
Low High
Influence

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Use case II: Hyperspectral images
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Outer space
Corona
Low High
Influence

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Use case II: Hyperspectral images
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Use case II: Hyperspectral images
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Low High
Influence

33. EuroVis 2016
Conclusion

34. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
• Hierarchical Stochastic Neighbor Embedding
• Novel hierarchical analysis of non-linear data
• Outperforms existing techniques
• Computation time
• Size of the data to be computed
• K-Nearest Neighbor Preservation
• Stability of the embeddings
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Conclusions

35. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //
Questions?
This project is founded by STW
through the V.An.P.I.Re project