Title: Topological methods in dimensionality reduction.
Stanford University, Mathematics Department
Abstract:
There are now many different techniques for finding a
low-dimensional representation of a high-dimensional data set. The representation
often takes the form of an embedding of the data in low-dimensional Euclidean
space. However, it is easy to envisage situations where the true structure of
the data may be obscured and not clarified by the embedding; in particular when
the low-dimensional structure has non-trivial topology. Motivated by these
examples, I discuss some alternative approaches to interpreting
high-dimensional data with low-dimensional structure.