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Hierarchical Stochastic Neighbor Embedding

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Nicola Pezzotti

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.

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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
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //EuroVis 2016 Hierarchical organization of data Image Collection Nature Man-made Ships Vehicles 2
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // • Visualizing relationships between data points • Parallel-Coordinate Plots do not scale Dimensionality Reduction (DR) 3 EmbeddingHigh-Dimensional Feature Vectors Dimensionality Reduction Dim-1 Dim-2 Data Feature Extraction
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 4
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Non-Linear DR with Landmarks 5 [Landmark-SNE, Landmark-ISOMAP] [LSP, P-LSP, LAMP, LoCH, Pekalska] Hybrid techniques Non linear Dim-1 Dim-2 Emb-Dim-1 Emb-Dim-1
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 6 Hierarchical SNE Emb-Dim-1
EuroVis 2016 Algorithm
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 8 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
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 9 Dim-1 Dim-2
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 10 Dim-1 Dim-2
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 11 Dim-1 Dim-2
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 12 Dim-1 Dim-2
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 13 Dim-1 Dim-2 Low High Distribution
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 14 Dim-1 Dim-2
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 15 Dim-1 Dim-2
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 16 Dim-1 Dim-2
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 17 Dim-1 Dim-2 66% 33% • Localized Area of Influence • Low memory footprint
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 18 Similarity Based Embedding tSNE
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 19 Similarity Based Embedding tSNE
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 20 •Random walks • More than 1k per ms •Hierarchical Analysis • Top-down • Link between scale given by the area of influence
EuroVis 2016 Use Case 1 Deep Learning
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Use case I: Deep Learning 22 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
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //EuroVis 2016 Use case I: Deep Learning Test set Nature Man-made 100k Images 92s 23
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //EuroVis 2016 Use case I: Deep Learning Nature Vehicles Appliances Ships Man-made 24
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //EuroVis 2016 Use case I: Deep Learning Appliances Ships Vehicles Trains Cars Buses 25
EuroVis 2016 Use Case 2 Hyperspectral Images
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Use case II: Hyperspectral images 27
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Use case II: Hyperspectral images 28 • Pixels • 1M Data points (1024x1024) • Images • 12 Dimensions • Clusters in the Embedding • Group of pixels that correspond to the same phenomenon
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Use case II: Hyperspectral images 29 Surface Space Low High Influence
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Use case II: Hyperspectral images 30 Outer space Corona Low High Influence
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Use case II: Hyperspectral images 31
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Use case II: Hyperspectral images 32 Low High Influence
EuroVis 2016 Conclusion
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 34 Conclusions
EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Questions? This project is founded by STW through the V.An.P.I.Re project

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Hierarchical Stochastic Neighbor Embedding

  • 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 2
  • 3. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // • Visualizing relationships between data points • Parallel-Coordinate Plots do not scale Dimensionality Reduction (DR) 3 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 4
  • 5. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Non-Linear DR with Landmarks 5 [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 6 Hierarchical SNE Emb-Dim-1
  • 8. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 8 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 13 Dim-1 Dim-2 Low High Distribution
  • 14. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 14 Dim-1 Dim-2
  • 15. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 15 Dim-1 Dim-2
  • 16. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 16 Dim-1 Dim-2
  • 17. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 17 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 18 Similarity Based Embedding tSNE
  • 19. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 19 Similarity Based Embedding tSNE
  • 20. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Hierarchical SNE - Algorithm 20 •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 22 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
  • 23. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //EuroVis 2016 Use case I: Deep Learning Test set Nature Man-made 100k Images 92s 23
  • 24. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //EuroVis 2016 Use case I: Deep Learning Nature Vehicles Appliances Ships Man-made 24
  • 25. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding //EuroVis 2016 Use case I: Deep Learning Appliances Ships Vehicles Trains Cars Buses 25
  • 26. EuroVis 2016 Use Case 2 Hyperspectral Images
  • 27. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Use case II: Hyperspectral images 27
  • 28. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Use case II: Hyperspectral images 28 • Pixels • 1M Data points (1024x1024) • Images • 12 Dimensions • Clusters in the Embedding • Group of pixels that correspond to the same phenomenon
  • 29. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Use case II: Hyperspectral images 29 Surface Space Low High Influence
  • 30. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Use case II: Hyperspectral images 30 Outer space Corona Low High Influence
  • 31. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Use case II: Hyperspectral images 31
  • 32. EuroVis 2016 Pezzotti et al. // Hierarchical Stochastic Neighbor Embedding // Use case II: Hyperspectral images 32 Low High Influence
  • 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 34 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

Editor's Notes

  • #3: 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