PDE Model Reduction Using SVD

Satellites, sensors, cameras, scanners, computer simulations 
are creating or capturing huge amounts of data.  Data miners
seek the "gold" in these mountains of trash and trivia.

The data might come from some orderly physical phenomenon
with well known underlying laws.  Then again, it might be
tracks from the latest Gnarls Barkley album.  But in any
case, we can apply techniques of reduced order modeling 
to the data, and search for underlying patterns and
information.  

In this talk, we will consider the analysis of data from
a fluid flow simulation, and show how the singular value
decomposition can expose underlying "designs" in the flow.
We will even see that these "designs" can be used as a
technique for further analysis of new fluid flow problems.

We will also discuss a facial recognition task, which begins 
with 600 photographs, and tries to answer the questions 
* "What do these faces have in common?", 
* "Is this a new picture of a face I've already seen?"
* "Is this a picture of a face or a pumpkin?"