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Since the metric will compute how well does the corrected sample 1 for donor A from batch 1 look like sample 2 for donor A from batch 2, most methods will make some changes to sample 1 to make it look more like sample 2. For positive control, we can just get it to return sample 2 instead of some form of corrected sample 1. This sample 2 will then be compared to the sample 2 and yield EMD of 0.
It is acceptable to have best possible EMD of 0 with the assumption that the difference between sample 1 and sample 2 are purely driven by batch effect because the two samples are technical replicates.
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