These functions calculate the recall, precision or F values of a measurement system for finding/retrieving relevant documents compared to reference results (the truth regarding relevance). The measurement and "truth" data must have the same two possible outcomes and one of the outcomes must be thought of as a "relevant" results.
recall(data, ...) # S3 method for table recall(data, relevant = rownames(data)[1], ...) # S3 method for default recall(data, reference, relevant = levels(reference)[1], na.rm = TRUE, ...) precision(data, ...) # S3 method for default precision(data, reference, relevant = levels(reference)[1], na.rm = TRUE, ...) # S3 method for table precision(data, relevant = rownames(data)[1], ...) F_meas(data, ...) # S3 method for default F_meas(data, reference, relevant = levels(reference)[1], beta = 1, na.rm = TRUE, ...) # S3 method for table F_meas(data, relevant = rownames(data)[1], beta = 1, ...)
| data | for the default functions, a factor containing the discrete
measurements. For the |
|---|---|
| ... | not currently used |
| relevant | a character string that defines the factor level corresponding to the "relevant" results |
| reference | a factor containing the reference values (i.e. truth) |
| na.rm | a logical value indicating whether |
| beta | a numeric value used to weight precision and recall. A value of 1 is traditionally used and corresponds to the harmonic mean of the two values but other values weight recall beta times more important than precision. |
A number between 0 and 1 (or NA).
The recall (aka sensitivity) is defined as the proportion of relevant
results out of the number of samples which were actually relevant. When
there are no relevant results, recall is not defined and a value of
NA is returned.
The precision is percentage of predicted truly relevant results of the total number of predicted relevant results and characterizes the "purity in retrieval performance" (Buckland and Gey, 1994)
The measure "F" is a combination of precision and recall (see below).
Suppose a 2x2 table with notation
| Reference | ||
| Predicted | relevant | Irrelevant |
| relevant | A | B |
| Irrelevant | C | D |
The formulas used here are: $$recall = A/(A+C)$$ $$precision = A/(A+B)$$ $$F_i = (1+i^2)*prec*recall/((i^2 * precision)+recall)$$
See the references for discussions of the statistics.
Kuhn, M. (2008), ``Building predictive models in R using the caret package, '' Journal of Statistical Software, (http://www.jstatsoft.org/article/view/v028i05/v28i05.pdf).
Buckland, M., & Gey, F. (1994). The relationship between Recall and Precision. Journal of the American Society for Information Science, 45(1), 12-19.
Powers, D. (2007). Evaluation: From Precision, Recall and F Factor to ROC, Informedness, Markedness and Correlation. Technical Report SIE-07-001, Flinders University
################### ## Data in Table 2 of Powers (2007) lvs <- c("Relevant", "Irrelevant") tbl_2_1_pred <- factor(rep(lvs, times = c(42, 58)), levels = lvs) tbl_2_1_truth <- factor(c(rep(lvs, times = c(30, 12)), rep(lvs, times = c(30, 28))), levels = lvs) tbl_2_1 <- table(tbl_2_1_pred, tbl_2_1_truth) precision(tbl_2_1)#> [1] 0.7142857precision(data = tbl_2_1_pred, reference = tbl_2_1_truth, relevant = "Relevant")#> [1] 0.7142857recall(tbl_2_1)#> [1] 0.5recall(data = tbl_2_1_pred, reference = tbl_2_1_truth, relevant = "Relevant")#> [1] 0.5tbl_2_2_pred <- factor(rep(lvs, times = c(76, 24)), levels = lvs) tbl_2_2_truth <- factor(c(rep(lvs, times = c(56, 20)), rep(lvs, times = c(12, 12))), levels = lvs) tbl_2_2 <- table(tbl_2_2_pred, tbl_2_2_truth) precision(tbl_2_2)#> [1] 0.7368421precision(data = tbl_2_2_pred, reference = tbl_2_2_truth, relevant = "Relevant")#> [1] 0.7368421recall(tbl_2_2)#> [1] 0.8235294recall(data = tbl_2_2_pred, reference = tbl_2_2_truth, relevant = "Relevant")#> [1] 0.8235294