$rankFusion (aggregation)

Command Fields

$rankFusion takes the following fields:

Collections

You can only use $rankFusion with a single collection. You cannot use this aggregation stage at a database scope.

De-Duplication

$rankFusion de-duplicates the results across multiple input pipelines in the final output. Each unique input document appears at most once in the $rankFusion output, regardless of the number of times that the document appears in input pipeline outputs.

Input Pipelines

Each input pipeline must be both a Selection Pipeline and a Ranked Pipeline.

Input Pipeline Names

Pipeline names in input must meet the following restrictions:

• Must not be an empty string

• Must not start with a $

• Must not contain the ASCII null character delimiter \0 anywhere in the string

• Must not contain a .

Reciprocal Rank Fusion (RRF) Formula

$rankFusion orders results according to the Reciprocal Rank Fusion (RRF) Formula. This stage places the RRF score for each document in the score metadata field of the output results. The RRF formula ranks documents with a combination of the following factors:

• The placement of documents in input pipeline results

• The number of times that a document appears in different input pipelines

• The weights of input pipelines.

For example, if a document has a high ranking in multiple pipeline result sets, the RRF score for that document would be higher than if that same document has the same ranking in some input pipelines, but is not present (or has a lower ranking) in the other pipelines

The Reciprocal Rank Fusion (RRF) Formula is equivalent to the following algebraic operation:

click to enlarge

The below table contains the variables that the RRF formula uses:

Each term in the summation represents the appearance of a document d in one of the input pipelines. The total RRF score for d is the summation of each of these terms across all the input pipelines that d appears in.

RRFscore(Document1) = 1/(60 + search_rank_of_Document1) + (1/(60 + vectorSearch_rank_of_Document1))
RRFscore(Document1) = 1/63 + 1/61
RRFscore(Document1) = 0.0322664585

scoreDetails

If you set scoreDetails to true, $rankFusion creates a scoreDetails metadata field for each document. The scoreDetails field contains information about the final ranking.

The scoreDetails field contains the following subfields:

Each array entry in the details field contains the following subfields:

For example, the following code blocks shows the scoreDetails field for a $rankFusion operation with $search, $vectorSearch, and $match input pipelines:

{
   value: 0.030621785881252923,
   description: "value output by reciprocal rank fusion algorithm, computed as sum of weight * (1 / (60 + rank)) across input pipelines from which this document is output, from:"
   details: [
         {
            inputPipelineName: 'search',
            rank: 2,
            weight: 1,
            value: 0.3876491287,
            description: "sum of:",
            details: [... omitted for brevity in this example ...]
         },
         {
            inputPipelineName: 'vector',
            rank: 9,
            weight: 3,
            value: 0.7793490886688232,
            details: [ ]
         },
         {
            inputPipelineName: 'match',
            rank: 10,
            weight: 1,
            details: []
         }
   ]
 }

Explain Results

MongoDB converts $rankFusion operations into a set of existing aggregation stages that, in combination, compute the output result prior to query execution. The Explain Results for a $rankFusion operation show the full execution of the underlying aggregation stages that $rankFusion uses to compose the final result.