Seminar Details
2006-10-10 (14.00 pm) : "Coupling between projected matrices and graph matching"
At Euler building
Organized by Mathematical Engineering
Speaker :
Catherine Fraikin (CESAME)
Abstract :
We consider the problem of finding the optimal
coupling between two projected matrices U_AU and V _BV .
The square matrices A and B are of different dimensions but the isometries U* and V* have
a common column dimension k. The coupling is measured by the real
function c(U, V ) = Rtrace(U_AUV _B_V ), which we maximize of the isometries U_U = V _V = Ik.
This problem can be viewed as an extension of the generalized numerical range of two matrices, which are
now allowed to be of different dimension. Two recursive algorithm are developed to solve the optimization
problem: the first one is based on the Singular Value Decomposition and the second one is a gradient-type
algorithm. We derive also the expressions for the fixed points of the algorithm. This problem can be applied
in the context of graph analysis. We consider here the fundamental task of graph matching which plays a
fundamental role e.g. in pattern recognition. More specifically, we are interested in the problem of matching
directed graphs of different size. In particular, we show how the matching between the two graphs can be
solved by optimally projecting the adjacency matrices in a lower-dimensional subspace.