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Manifold Learning and
Data Visualization
Hamburg, March 1st, 2018
PyData Hamburg
Dr. Stefan Kühn
https://www.xing.com/profile/Stefan_Kuehn46
https://de.slideshare.net/StefanKhn4
What is a manifold?
Mathematical concept from Differential Geometry
Manifold Learning and Data Visualization
What are properties of a manifold?
Important Properties – Topology and more
• Number of Connected Components
• Holes
• Curvature
• Smoothness
• Dimensionality
• …you_name_it…
Manifold Learning and Data Visualization
What are properties of a good visualization?
Preserve important properties
• Number of connected components?
• Holes?
• Curvature?
• Smoothness?
• Dimensionality?
• Distances between points?
• Angles, orientations?
• Local versus global properties?
Manifold Learning and Data Visualization
You cannot have it all!
Manifold Learning Methods in sklearn
• Locally Linear Embedding
• Neighborhood-preserving
• Isomap
• Quasi-isometric
• Multi-Dimensional Scaling (MDS)
• Quasi-isometric
• Spectral Embedding
• Spectral clustering based on similarity
• T-Distributed Stochastic Neighbor Embedding (tSNE)
• Preserves probabilities
• Local Tangent Space Alignment (LTSA)
Manifold Learning and Data Visualization
Local Tangent Space Alignment
Manifold Learning and Data Visualization
Demo Time
Sometimes, words are insufficient…
But then God gave us code!
Manifold Learning and Data Visualization
Resources
Scikit-learn documentation
http://scikit-learn.org/stable/modules/manifold.html
http://scikit-learn.org/stable/auto_examples/manifold/plot_compare_methods.html
http://scikit-learn.org/stable/auto_examples/manifold/plot_manifold_sphere.html
http://scikit-learn.org/stable/modules/random_projection.html
http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html
Github repo with worked examples
https://github.com/cc-skuehn/Manifold_Learning
Jupyter Lab
https://jupyterlab.readthedocs.io/en/stable/index.html
Citation
Scikit-learn: Machine Learning in Python, Pedregosa et al., JMLR 12, pp. 2825-2830, 2011.
http://jmlr.csail.mit.edu/papers/v12/pedregosa11a.html
Manifold Learning and Data Visualization
Thank you!
Hamburg, March 1st, 2018

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