Github user Yunni commented on the issue:
https://github.com/apache/spark/pull/15148
@jkbradley I agree with most of your comments above. And I would like to
suggest the following:
- I would recommend a more intuitive name like `HyperplaneProjection`
instead of `PStableHashing` if we adopt the LSH function @sethah suggested.
- `x.toDense.values.zip(y.toDense.values).map(pair => pair._1 ==
pair._2).sum / x.size` is AND-amplification. I think we should use
OR-amplification here. I have already made a pull request to fix the issue in
#15800.
- I think for MinHash, multi-probing NN Search is either single probing or
full scan.
- Here is my reference for Multi-probing:
http://www.cs.princeton.edu/cass/papers/mplsh_vldb07.pdf
@sethah @karlhigley Now I see your LSH function for Euclidean distance is
the AND-amplification of what I have implemented.
- Do you have any reference for compound AND/OR-amplification? I see this
is not always working without assumptions on distance threshold and
sensitivity, for example, `(0.6, 0.4)` => `(0.426, 0.098)` for `L = 4, d = 4`,
and `(0.8, 0.2)` => `(0.678, 0.000)` for `L = 10, d = 10`
- For the schema of `transform()`, I think we either add a generic type for
the output column in LSH class or change the output type to `Array[Vector]`. I
would recommend the latter way because (1) it's very easy to explode the array
to get what @sethah suggested (2) The type of output column still needs to be
spark sql compatible, which is not so generic.
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