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

SIAM Student Seminar
Friday, January 29, 2010 - 1:00pm for 1 hour (actually 50 minutes)
Skiles 255
Kai Ni – School of Mathematics, Georgia Tech
Linwei Xin
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.