Page 118 - DLIS402_INFORMATION_ANALYSIS_AND_REPACKAGING

Unit 6: Information Retrieval Model and Search Strategies

F-measure Notes
Main article: F-score
The weighted harmonic mean of precision and recall, the traditional F-measure or balanced F-score
is:

2 . precision . recall
F =
(precision + recall)
This is also known as the F measure, because recall and precision are evenly weighted.
1
The general formula for non-negative real β is:
.
(1 + β 2 ) (precision . recall)
F = β ( 2 . precision + recall) .
β
Two other commonly used F measures are the F measure, which weights recall twice as much as
2
precision, and the F measure, which weights precision twice as much as recall.
0.5
The F-measure was derived by van Rijsbergen (1979) so that F “measures the effectiveness of retrieval
β
with respect to a user who attaches β times as much importance to recall as precision”. It is based on
1
van Rijsbergen’s effectiveness measure E = 1 – . Their relationship is F = 1 “ E where
α + 1 − α β
P R

1
α = .
1 +β 2

Average Precision
Precision and recall are single-value metrics based on the whole list of documents returned by the
system. For systems that return a ranked sequence of documents, it is desirable to also consider the
order in which the returned documents are presented. Average precision emphasizes ranking relevant
documents higher. It is the average of precisions computed at the point of each of the relevant
documents in the ranked sequence:

N
∑ ( P( r × rel ( ))
)
r
r = 1
AveP =
number of relevant documents
where r is the rank, N the number retrieved, rel() a binary function on the relevance of a given rank,
and P(r) precision at a given cut-off rank:
|{relevant retrieved documents of rank or less}|
r
P(r) =
r
This metric is also sometimes referred to geometrically as the area under the Precision-Recall curve.

The denominator (number of relevant documents) is the number of relevant documents
in the entire collection, so that the metric reflects performance over all relevant
documents, regardless of a retrieval cut off.

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