/Manifold-Learning

Introduction to manifold learning - mathematical theory and applied python examples (Multidimensional Scaling, Isomap, Locally Linear Embedding, Spectral Embedding/Laplacian Eigenmaps)

Primary LanguageJupyter Notebook

Manifold Learning: Introduction and Foundational Algorithms

Mathematical Theory with Examples and Applications in Python

KleinDual

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