Another thing is that the data generation process using faiss index seems like a rather far fetched idea... Using L2 norm to find the first k' nearest neighbours and then switching to another metric to choose a subset from these neighbours of size k doesn't sound very convincing.
There is a rather brief explanation of this approach in the supplementary material. Basically L2 norm is treated as an approximation for the desired metric during faiss search. In other words, we use faiss to find many L2 neighbours and then hope to find true nearest neighbours among them. In the paper the values were k' = 500 and k = 5.
Another thing is that the data generation process using faiss index seems like a rather far fetched idea... Using L2 norm to find the first k' nearest neighbours and then switching to another metric to choose a subset from these neighbours of size k doesn't sound very convincing.
There is a rather brief explanation of this approach in the supplementary material. Basically L2 norm is treated as an approximation for the desired metric during faiss search. In other words, we use faiss to find many L2 neighbours and then hope to find true nearest neighbours among them. In the paper the values were k' = 500 and k = 5.