MSE Research Project Database

Manifold learning


Project Leader: Jonathan Manton
Primary Contact: Jonathan Manton (jmanton@unimelb.edu.au)
Keywords: signal processing; signals and systems
Disciplines: Electrical & Electronic Engineering
Domains:
Research Centre: Nonlinear Signal Processing Lab

While linear regression fits a straight line to data points, manifold learning fits smooth surfaces to data points. Manifold learning has many applications, including to non-linear dimensionality reduction. For example, researchers have claimed that the set of all real-world images lies on a low-dimensional manifold embedded in a high-dimensional space. Most manifold learning algorithms to date focus mainly on local fitting. On the other hand, mathematicians have developed a theory of persistent homology for deducing the global topology from only a finite number of sampled data points. This project develops novel manifold learning algorithms that focus on both local and global properties.