Does kmeans support INNER_PRODUCT distance?

[zhanghan9797]

Hi, I want to know if the faiss.IndexIVFFlat index is using the kmeans method during training, can the distance calculation only use L2? Is it possible to use INNER_PRODUCT?
Can I use INNER_PRODUCT as distance for kmeans?

I want to implement it this way, is this correct?

quantizer = faiss.IndexFlatIP(emb_size)
index = faiss.IndexIVFFlat(quantizer, emb_size, ivf_centers_num,faiss.METRIC_INNER_PRODUCT)

At the same time I also want to know what does quantizer and faiss.METRIC_INNER_PRODUCT mean here?

Looking forward to your reply！

[mdouze]

Inner product is supported.
It does not use L2 at search time, but inner product, as expected.

[meghbhalerao]

Hi - I am not sure this is the right place to ask this, but I would like to know the exact place in the source code where the k means clustering is happening which is using inner product as a similarity metric rather than the Euclidean L2 distance.
If inner product is being used as a similarity metric, then how are the cluster centers being calculated - since I dont think it makes sense to use the arithmetic mean as the cluster center since that is specific to the Euclidean space and distance metric. Thanks and please let me know if I am missing something.

--Megh

[mdouze]

Yes the arithmetic mean is used to compute centroids.

Indeed the decreasing mean squared error guarantee does not hold with anything else than L2 assignment. However the inner product assignment is useful, especially in combination with the L2 normalization of the centroids after each iteration.

[ghost]

Could you briefly describe how we can assign do inner product assignment in the python interface?

Yes the arithmetic mean is used to compute centroids.

Indeed the decreasing mean squared error guarantee does not hold with anything else than L2 assignment. However the inner product assignment is useful, especially in combination with the L2 normalization of the centroids after each iteration.