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Colin97 avatar Colin97 commented on July 21, 2024

The EMD implementation is based on an approximation algorithm (auction algorithm). It employs a parameter eps to balance the error rate and the speed of convergence. Smaller eps achieves more optimal assignment but needs a longer time for convergence. The time complexity is $O(n^2k)$, where $k$ is the number of iterations. Since it may take a long time to achieve the convergence (one-one matching), we set a fixed number of iterations, and our implementation thus cannot guarantee a (but near) one-one matching, which means there may be a small number of “many to one” pairs in our results.

For a given eps, as k increases, there will be fewer "one-to-many" pairs and the result will be more accurate.

We set a $eps = 0.005, k = 50$ during training and a $eps = 0.002, k = 10000$ during testing.

Please refer to the paper for the role of eps.

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theodeprelle avatar theodeprelle commented on July 21, 2024

Thanks! In your code you are using a block size of 2048. If I halve it size, do I have to change the values of k and eps ?

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Colin97 avatar Colin97 commented on July 21, 2024

I do not think so.

Thanks! In your code you are using a block size of 2048. If I halve it size, do I have to change the values of k and eps ?

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