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- Overview of manifolds and the basic topology of data
- Statistical learning and instrinsic dimensionality
- The manifold hypothesis
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Chapter 1: Multidimensional Scaling
- Classical, metric, and non-metric MDS algorithms
- Example applications to quantitative psychology and social science
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- Geodesic distances and the isometric mapping algorithm
- Implementation details and applications with facial images and coil-100 object images
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Chapter 3: Local Linear Embedding
- Locally linear reconstructions and optimization problems
- Example applications with image data
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Chapter 4: Laplacian Eigenmaps/Spectral Embedding
- From the general to the discrete Laplacian operators
- Visualizing spectral embedding with the networkx library
- Spectral embedding with NLTK and the Brown text corpus
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Introduction to manifold learning - mathematical theory and applied python examples (Multidimensional Scaling, Isomap, Locally Linear Embedding, Spectral Embedding/Laplacian Eigenmaps)
Home Page: https://drewwilimitis.github.io/Manifold-Learning/