Quotient category

In statistical analysis of Binary classification, the F₁ score (also F-score or F-measure) is a measure of a test's accuracy. It considers both the precision p and the recall r of the test to compute the score: p is the number of correct results divided by the number of all returned results and r is the number of correct results divided by the number of results that should have been returned. The F₁ score can be interpreted as a weighted average of the precision and recall, where an F₁ score reaches its best value at 1 and worst score at 0.

The traditional F-measure or balanced F-score (F₁ score) is the harmonic mean of precision and recall:

$F_{1}=2\cdot {\frac {\mathrm {precision} \cdot \mathrm {recall} }{\mathrm {precision} +\mathrm {recall} }}$.

The general formula for positive real β is:

$F_{\beta }=(1+\beta ^{2})\cdot {\frac {\mathrm {precision} \cdot \mathrm {recall} }{(\beta ^{2}\cdot \mathrm {precision} )+\mathrm {recall} }}$.

The formula in terms of Type I and type II errors:

$F_{\beta }={\frac {(1+\beta ^{2})\cdot \mathrm {true\ positive} }{(1+\beta ^{2})\cdot \mathrm {true\ positive} +\beta ^{2}\cdot \mathrm {false\ negative} +\mathrm {false\ positive} }}\,$.

Two other commonly used F measures are the $F_{2}$ measure, which weights recall higher than precision, and the $F_{0.5}$ measure, which puts more emphasis on precision than recall.

The F-measure was derived so that $F_{\beta }$ "measures the effectiveness of retrieval with respect to a user who attaches β times as much importance to recall as precision". It is based on Van Rijsbergen's effectiveness measure

$E=1-\left({\frac {\alpha }{P}}+{\frac {1-\alpha }{R}}\right)^{-1}$.

Their relationship is $F_{\beta }=1-E$ where $\alpha ={\frac {1}{1+\beta ^{2}}}$.

Diagnostic Testing

This is related to the field of binary classification where recall is often termed as Sensitivity. There are several reason that the F1 score can be criticized in particular circumstances.

Applications

The F-score is often used in the field of information retrieval for measuring search, document classification, and query classification performance. Earlier works focused primarily on the F₁ score, but with the proliferation of large scale search engines, performance goals changed to place more emphasis on either precision or recall and so $F_{\beta }$ is seen in wide application.

The F-score is also used in machine learning. Note, however, that the F-measures do not take the true negative rate into account, and that measures such as the Phi coefficient, Matthews correlation coefficient, Informedness or Cohen's kappa may be preferable to assess the performance of a binary classifier.

The F-score has been widely used in the natural language processing literature, such as the evaluation of named entity recognition, Chinese word segmentation, etc. F-score is usually measured by IV F-score and OOV F-score, where the IV means in vocabulary and OOV means out of vocabulary. IV and OOV are distinguished by whether the testing words exist in the training data.

G-measure

While the F-measure is the Harmonic mean of Recall and Precision the G-measure is the Geometric Mean of Recall and Precision. Information content corresponds to the Arithmetic Mean of the Information represented by Recall and Precision.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.

$G={\sqrt {\mathrm {precision} \cdot \mathrm {recall} }}$.

See also

• Precision and recall
• BLEU
• NIST (metric)
• METEOR
• ROUGE (metric)
• Word Error Rate (WER)
• Receiver operating characteristic
• Matthews correlation coefficient

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.