Permanents, Transport Polytopes and Positive Definite Kernels on Histograms

  title={Permanents, Transport Polytopes and Positive Definite Kernels on Histograms},
  author={Marco Cuturi},
For two integral histograms r = (r1, . . . , rd) and c = (c1, . . . , cd) of equal sum N , the MongeKantorovich distance dMK(r, c) between r and c parameterized by a d × d distance matrix T is the minimum of all costs < F, T > taken over matrices F of the transportation polytope U(r, c). Recent results suggest that this distance is not negative definite, and hence, through Schoenberg’s well-known result, exp(− 1 t dMK) may not be a positive definite kernel for all t > 0. Rather than using… CONTINUE READING

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