[DOCS] Reformat `min_hash` token filter docs (#57181)

Changes:

* Rewrites description and adds a Lucene link
* Reformats the configurable parameters as a definition list
* Changes the `Theory` heading to `Using the min_hash token filter for
  similarity search`
* Adds some additional detail to the analyzer example

docs/reference/analysis/tokenfilters/minhash-tokenfilter.asciidoc

@@ -4,59 +4,82 @@
 <titleabbrev>MinHash</titleabbrev>
 ++++
 
-The `min_hash` token filter hashes each token of the token stream and divides
-the resulting hashes into buckets, keeping the lowest-valued hashes per
-bucket. It then returns these hashes as tokens.
+Uses the https://en.wikipedia.org/wiki/MinHash[MinHash] technique to produce a
+signature for a token stream. You can use MinHash signatures to estimate the
+similarity of documents. See <<analysis-minhash-tokenfilter-similarity-search>>.
 
-The following are settings that can be set for a `min_hash` token filter.
+The `min_hash` filter performs the following operations on a token stream in
+order:
 
-[cols="<,<", options="header",]
-|=======================================================================
-|Setting |Description
-|`hash_count` |The number of hashes to hash the token stream with. Defaults to `1`.
+. Hashes each token in the stream.
+. Assigns the hashes to buckets, keeping only the smallest hashes of each
+  bucket.
+. Outputs the smallest hash from each bucket as a token stream.
 
-|`bucket_count` |The number of buckets to divide the minhashes into. Defaults to `512`.
+This filter uses Lucene's
+{lucene-analysis-docs}/minhash/MinHashFilter.html[MinHashFilter].
 
-|`hash_set_size` |The number of minhashes to keep per bucket. Defaults to `1`.
+[[analysis-minhash-tokenfilter-configure-parms]]
+==== Configurable parameters
 
-|`with_rotation` |Whether or not to fill empty buckets with the value of the first non-empty
-bucket to its circular right. Only takes effect if hash_set_size is equal to one.
-Defaults to `true` if bucket_count is greater than one, else `false`.
-|=======================================================================
+`bucket_count`::
+(Optional, integer)
+Number of buckets to which hashes are assigned. Defaults to `512`.
 
-Some points to consider while setting up a `min_hash` filter:
+`hash_count`::
+(Optional, integer)
+Number of ways to hash each token in the stream. Defaults to `1`.
+
+`hash_set_size`::
+(Optional, integer)
+Number of hashes to keep from each bucket. Defaults to `1`.
++
+Hashes are retained by ascending size, starting with the bucket's smallest hash
+first.
+
+`with_rotation`::
+(Optional, boolean)
+If `true`, the filter fills empty buckets with the value of the first non-empty
+bucket to its circular right if the `hash_set_size` is `1`. If the
+`bucket_count` argument is greater than `1`, this parameter defaults to `true`.
+Otherwise, this parameter defaults to `false`.
+
+[[analysis-minhash-tokenfilter-configuration-tips]]
+==== Tips for configuring the `min_hash` filter
 
 * `min_hash` filter input tokens should typically be k-words shingles produced
-from <<analysis-shingle-tokenfilter,shingle token filter>>.  You should
+from <<analysis-shingle-tokenfilter,shingle token filter>>. You should
 choose `k` large enough so that the probability of any given shingle
-occurring in a  document is low. At the same time, as
+occurring in a document is low. At the same time, as
 internally each shingle is hashed into to 128-bit hash, you should choose
 `k` small enough so that all possible
 different k-words shingles can be hashed to 128-bit hash with
 minimal collision.
 
-* choosing the right settings for `hash_count`, `bucket_count` and
-`hash_set_size` needs some experimentation.
-** to improve the precision, you should increase `bucket_count` or
-`hash_set_size`. Higher values of `bucket_count` or `hash_set_size`
-will provide a higher guarantee that different tokens are
-indexed to different buckets.
-** to improve the recall,
-you should increase `hash_count` parameter. For example,
-setting `hash_count=2`, will make each token to be hashed in
-two different ways, thus increasing the number of potential
-candidates for search.
-
-* the default settings makes the  `min_hash` filter to produce for
-each document 512 `min_hash` tokens, each is of size 16 bytes.
-Thus, each document's size will be increased by around 8Kb.
-
-* `min_hash` filter is used to hash for Jaccard similarity. This means
+* We recommend you test different arguments for the `hash_count`, `bucket_count` and
+  `hash_set_size` parameters:
+
+** To improve precision, increase the `bucket_count` or
+   `hash_set_size` arguments. Higher `bucket_count` and `hash_set_size` values
+   increase the likelihood that different tokens are indexed to different
+   buckets.
+
+** To improve the recall, increase the value of the `hash_count` argument. For
+   example, setting `hash_count` to `2` hashes each token in two different ways,
+   increasing the number of potential candidates for search.
+
+* By default, the `min_hash` filter produces 512 tokens for each document. Each
+token is 16 bytes in size. This means each document's size will be increased by
+around 8Kb.
+
+* The `min_hash` filter is used for Jaccard similarity. This means
 that it doesn't matter how many times a document contains a certain token,
 only that if it contains it or not.
 
-==== Theory
-MinHash token filter allows you to hash documents for similarity search.
+[[analysis-minhash-tokenfilter-similarity-search]]
+==== Using the `min_hash` token filter for similarity search
+
+The `min_hash` token filter allows you to hash documents for similarity search.
 Similarity search, or nearest neighbor search is a complex problem.
 A naive solution requires an exhaustive pairwise comparison between a query
 document and every document in an index. This is a prohibitive operation
@@ -88,18 +111,33 @@ document's tokens and chooses the minimum hash code among them.
 The minimum hash codes from all hash functions are combined
 to form a signature for the document.
 
+[[analysis-minhash-tokenfilter-customize]]
+==== Customize and add to an analyzer
+
+To customize the `min_hash` filter, duplicate it to create the basis for a new
+custom token filter. You can modify the filter using its configurable
+parameters.
 
-==== Example of setting MinHash Token Filter in Elasticsearch
-Here is an example of setting up a `min_hash` filter:
+For example, the following <<indices-create-index,create index API>> request
+uses the following custom token filters to configure a new
+<<analysis-custom-analyzer,custom analyzer>>:
 
-[source,js]
---------------------------------------------------
-POST /index1
+* `my_shingle_filter`, a custom <<analysis-shingle-tokenfilter,`shingle`
+  filter>>. `my_shingle_filter` only outputs five-word shingles.
+* `my_minhash_filter`, a custom `min_hash` filter. `my_minhash_filter` hashes
+  each five-word shingle once. It then assigns the hashes into 512 buckets,
+  keeping only the smallest hash from each bucket.
+
+The request also assigns the custom analyzer to the `fingerprint` field mapping.
+
+[source,console]
+----
+PUT /my_index
 {
   "settings": {
     "analysis": {
       "filter": {
-        "my_shingle_filter": { <1>
+        "my_shingle_filter": {      <1>
           "type": "shingle",
           "min_shingle_size": 5,
           "max_shingle_size": 5,
@@ -107,10 +145,10 @@ POST /index1
         },
         "my_minhash_filter": {
           "type": "min_hash",
-          "hash_count": 1,   <2>
-          "bucket_count": 512, <3>
-          "hash_set_size": 1, <4>
-          "with_rotation": true <5>
+          "hash_count": 1,          <2>
+          "bucket_count": 512,      <3>
+          "hash_set_size": 1,       <4>
+          "with_rotation": true     <5>
         }
       },
       "analyzer": {
@@ -133,10 +171,10 @@ POST /index1
     }
   }
 }
---------------------------------------------------
-// NOTCONSOLE
-<1> setting a shingle filter with 5-word shingles
-<2> setting min_hash filter to hash with 1 hash
-<3> setting min_hash filter to hash tokens into 512 buckets
-<4> setting min_hash filter to keep only a single smallest hash in each bucket
-<5> setting min_hash filter to fill empty buckets with values from neighboring buckets
+----
+
+<1> Configures a custom shingle filter to output only five-word shingles.
+<2> Each five-word shingle in the stream is hashed once.
+<3> The hashes are assigned to 512 buckets.
+<4> Only the smallest hash in each bucket is retained.
+<5> The filter fills empty buckets with the values of neighboring buckets.