Implements a new histogram aggregation called `variable_width_histogram` which
dynamically determines bucket intervals based on document groupings. These
groups are determined by running a one-pass clustering algorithm on each shard
and then reducing each shard's clusters using an agglomerative
clustering algorithm.
This PR addresses #9572.
The shard-level clustering is done in one pass to minimize memory overhead. The
algorithm was lightly inspired by
[this paper](https://ieeexplore.ieee.org/abstract/document/1198387). It fetches
a small number of documents to sample the data and determine initial clusters.
Subsequent documents are then placed into one of these clusters, or a new one
if they are an outlier. This algorithm is described in more details in the
aggregation's docs.
At reduce time, a
[hierarchical agglomerative clustering](https://en.wikipedia.org/wiki/Hierarchical_clustering)
algorithm inspired by [this paper](https://arxiv.org/abs/1802.00304)
continually merges the closest buckets from all shards (based on their
centroids) until the target number of buckets is reached.
The final values produced by this aggregation are approximate. Each bucket's
min value is used as its key in the histogram. Furthermore, buckets are merged
based on their centroids and not their bounds. So it is possible that adjacent
buckets will overlap after reduction. Because each bucket's key is its min,
this overlap is not shown in the final histogram. However, when such overlap
occurs, we set the key of the bucket with the larger centroid to the midpoint
between its minimum and the smaller bucket’s maximum:
`min[large] = (min[large] + max[small]) / 2`. This heuristic is expected to
increases the accuracy of the clustering.
Nodes are unable to share centroids during the shard-level clustering phase. In
the future, resolving https://github.com/elastic/elasticsearch/issues/50863
would let us solve this issue.
It doesn’t make sense for this aggregation to support the `min_doc_count`
parameter, since clusters are determined dynamically. The `order` parameter is
not supported here to keep this large PR from becoming too complex.
Co-authored-by: James Dorfman <jamesdorfman@users.noreply.github.com>
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