  Based on an idea in [4] we propose a new iterative multiplicative filtering
algorithm for label assignment matrices which can be used for the supervised
partitioning of data. Starting with a row-normalized matrix containing the
averaged distances between prior features and the observed ones the method
assigns in a very efficient way labels to the data. We interpret the algorithm
as a gradient ascent method with respect to a certain function on the product
manifold of positive numbers followed by a reprojection onto a subset of the
probability simplex consisting of vectors whose components are bounded away
from zero by a small constant. While such boundedness away from zero is
necessary to avoid an arithmetic underflow, our convergence results imply that
they are also necessary for theoretical reasons. Numerical examples show that
the proposed simple and fast algorithm leads to very good results. In
particular we apply the method for the partitioning of manifold-valued images.
