Amir massoud Farahmand

Manifold Learning

Amir Massoud Farahmand
Dept. of Computing Science, University of Alberta

In many real-world problems, such as visually-guided robots, we need to deal with high-dimensional data. Unfortunately, what is so called as "the curse of dimensionality" states that dealing with a problem with a high-dimensional input can be very difficult in the worst case unless there is some regularities in the problem which we exploit.

Manifold learning is an umbrella term for research directions and methods that try to benefit from the possibility that the data come from a lower-dimensional submanifold embedded in a higher-dimensional space. The hope is that by exploiting this kind of regularity, using methods from the mathematics of differential manifolds, we have data analysis methods that efficiently work in problems with high-dimensional input space.

In the first part of my talk, I introduce some prominent manifold learning methods such as Isomap, Locally Linear Embedding, and Laplacian Eigenmaps. These are basically nonlinear dimension reduction methods.

In the second part of the talk, I represent my work and show that there are certain machine learning methods that can provably benefit from the fact that the data are lying on a lower-dimensional submanifold.


Amir massoud Farahmand has a B.S. and M.S. in electrical engineering, and is a Ph.D. student in the department of Computing Science. Nowadays, his research interest is studying reinforcement learning methods that can benefit from regularities of data such as smoothness and having a low-dimensional submanifold structure.