Multi-object tracking with representations of the symmetric group

We present an efficient algorithm for approx- imately maintaining and updating a distri- bution over permutations matching tracks to real world objects. The algorithm hinges on two insights from the theory of harmonic analysis on noncommutative groups. The first is that most of the information in the distribution over permutations is captured by certain "low frequency" Fourier components. The second is that Bayesian updates of these components can be efficiently realized by ex- tensions of Clausen's FFT for the symmetric group.