Riemannian Geometry Cheat sheet

Target audience: Beginner

Estimated reading time: 3'

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Newsletter: Geometric Learning in Python        

A visual overview of Riemannian geometry for everyone.

Riemannian geometry is core component of geometric learning that tackles the challenges of high-dimensional, densely packed but limited data, and complex distributions. Riemannian geometry provides a solution by helping data scientists understand the true shape and distribution of data.

Riemannian geometry provides data scientists with a mathematical framework facilitates the creation of models that are accurate and complex by leveraging geometric and topological insights.

References

Here is the list of published articles related to geometric learning:

• Foundation of Geometric Learning introduces differential geometry as an applied to machine learning and its basic components.
• Differentiable Manifolds for Geometric Learning describes manifold components such as tangent vectors, geodesics with implementation in Python for Hypersphere using the Geomstats library.
• Intrinsic Representation in Geometric learning reviews the various coordinates system using extrinsic and intrinsic representation.
• Vector and Covector fields in Python describes vector and co-vector fields with Python implementation in 2 and 3-dimension spaces.
• Geometric Learning in Python: Vector Operators illustrates the differential operators, gradient, divergence, curl and laplacian using SymPy library.
• Functional Data Analysis in Python describes the key elements of non-linear functional data analysis to analysis curves, images, or functions in very  high-dimensional spaces
• Riemann Metric & Connection for Geometric Learning reviews Riemannian metric tensor, Levi-Civita connection and parallel transport for hypersphere.
• Riemann Curvature in Python describes the intricacies of Riemannian metric curvature tensor and its implementation in Python using Geomstats library.
• K-means on Riemann Manifolds compares the implementation of k-means algorithm on Euclidean space using Scikit-learn and hypersphere using Geomstats
  

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Patrick Nicolas has over 25 years of experience in software and data engineering, architecture design and end-to-end deployment and support with extensive knowledge in machine learning. 
He has been director of data engineering at Aideo Technologies since 2017 and he is the author of "Scala for Machine Learning", Packt Publishing ISBN 978-1-78712-238-3 and Geometric Learning in Python Newsletter on LinkedIn.