### The limit distribution the longest significance path(LSP) in point cloud

- Series
- SIAM Student Seminar
- Time
- Friday, January 29, 2010 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Kai Ni – School of Mathematics, Georgia Tech

In 2006, my coadvisor Xiaoming Huo and his colleague published an
annal of statistics paper which designs an asymptotically powerful
testing algorithm to detect the potential curvilinear structure in a
messy point cloud image. However, such an algorithm involves a
membership threshold and a decision threshold which are not well
defined in that paper because the distribution of LSP was unknown.
Later on, Xiaoming's student Chen, Jihong found some connections
between the distribution of LSP and the so-called Erdos-Renyi law.
In some sense, the distribution of LSP is just a generalization of
the Erdos-Renyi law. However this JASA paper of Chen, Jihong had
some restrictions and only partially found out the distribution of
LSP. In this talk, I will show the result of the JASA paper is
actually very close to the distribution of LSP. However, these is
still much potential work to do in order to strengthen this
algorithm.