Supplementary material for the paper: Co-clustering through Optimal Transport
نویسندگان
چکیده
For the sake of completeness, we first present the Sinkhorn’s theorem and explain how it was used to derive the solution of the regularized optimal transport. Theorem ((Sinkhorn & Knopp, 1967)). If A is an n × n matrix with strictly positive elements, then there exist diagonal matrices D1 and D2 with strictly positive diagonal elements such that D1 ∗ A ∗ D2 is doubly stochastic. The matrices D1 and D2 are unique modulo multiplying the first matrix by a positive number and dividing the second one by the same number.
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