Learning Structured Dictionaries for Manifold-type Data based on a Geometric Multi-Resolution Analysis

Start: 09/04/2013 - 1:15pm
End  : 09/04/2013 - 2:15pm

Applied Math Seminar

Guangliang Chen (CMC)

Data sets are often modeled as samples from a probability distribution
in high dimensions, but assumed to have some interesting low-dimensional
structure, for example that of a $ d $-dimensional submanifold $ \mathcal{M} $ of $ \mathbb{R}^D $,
with $ d\ll D $. When $ \mathcal{M} $ is simply a linear subspace, one may encode
efficiently the data by projection onto a dictionary consisting of the
top $ d $ singular vectors, with a cost of $ d(N+D) $ (where $ N $ is the data size).
When $ \mathcal{M} $ is nonlinear, there are no "explicit" and fast constructions of
dictionaries that achieve a similar efficiency: typically one uses
either random dictionaries, or dictionaries obtained by black-box global
optimization. In this talk we present an efficient construction of
data-dependent dictionaries for manifold-type data based on a geometric
multiresolution analysis, aiming at efficiently encoding and
manipulating the data. We will also mention its application to anomaly detection.



CMC Campus, Adams Hall, Davidson (the largest lecture room on the first floor)