The document presents the Hierarchical Stochastic Neighbor Embedding (HSNE) method, which enables efficient visualization and hierarchical organization of complex, high-dimensional data. It outlines the advantages of HSNE, including its capacity for non-linear dimensionality reduction and low memory footprint, as well as its application in deep learning and hyperspectral imaging. The approach is demonstrated to outperform existing techniques in terms of computation time and stability of embeddings.

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

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Hierarchical organization of data
Image Collection
Nature
Man-made
Ships
Vehicles
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• 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

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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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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

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•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

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Algorithm

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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

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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

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Hierarchical SNE - Algorithm
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Dim-1
Dim-2

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Hierarchical SNE - Algorithm
12
Dim-1
Dim-2

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Hierarchical SNE - Algorithm
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Dim-1
Dim-2
Low High
Distribution

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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

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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

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Hierarchical SNE - Algorithm
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Similarity
Based
Embedding
tSNE

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Hierarchical SNE - Algorithm
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Similarity
Based
Embedding
tSNE

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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

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Use Case 1
Deep Learning

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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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Use case I: Deep Learning
Nature
Vehicles
Appliances
Ships
Man-made
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Use case I: Deep Learning
Appliances
Ships
Vehicles Trains
Cars
Buses
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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

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Conclusion

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• 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

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Questions?
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