F1 score

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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 positive results divided by the number of all positive results, and r is the number of correct positive results divided by the number of positive 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 at 0.

The traditional F-measure or balanced F-score (F1 score) is the harmonic mean of precision and recall — multiplying the constant of 2 scales the score to 1 when both recall and precision are 1:

.

The general formula for positive real β is:

.

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

.

Two other commonly used F measures are the measure, which weighs recall higher than precision (by placing more emphasis on false negatives), and the measure, which weighs recall lower than precision (by attenuating the influence of false negatives).

The F-measure was derived so that "measures the effectiveness of retrieval with respect to a user who attaches β times as much importance to recall as precision".[1] It is based on Van Rijsbergen's effectiveness measure

.

Their relationship is where .

The F1 score is also known as the Sørensen–Dice coefficient or Dice similarity coefficient (DSC).

Diagnostic Testing[edit]

This is related to the field of binary classification where recall is often termed as Sensitivity. There are several reasons that the F1 score can be criticized in particular circumstances.[2]


predicted condition
total population prediction positive prediction negative Prevalence = Σ condition positive/Σ total population
true
condition
condition
positive
True Positive (TP) False Negative (FN)
(type II error)
True Positive Rate (TPR), Sensitivity, Recall, Probability of Detection = Σ TP/Σ condition positive False Negative Rate (FNR), Miss Rate = Σ FN/Σ condition positive
condition
negative
False Positive (FP)
(Type I error)
True Negative (TN) False Positive Rate (FPR), Fall-out, Probability of False Alarm = Σ FP/Σ condition negative True Negative Rate (TNR), Specificity (SPC) = Σ TN/Σ condition negative
Accuracy = Σ TP + Σ TN/Σ total population Positive Predictive Value (PPV), Precision = Σ TP/Σ prediction positive False Omission Rate (FOR) = Σ FN/Σ prediction negative Positive Likelihood Ratio (LR+) = TPR/FPR Diagnostic Odds Ratio (DOR) = LR+/LR−
False Discovery Rate (FDR) = Σ FP/Σ prediction positive Negative Predictive Value (NPV) = Σ TN/Σ prediction negative Negative Likelihood Ratio (LR−) = FNR/TNR

Applications[edit]

The F-score is often used in the field of information retrieval for measuring search, document classification, and query classification performance.[3] 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[4] and so is seen in wide application.

The F-score is also used in machine learning.[5] Note, however, that the F-measures do not take the true negatives into account, and that measures such as the Matthews correlation coefficient, Informedness or Cohen's kappa may be preferable to assess the performance of a binary classifier.[2]

The F-score has been widely used in the natural language processing literature, such as the evaluation of named entity recognition and word segmentation.

G-measure[edit]

While the F-measure is the harmonic mean of Recall and Precision, the G-measure is the geometric mean.[2]

.
. [6]

This is also known as the Fowlkes–Mallows index.

See also[edit]

References[edit]

  1. ^ Van Rijsbergen, C. J. (1979). Information Retrieval (2nd ed.). Butterworth. 
  2. ^ a b c Powers, David M W (2011). "Evaluation: From Precision, Recall and F-Measure to ROC, Informedness, Markedness & Correlation" (PDF). Journal of Machine Learning Technologies. 2 (1): 37–63. 
  3. ^ Beitzel., Steven M. (2006). On Understanding and Classifying Web Queries (Ph.D. thesis). IIT. CiteSeerX 10.1.1.127.634Freely accessible. 
  4. ^ X. Li; Y.-Y. Wang; A. Acero (July 2008). Learning query intent from regularized click graphs (PDF). Proceedings of the 31st SIGIR Conference. 
  5. ^ See, e.g., the evaluation of the CoNLL 2002 shared task.
  6. ^ Li, Guo-Zheng, et al. "Inquiry diagnosis of coronary heart disease in Chinese medicine based on symptom-syndrome interactions." Chinese medicine 7.1 (2012): 1.