Manifold Learning: Introduction and Foundational Algorithms

Mathematical Theory with Examples and Applications in Python

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Contents

• Introduction:

  • Overview of manifolds and the basic topology of data
  • Statistical learning and instrinsic dimensionality
  • The manifold hypothesis

• Chapter 1: Multidimensional Scaling

  • Classical, metric, and non-metric MDS algorithms
  • Example applications to quantitative psychology and social science

• Chapter 2: ISOMAP

  • Geodesic distances and the isometric mapping algorithm
  • Implementation details and applications with facial images and coil-100 object images

• Chapter 3: Local Linear Embedding

  • Locally linear reconstructions and optimization problems
  • Example applications with image data

• 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