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High Dimensional Data Visualization

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Fabian Keller

Presentation for the seminar course "Large Scale Visualization" at the University of Stuttgart in the summer term 2015.

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High Dimensional Data Visualization Presented by Fabian Keller Seminar: Large Scale Visualization Advisor: Steffen Koch University of Stuttgart, Summer Term 2015
Motivation What do you see? 16.07.2015 Fabian Keller 2
Motivation I can see… 16.07.2015 Fabian Keller 3
Agenda • Introduction • Dimension Reduction Techniques PCA / LLE / ISOMAP / t-SNE • Visualization Techniques Scatterplots / Parallel Coordinate Plots / Glyphs • Conclusion 16.07.2015 Fabian Keller 4
Goal Of dimensionality reduction • High Dimensional Data (>>1000 dimensions) • Reduce Dimensions (for Clustering / Learning / …) • Extract Meaning • Visualize and Interact 16.07.2015 Fabian Keller 5 [c.f. Card et al 1999; dos Santos and Brodlie 2004]
Intrinsic Dimensionality How many dimensions can we reduce? 2D  1D 3D  1D 16.07.2015 Fabian Keller 6  Intrinsic Dimensionality: 1
Agenda • Introduction • Dimension Reduction Techniques PCA / LLE / ISOMAP / t-SNE • Visualization Techniques Scatterplots / Parallel Coordinate Plots / Glyphs • Conclusion 16.07.2015 Fabian Keller 7
Dimension Reduction What techniques are there? DR Techniques Linear Principal Component Analysis Non-Linear Local Local Linear Embedding Global ISOMAP t-SNE 16.07.2015 Fabian Keller 8
Principal Component Analysis (PCA) Eigen-* 16.07.2015 Fabian Keller 9 • Linear, Global • Find “Principal Components” • Minimize Reconstruction Error [isomorphismes, 2014]
Principal Component Analysis (PCA) Eigen-Faces 16.07.2015 Fabian Keller 10
Local-Linear Embedding (LLE) Assumes the data is locally linear • Non-Linear, Local • Select neighbors and approximate linearly • Map to lower dimension 16.07.2015 Fabian Keller 11 [Roweis, 2000]
ISOMAP Isometric feature mapping 16.07.2015 Fabian Keller 12 • Non-linear, Global • K-Nearest Neighbors • Construct neighborhood graph • Compute shortest paths [Balasubramanian, 2002]
t-SNE Stochastic Neighbor Embedding • Non-linear, Global • Uses Gaussian similarities • Preserves the similarities in lower dimensions 16.07.2015 Fabian Keller 13
Agenda • Introduction • Dimension Reduction Techniques PCA / LLE / ISOMAP / t-SNE • Visualization Techniques Scatterplots / Parallel Coordinate Plots / Glyphs • Conclusion 16.07.2015 Fabian Keller 14
2D Scatter Plots Commonly used • Easy Perception • (No) Interaction • Limited to two dimensions • Colors?! 16.07.2015 Fabian Keller 15
2D Scatter Plot Matrices Show relationships with scatter plots • Slow perception • May have interaction • Does not scale well 16.07.2015 Fabian Keller 16
2D Scatter Plot Matrices Let an algorithm choose the plots 16.07.2015 Fabian Keller 17 [Zheng, 2014]
3D Scatter Plots Interactive • Only one additional dimension • Expensive interaction, useless without! • Limited benefit compared to 2D scatter plots 16.07.2015 Fabian Keller 18 [Sedlmair, 2013]
Parallel Coordinate Plot Display >2 dimensions 16.07.2015 Fabian Keller 19 Interaction Examples: https://syntagmatic.github.io/parallel-coordinates/ • Noisy • Slow perception • Meaning of x-axis?! [Harvard Business Manager, 2015-07]
Glyphs Encode important information • Memorable semantics • Small • Details through interaction • Overwhelming? 16.07.2015 Fabian Keller 20 [Fuchs, 2013]
Glyphs Domain-specific clues 16.07.2015 Fabian Keller 21 [Fuchs, 2014]
Glyphs Time series data 16.07.2015 Fabian Keller 22 [Kintzel, 2011]
Conclusion High Dimensional Data Visualization • Lots of DR / visualization techniques • Even more combinations • Application needs to be tailored to needs 16.07.2015 Fabian Keller 23 “A problem well put is half-solved” – John Dewey
Thank you for your attention! Questions?
Literature • Sedlmair, Michael; Munzner, Tamara; Tory, Melanie (2013): Empirical guidance on scatterplot and dimension reduction technique choices. • Zheng, Yunzhu; Suematsu, Haruka; Itoh, Takayuki; Fujimaki, Ryohei; Morinaga, Satoshi; Kawahara, Yoshinobu (2014): Scatterplot layout for high-dimensional data visualization. • Card, S. K., Mackinlay, J. D., and Shneiderman, B., editors. Readings in Information Visualization: Using Vision to Think. Morgan Kaufmann, San Francisco. 1999. • Fuchs, Johannes, et al. "Evaluation of alternative glyph designs for time series data in a small multiple setting." Proceedings of the SIGCHI Conference on Human Factors in Computing Systems. ACM, 2013. • Christopher Kintzel, Johannes Fuchs, and Florian Mansmann. 2011. Monitoring large IP spaces with ClockView. • Fuchs, Johaness et al. “Leaf Glyph Visualizing Multi-Dimensional Data with Environmental Cues“. 2014. • Balasubramanian, Mukund, and Eric L. Schwartz. "The isomap algorithm and topological stability." Science 295.5552 (2002): 7-7. • Roweis, Sam T.; Saul, Lawrence K. (2000): Nonlinear dimensionality reduction by locally linear embedding. • dos Santos, S. and Brodlie, K. Gaining understanding of multivariate and multidimensional data through visualization. Computers & Graphics, 28(3):311–325. 2004. • Harvard Business Manager, 2015-07: Andere Länder, anderer Stil http://www.harvardbusinessmanager.de/heft/d-135395625.html • isomorphismes (2014). pca - making sense of principal component analysis, eigenvectors & eigenvalues - cross validated. http://stats.stackexchange.com/a/82427/80011 16.07.2015 Fabian Keller 25
Example Applications • Biological / Medical (genes, fMRI) • Finance (time series) • Geological (climate, spatial, temporal) • Big Data Analysis (Netflix Movie Rating Data) 16.07.2015 Fabian Keller 26
Other DR techniques Matlab toolbox for dimensionality reduction 16.07.2015 Fabian Keller 27 • Principal Component Analysis (PCA) • Probabilistic PCA • Factor Analysis (FA) • Classical multidimensional scaling (MDS) • Sammon mapping • Linear Discriminant Analysis (LDA) • Isomap • Landmark Isomap • Local Linear Embedding (LLE) • Laplacian Eigenmaps • Hessian LLE • Local Tangent Space Alignment (LTSA) • Conformal Eigenmaps (extension of LLE) • Maximum Variance Unfolding (extension of LLE) • Landmark MVU (LandmarkMVU) • Fast Maximum Variance Unfolding (FastMVU) • Kernel PCA • Generalized Discriminant Analysis (GDA) • Diffusion maps • Neighborhood Preserving Embedding (NPE) • Locality Preserving Projection (LPP) • Linear Local Tangent Space Alignment (LLTSA) • Stochastic Proximity Embedding (SPE) • Deep autoencoders (using denoising autoencoder pretraining) • Local Linear Coordination (LLC) • Manifold charting • Coordinated Factor Analysis (CFA) • Gaussian Process Latent Variable Model (GPLVM) • Stochastic Neighbor Embedding (SNE) • Symmetric SNE • t-Distributed Stochastic Neighbor Embedding (t-SNE) • Neighborhood Components Analysis (NCA) • Maximally Collapsing Metric Learning (MCML) • Large-Margin Nearest Neighbor (LMNN) See: http://lvdmaaten.github.io/drtoolbox/

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High Dimensional Data Visualization

  • 1. High Dimensional Data Visualization Presented by Fabian Keller Seminar: Large Scale Visualization Advisor: Steffen Koch University of Stuttgart, Summer Term 2015
  • 2. Motivation What do you see? 16.07.2015 Fabian Keller 2
  • 4. Agenda • Introduction • Dimension Reduction Techniques PCA / LLE / ISOMAP / t-SNE • Visualization Techniques Scatterplots / Parallel Coordinate Plots / Glyphs • Conclusion 16.07.2015 Fabian Keller 4
  • 5. Goal Of dimensionality reduction • High Dimensional Data (>>1000 dimensions) • Reduce Dimensions (for Clustering / Learning / …) • Extract Meaning • Visualize and Interact 16.07.2015 Fabian Keller 5 [c.f. Card et al 1999; dos Santos and Brodlie 2004]
  • 6. Intrinsic Dimensionality How many dimensions can we reduce? 2D  1D 3D  1D 16.07.2015 Fabian Keller 6  Intrinsic Dimensionality: 1
  • 7. Agenda • Introduction • Dimension Reduction Techniques PCA / LLE / ISOMAP / t-SNE • Visualization Techniques Scatterplots / Parallel Coordinate Plots / Glyphs • Conclusion 16.07.2015 Fabian Keller 7
  • 8. Dimension Reduction What techniques are there? DR Techniques Linear Principal Component Analysis Non-Linear Local Local Linear Embedding Global ISOMAP t-SNE 16.07.2015 Fabian Keller 8
  • 9. Principal Component Analysis (PCA) Eigen-* 16.07.2015 Fabian Keller 9 • Linear, Global • Find “Principal Components” • Minimize Reconstruction Error [isomorphismes, 2014]
  • 10. Principal Component Analysis (PCA) Eigen-Faces 16.07.2015 Fabian Keller 10
  • 11. Local-Linear Embedding (LLE) Assumes the data is locally linear • Non-Linear, Local • Select neighbors and approximate linearly • Map to lower dimension 16.07.2015 Fabian Keller 11 [Roweis, 2000]
  • 12. ISOMAP Isometric feature mapping 16.07.2015 Fabian Keller 12 • Non-linear, Global • K-Nearest Neighbors • Construct neighborhood graph • Compute shortest paths [Balasubramanian, 2002]
  • 13. t-SNE Stochastic Neighbor Embedding • Non-linear, Global • Uses Gaussian similarities • Preserves the similarities in lower dimensions 16.07.2015 Fabian Keller 13
  • 14. Agenda • Introduction • Dimension Reduction Techniques PCA / LLE / ISOMAP / t-SNE • Visualization Techniques Scatterplots / Parallel Coordinate Plots / Glyphs • Conclusion 16.07.2015 Fabian Keller 14
  • 15. 2D Scatter Plots Commonly used • Easy Perception • (No) Interaction • Limited to two dimensions • Colors?! 16.07.2015 Fabian Keller 15
  • 16. 2D Scatter Plot Matrices Show relationships with scatter plots • Slow perception • May have interaction • Does not scale well 16.07.2015 Fabian Keller 16
  • 17. 2D Scatter Plot Matrices Let an algorithm choose the plots 16.07.2015 Fabian Keller 17 [Zheng, 2014]
  • 18. 3D Scatter Plots Interactive • Only one additional dimension • Expensive interaction, useless without! • Limited benefit compared to 2D scatter plots 16.07.2015 Fabian Keller 18 [Sedlmair, 2013]
  • 19. Parallel Coordinate Plot Display >2 dimensions 16.07.2015 Fabian Keller 19 Interaction Examples: https://syntagmatic.github.io/parallel-coordinates/ • Noisy • Slow perception • Meaning of x-axis?! [Harvard Business Manager, 2015-07]
  • 20. Glyphs Encode important information • Memorable semantics • Small • Details through interaction • Overwhelming? 16.07.2015 Fabian Keller 20 [Fuchs, 2013]
  • 22. Glyphs Time series data 16.07.2015 Fabian Keller 22 [Kintzel, 2011]
  • 23. Conclusion High Dimensional Data Visualization • Lots of DR / visualization techniques • Even more combinations • Application needs to be tailored to needs 16.07.2015 Fabian Keller 23 “A problem well put is half-solved” – John Dewey
  • 24. Thank you for your attention! Questions?
  • 25. Literature • Sedlmair, Michael; Munzner, Tamara; Tory, Melanie (2013): Empirical guidance on scatterplot and dimension reduction technique choices. • Zheng, Yunzhu; Suematsu, Haruka; Itoh, Takayuki; Fujimaki, Ryohei; Morinaga, Satoshi; Kawahara, Yoshinobu (2014): Scatterplot layout for high-dimensional data visualization. • Card, S. K., Mackinlay, J. D., and Shneiderman, B., editors. Readings in Information Visualization: Using Vision to Think. Morgan Kaufmann, San Francisco. 1999. • Fuchs, Johannes, et al. "Evaluation of alternative glyph designs for time series data in a small multiple setting." Proceedings of the SIGCHI Conference on Human Factors in Computing Systems. ACM, 2013. • Christopher Kintzel, Johannes Fuchs, and Florian Mansmann. 2011. Monitoring large IP spaces with ClockView. • Fuchs, Johaness et al. “Leaf Glyph Visualizing Multi-Dimensional Data with Environmental Cues“. 2014. • Balasubramanian, Mukund, and Eric L. Schwartz. "The isomap algorithm and topological stability." Science 295.5552 (2002): 7-7. • Roweis, Sam T.; Saul, Lawrence K. (2000): Nonlinear dimensionality reduction by locally linear embedding. • dos Santos, S. and Brodlie, K. Gaining understanding of multivariate and multidimensional data through visualization. Computers & Graphics, 28(3):311–325. 2004. • Harvard Business Manager, 2015-07: Andere Länder, anderer Stil http://www.harvardbusinessmanager.de/heft/d-135395625.html • isomorphismes (2014). pca - making sense of principal component analysis, eigenvectors & eigenvalues - cross validated. http://stats.stackexchange.com/a/82427/80011 16.07.2015 Fabian Keller 25
  • 26. Example Applications • Biological / Medical (genes, fMRI) • Finance (time series) • Geological (climate, spatial, temporal) • Big Data Analysis (Netflix Movie Rating Data) 16.07.2015 Fabian Keller 26
  • 27. Other DR techniques Matlab toolbox for dimensionality reduction 16.07.2015 Fabian Keller 27 • Principal Component Analysis (PCA) • Probabilistic PCA • Factor Analysis (FA) • Classical multidimensional scaling (MDS) • Sammon mapping • Linear Discriminant Analysis (LDA) • Isomap • Landmark Isomap • Local Linear Embedding (LLE) • Laplacian Eigenmaps • Hessian LLE • Local Tangent Space Alignment (LTSA) • Conformal Eigenmaps (extension of LLE) • Maximum Variance Unfolding (extension of LLE) • Landmark MVU (LandmarkMVU) • Fast Maximum Variance Unfolding (FastMVU) • Kernel PCA • Generalized Discriminant Analysis (GDA) • Diffusion maps • Neighborhood Preserving Embedding (NPE) • Locality Preserving Projection (LPP) • Linear Local Tangent Space Alignment (LLTSA) • Stochastic Proximity Embedding (SPE) • Deep autoencoders (using denoising autoencoder pretraining) • Local Linear Coordination (LLC) • Manifold charting • Coordinated Factor Analysis (CFA) • Gaussian Process Latent Variable Model (GPLVM) • Stochastic Neighbor Embedding (SNE) • Symmetric SNE • t-Distributed Stochastic Neighbor Embedding (t-SNE) • Neighborhood Components Analysis (NCA) • Maximally Collapsing Metric Learning (MCML) • Large-Margin Nearest Neighbor (LMNN) See: http://lvdmaaten.github.io/drtoolbox/