[BUG] IVF-PQ support of IP distance assumes vectors have been normalized

[cjnolet]

IVFPQ w/ IP distance assumes vectors have been normalized, but not all users would expect or think to do this. Essentially, kmeans works with L2 distance or with IP and l2 normalized vectors. Currently if IP is used with vectors that aren't normalized then it runs into degenerate cases where most vectors are placed in a single cluster, and that causes issues for downstream algorithms (like the IVF portions).

One way to deal with this is to do normalization in-place or to normalize the input dataset then return it to its original state after the clustering is done.

[tarang-jain]

If we do the normalization, it essentially becomes the cosine metric, which is already an available metric, right? I think the fact that with inner product, the vectors end up in the same cluster is the nature of the metric itself and possibly the incorrect metric choice, rather than a bug in the implementation.

[cjnolet]

@tarang-jain we are being asked to support inner product, but the assumption for kmeans is that the data is normalized. We need to normalize the data only in kmeans to avoid these degenerate cases.

That's the ask, and the solution here. If that means using the cosine solution just for the normalization in kmeans then that's fine too.