Reciprocal Rank Fusion

Background Knowledge

The Reciprocal Rank Fusion (RRF) method is used to combine multiple ranked lists into a single list. This technique is commonly applied in information retrieval systems where multiple ranking models or algorithms are used to retrieve documents based on a query. The goal of RRF is to fuse these rankings to produce a more accurate and robust ranking. The RRF score for a document $d$ is calculated as $\text{RRF}(d) = \sum_{r \in R} \frac{1}{k + \text{rank}_r(d)}$, where $k$ is a constant and $\text{rank}_r(d)$ is the rank of document $d$ in ranking $r$.

In the context of information retrieval, rankings refer to the ordered lists of documents retrieved by a system in response to a query. Each document in the list is assigned a rank, which represents its position in the list. The reciprocal rank of a document is the reciprocal of its rank, which gives more weight to documents that appear higher in the ranking. By summing the reciprocal ranks of a document across multiple rankings, RRF aims to identify documents that consistently appear near the top of the rankings.

The constant $k$ in the RRF formula is used to prevent division by zero and to give more weight to documents that appear in multiple rankings. A typical value for $k$ is 60, but this can be adjusted depending on the specific application. The RRF method is simple to implement and has been shown to be effective in combining multiple rankings, but it can be sensitive to the choice of $k$ and the quality of the input rankings.