 
Summary: Iterative Methods for Low Rank Approximation of
Graph Similarity Matrices
T. P. Cason, P.A. Absil, P. Van Dooren
Department of Mathematical Engineering, ICTEAM Institute, Universit´e catholique de
Louvain, B1348 LouvainlaNeuve, Belgium
Abstract
In this paper, we analyze an algorithm to compute a lowrank approximation
of the similarity matrix S introduced by Blondel et al. in [1]. This problem
can be reformulated as an optimization problem of a continuous function
(S) = tr ST
M2
(S) where S is constrained to have unit Frobenius norm,
and M2
is a nonnegative linear map. We restrict the feasible set to the
set of matrices of unit Frobenius norm with either k nonzero identical sin
gular values or at most k nonzero (not necessarily identical) singular values.
We first characterize the stationary points of the associated optimization
problems and further consider iterative algorithms to find one of them. We
analyze the convergence properties of our algorithm and prove that accumu
lation points are stationary points of (S). We finally compare our method
