  Matching one set of objects to another is a ubiquitous task in machine
learning and computer vision that often reduces to some form of the quadratic
assignment problem (QAP). The QAP is known to be notoriously hard, both in
theory and in practice. Here, we investigate if this difficulty can be
mitigated when some additional piece of information is available: (a) that all
QAP instances of interest come from the same application, and (b) the correct
solution for a set of such QAP instances is given. We propose a new approach to
accelerate the solution of QAPs based on learning parameters for a modified
objective function from prior QAP instances. A key feature of our approach is
that it takes advantage of the algebraic structure of permutations, in
conjunction with special methods for optimizing functions over the symmetric
group Sn in Fourier space. Experiments show that in practical domains the new
method can outperform existing approaches.
