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This random hyper plane algorithm is actually a pretty elegant algorithm. It has the following amazing property: as your dimension increases, the quality of the random hyper planes actually gets better!

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What exactly is elegant about this algorithm? The approach seems computationally quite inefficient to me.

It is inefficient to build (unless on GPU), but good for search. Moreover, the search naturally benefits from data locality after ordering - this allows using MergeTree tables in ClickHouse. See https://news.ycombinator.com/item?id=36341754

And it is around 10 lines of code in SQL: https://presentations.clickhouse.com/meetup74/ai/#35

That's the thing though, it's very easy to perform approximate nearest neighbor search in an efficient way. There are plenty of simple solutions for that. The real challenge is to design an algorithm that can scale & that remains robust even when there are additions and deletions to the set.

That presentation was pretty cool, thanks for posting.

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