elasticsearch/docs/reference/search/rrf.asciidoc

[[rrf]]
=== Reciprocal rank fusion

preview::[]

https://plg.uwaterloo.ca/~gvcormac/cormacksigir09-rrf.pdf[Reciprocal rank fusion (RRF)]
is a method for combining multiple result sets with different relevance
indicators into a single result set. RRF requires no tuning, and the different
relevance indicators do not have to be related to each other to achieve high-quality
results.

RRF uses the following formula to determine the score for ranking each document:

[source,python]
----
score = 0.0
for q in queries:
    if d in result(q):
        score += 1.0 / ( k + rank( result(q), d ) )
return score

# where
# k is a ranking constant
# q is a query in the set of queries
# d is a document in the result set of q
# result(q) is the result set of q
# rank( result(q), d ) is d's rank within the result(q) starting from 1
----
// NOTCONSOLE

[[rrf-api]]
==== Reciprocal rank fusion API

You can use RRF as part of a <<search-search, search>> to combine and rank
documents using multiple result sets from

* 1 query and 1 or more kNN searches
* 2 or more kNN searches

The `rrf` parameter is an optional object defined as part of a search request's
<<request-body-rank, rank parameter>>. The `rrf` object contains the following
parameters:

`rank_constant`::
(Optional, integer) This value determines how much influence documents in individual
result sets per query have over the final ranked result set. A higher value indicates
that lower ranked documents have more influence. This value must be greater than or
equal to `1`. Defaults to `60`.

`window_size`::
(Optional, integer) This value determines the size of the individual result sets per
query. A higher value will improve result relevance at the cost of performance. The final
ranked result set is pruned down to the search request's <<search-size-param, size>.
`window_size` must be greater than or equal to `size` and greater than or equal to `1`.
Defaults to `100`.

An example request using RRF:

[source,console]
----
GET example-index/_search
{
    "query": {
        "term": {
            "text": "shoes"
        }
    },
    "knn": {
        "field": "vector",
        "query_vector": [1.25, 2, 3.5],
        "k": 50,
        "num_candidates": 100
    },
    "rank": {
        "rrf": {
            "window_size": 50,
            "rank_constant": 20
        }
    }
}
----
// TEST[skip:example fragment]

In the above example, we first execute the kNN search to get its global top 50 results.
Then we execute the query to get its global top 50 results. Afterwards, on a coordinating
node, we combine the knn search results with the query results and rank them based on the
RRF method to get the final top 10 results.

Note that if `k` from a knn search is larger than `window_size`, the results are
truncated to `window_size`. If `k` is smaller than `window_size`, the results are
`k` size.

[[rrf-supported-features]]
==== Reciprocal rank fusion supported features

RRF does support:

* <<search-from-param, from>>
* <<search-aggregations, aggregations>>

RRF does not currently support:

* <<search-api-scroll-query-param, scroll>>
* <<search-api-pit, point in time>>
* <<search-sort-param, sort>>
* <<rescore, rescore>>
* <<search-suggesters, suggesters>>
* <<highlighting, highlighting>>
* <<collapse-search-results, collapse>>
* <<request-body-search-explain, explain>>
* <<profiling-queries, profiling>>

Using unsupported features as part of a search using RRF will result
in an exception.

[[rrf-full-example]]
==== Reciprocal rank fusion full example

We begin by creating a mapping for an index with a text field, a vector field,
and an integer field along with indexing several documents. For this example we
are going to use a vector with only a single dimension to make the ranking easier
to explain.

[source,console]
----
PUT example-index
{
  "mappings": {
        "properties": {
            "text" : {
                "type" : "text"
            },
            "vector": {
                "type": "dense_vector",
                "dims": 1,
                "index": true,
                "similarity": "l2_norm"
            },
            "integer" : {
                "type" : "integer"
            }
        }
    }
}

PUT example-index/_doc/1
{
    "text" : "rrf",
    "vector" : [5],
    "integer": 1
}

PUT example-index/_doc/2
{
    "text" : "rrf rrf",
    "vector" : [4],
    "integer": 2
}

PUT example-index/_doc/3
{
    "text" : "rrf rrf rrf",
    "vector" : [3],
    "integer": 1
}

PUT example-index/_doc/4
{
    "text" : "rrf rrf rrf rrf",
    "integer": 2
}

PUT example-index/_doc/5
{
    "vector" : [0],
    "integer": 1
}

POST example-index/_refresh
----
// TEST

We now execute a search using RRF with a query, a kNN search, and
a terms aggregation.

[source,console]
----
GET example-index/_search
{
    "query": {
        "term": {
            "text": "rrf"
        }
    },
    "knn": {
        "field": "vector",
        "query_vector": [3],
        "k": 5,
        "num_candidates": 5
    },
    "rank": {
        "rrf": {
            "window_size": 5,
            "rank_constant": 1
        }
    },
    "size": 3,
    "aggs": {
        "int_count": {
            "terms": {
                "field": "integer"
            }
        }
    }
}
----
// TEST[continued]

And we receive the response with ranked `hits` and the terms
aggregation result. Note that `_score` is `null`, and we instead
use `_rank` to show our top-ranked documents.

[source,console-response]
----
{
    "took": ...,
    "timed_out" : false,
    "_shards" : {
        "total" : 1,
        "successful" : 1,
        "skipped" : 0,
        "failed" : 0
    },
    "hits" : {
        "total" : {
            "value" : 5,
            "relation" : "eq"
        },
        "max_score" : null,
        "hits" : [
            {
                "_index" : "example-index",
                "_id" : "3",
                "_score" : null,
                "_rank" : 1,
                "_source" : {
                    "integer" : 1,
                    "vector" : [
                        3
                    ],
                    "text" : "rrf rrf rrf"
                }
            },
            {
                "_index" : "example-index",
                "_id" : "2",
                "_score" : null,
                "_rank" : 2,
                "_source" : {
                    "integer" : 2,
                    "vector" : [
                        4
                    ],
                    "text" : "rrf rrf"
                }
            },
            {
                "_index" : "example-index",
                "_id" : "4",
                "_score" : null,
                "_rank" : 3,
                "_source" : {
                    "integer" : 2,
                    "text" : "rrf rrf rrf rrf"
                }
            }
        ]
    },
    "aggregations" : {
        "int_count" : {
            "doc_count_error_upper_bound" : 0,
            "sum_other_doc_count" : 0,
            "buckets" : [
                {
                    "key" : 1,
                    "doc_count" : 3
                },
                {
                    "key" : 2,
                    "doc_count" : 2
                }
            ]
        }
    }
}
----
// TESTRESPONSE[s/: \.\.\./: $body.$_path/]

Let's break down how these hits were ranked. We
start by running the query and the kNN search
separately to collect what their individual hits are.

First, we look at the hits for the query.

[source,console-result]
----
"hits" : [
    {
        "_index" : "example-index",
        "_id" : "4",
        "_score" : 0.16152832,              <1>
        "_source" : {
            "integer" : 2,
            "text" : "rrf rrf rrf rrf"
        }
    },
    {
        "_index" : "example-index",
        "_id" : "3",                        <2>
        "_score" : 0.15876243,
        "_source" : {
            "integer" : 1,
            "vector" : [3],
            "text" : "rrf rrf rrf"
        }
    },
    {
        "_index" : "example-index",
        "_id" : "2",                        <3>
        "_score" : 0.15350538,
        "_source" : {
            "integer" : 2,
            "vector" : [4],
            "text" : "rrf rrf"
        }
    },
    {
        "_index" : "example-index",
        "_id" : "1",                        <4>
        "_score" : 0.13963442,
        "_source" : {
            "integer" : 1,
            "vector" : [5],
            "text" : "rrf"
        }
    }
]
----
// TEST[skip:example fragment]
<1> rank 1, `_id` 4
<2> rank 2, `_id` 3
<3> rank 3, `_id` 2
<4> rank 4, `_id` 1

Note that our first hit doesn't have a value for the `vector` field. Now,
we look at the results for the kNN search.

[source,console-result]
----
"hits" : [
    {
        "_index" : "example-index",
        "_id" : "3",                   <1>
        "_score" : 1.0,
        "_source" : {
            "integer" : 1,
            "vector" : [3],
            "text" : "rrf rrf rrf"
        }
    },
    {
        "_index" : "example-index",
        "_id" : "2",                   <2>
        "_score" : 0.5,
        "_source" : {
            "integer" : 2,
            "vector" : [4],
            "text" : "rrf rrf"
        }
    },
    {
        "_index" : "example-index",
        "_id" : "1",                   <3>
        "_score" : 0.2,
        "_source" : {
            "integer" : 1,
            "vector" : [5],
            "text" : "rrf"
        }
    },
    {
        "_index" : "example-index",
        "_id" : "5",                   <4>
        "_score" : 0.1,
        "_source" : {
            "integer" : 1,
            "vector" : [0]
        }
    }
]
----
// TEST[skip:example fragment]
<1> rank 1, `_id` 3
<2> rank 2, `_id` 2
<3> rank 3, `_id` 1
<4> rank 4, `_id` 5

We can now take the two individually ranked result sets and apply the
RRF formula to them to get our final ranking.

[source,python]
----
# doc  | query     | knn       | score
_id: 1 = 1.0/(1+4) + 1.0/(1+3) = 0.4500
_id: 2 = 1.0/(1+3) + 1.0/(1+2) = 0.5833
_id: 3 = 1.0/(1+2) + 1.0/(1+1) = 0.8333
_id: 4 = 1.0/(1+1)             = 0.5000
_id: 5 =             1.0/(1+4) = 0.2000
----
// NOTCONSOLE

We rank the documents based on the RRF formula with a `window_size` of `5`
truncating the bottom `2` docs in our RRF result set with a `size` of `3`.
We end with `_id: 3` as `_rank: 1`, `_id: 2` as `_rank: 2`, and
`_id: 4` as `_rank: 3`. This ranking matches the result set from the
original RRF search as expected.