Visualizing high-dimensional data with R and Python plus some interesting fact about how human perception works

1. Visualizing
High-dimensional
Data
Dr. Stefan Kühn
Lead Data Scientist
code.talks - 30.09.2016

2. Overview
• Data Visualization as you might know it
• Main Properties of Graphics (and Humans)
• A short story about Charts
• Pair Plots and Correlations
• Data Visualization as you might not know it
• Fundamental Problems
• SVD, t-SNE and other approximations
• Principal Components and Principal Curves
• Parallel Coordinates
• The Grand Tour
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3. Takeaways - hopefully ;-)
• Data Visualization is complicated
• There is always an approximation
• There is always a bias
• There is always a misinterpretation
• Data Visualization is simple
• Lots of packages available
• Lots of studies + literature
• Lots of examples to learn from
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4. Data Visualization Basics
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5. The Modes of Perception
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X
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O
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O O
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O
X
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O
O
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O
X
X
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X
O
O
O O
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X
X X
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O
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Fast Slow
Find the outlier

6. The Modes of Perception
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• Pre-attentive
• fast
• parallel processing
• effortless
• Pattern recognition
• semi-fast
• governed by laws of per by
• Attentive
• slow
• sequential
• high effort (attention a very limited resource)

7. Main Properties of Graphics
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Category Example
Position
Shape
Size
Color
Orientation (Line)
Length (Line)
Type and Size (Line)
Brightness

8. Main Properties of Graphics Humans
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Category Amount of pre-attentive information
Position very high
Shape ———
Size approx. 4
Color approx. 8
Orientation (Line) approx. 4
Length (Line) ———
Type and Size (Line) ———
Brightness approx. 8

9. Pre-attentive perception
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• Position
• fast
• effective
• high number of different positions
• Color
• use with care
• Shape
• Orientation
Pre-attentive perception is effortless.
Exploit this as much as you can.

10. Pattern detection
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„It is interesting to note that our brain […]
subconsciously always prefers meaningful
situations and objects.“
• Emergence
• Reiification
• Multi-stability
• Invariance
Pattern detection can be trained.
Exploit this for frequent visualizations.

11. What is this?
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12. What is this?
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13. What is this?
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14. Laws of Gestalt
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„It is interesting to note that our brain, in
accordance with the laws of Gestalt,
subconsciously always prefers meaningful
situations and objects.“

15. Accuracy of Graphics
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Square Pie vs Stacked Bar vs Pie vs Donut
What do you think?
https://eagereyes.org/blog/2016/a-reanalysis-of-a-study-about-square-pie-charts-from-2009

16. Demo
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17. Beyond the Basics
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18. Fundamental Problems
• No accurate method in higher dimensions
• Approximations methods
• „Simulated“ dimensions (color, size, shape)
• Animations?
• No notion of quality or accuracy for
Visualizations
• Information Theory?
• „Stability“?
All Visualizations are wrong, but some are useful.
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19. Approximation methods
• Pair Plots
• Axis-aligned projections
• Interpretable in terms of original variables
• Singular Value Decomposition
• Optimal with respect to 2-norm (Euclidean norm)
and supremum norm
• Comes with an error estimate
• Other methods
• Stochastic Neighborhood Embedding (t-SNE)
• „Manifold Learning“
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20. Demo
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21. Manifold Learning Methods
• Locally Linear Embedding
• Neighborhood-preserving embedding
• Isomap
• quasi-isometric
• Multi-dimensional scaling
• quasi-isometric
• Spectral Embedding
• Spectral clustering based on similarity
• Stochastic Neighborhood Embedding (SNE, t-SNE)
• preserves probabilities
• Local Tangent Space Alignement (LTSA)
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22. Local Tangent Space Alignement
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23. Principal Components and Curves
• Principal Component Analysis
• orthogonal decomposition based on SVD
• linear in all variables
• tries to preserve variance
• Principal Curves
• minimize the Sum of Squared Errors with respect
to all variables (as PCA, preserve variance)
• nonlinear
• smooth
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24. Principal Components and Curves
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25. Parallel Coordinates
• Parallel Coordinates
• especially useful for high-dimensional data
• depends on ordering and scaling
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26. Demo
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27. The Grand Tour
• Animated sequence of 2-D projections
• https://en.wikipedia.org/wiki/
Grand_Tour_(data_visualisation)
• Asimov (1985): The grand tour: a tool for viewing
multidimensional data.
• Underlying idea
• Randomly generate 2-D projections (random
walk)
• Over time generate a dense subset of all
possible 2-D projections
• Optional: Follow a given path / guided tour
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28. The Grand Tour
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29. The Grand Tour
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30. Demo
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31. 31
Thanks a lot!
www.codecentric.de
blog.codecentric.de
stefan.kuehn@codecentric.de
datascience@codecentric.de