Last updated: 2025-11-03
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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | 4a94ae8 | Dave Tang | 2025-11-03 | Run R code for yardstick::mcc_vec() |
| html | d44b00d | Dave Tang | 2025-11-03 | Build site. |
| Rmd | 0be926e | Dave Tang | 2025-11-03 | Matthews Correlation Coefficient |
The Matthews Correlation Coefficient (MCC) is a single-number measure of how well a binary classification model performs. It takes into account true and false positives and negatives, providing a balanced evaluation even when classes are unevenly distributed.
Imagine an email classifier that predicts whether an email is
spam (1) or not spam
(0).
| Predicted Positive | Predicted Negative | |
|---|---|---|
| Actual Positive | True Positive (TP) | False Negative (FN) |
| Actual Negative | False Positive (FP) | True Negative (TN) |
The MCC is calculated following:
\[ \text{MCC} = \frac{(TP \times TN) - (FP \times FN)}{\sqrt{(TP+FP)(TP+FN)(TN+FP)(TN+FN)}} \]
MCC works well even with class imbalance and provides a balanced score.
Given the following predictions and actual outcomes:
actual <- c(1, 0, 1, 1, 0, 0, 1, 0)
predicted <- c(1, 0, 1, 0, 0, 0, 1, 1)
table(actual, predicted) predicted
actual 0 1
0 3 1
1 1 3Calculate the MCC:
TP <- 3
TN <- 3
FP <- 1
FN <- 1
my_mcc <- (TP * TN - FP * FN) /
sqrt((TP + FP) * (TP + FN) * (TN + FP) * (TN + FN))
my_mcc[1] 0.5Suppose we have a model predicting three possible classes: “A”, “B”, and “C”.
# Ground truth (actual labels)
truth <- factor(c("A", "B", "C", "A", "B", "C", "A", "C", "B", "B"))
# Model predictions
predicted <- factor(c("A", "C", "C", "A", "B", "B", "C", "C", "B", "A"))
results <- tibble(
truth = truth,
estimate = predicted
)
results# A tibble: 10 × 2
truth estimate
<fct> <fct>
1 A A
2 B C
3 C C
4 A A
5 B B
6 C B
7 A C
8 C C
9 B B
10 B A Using {yardstick}.
yardstick::mcc_vec(truth, predicted)[1] 0.4090909
sessionInfo()R version 4.5.0 (2025-04-11)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.3 LTS
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
time zone: Etc/UTC
tzcode source: system (glibc)
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] yardstick_1.3.2 lubridate_1.9.4 forcats_1.0.0 stringr_1.5.1
[5] dplyr_1.1.4 purrr_1.0.4 readr_2.1.5 tidyr_1.3.1
[9] tibble_3.3.0 ggplot2_3.5.2 tidyverse_2.0.0 workflowr_1.7.1
loaded via a namespace (and not attached):
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[5] hms_1.1.3 digest_0.6.37 magrittr_2.0.3 timechange_0.3.0
[9] evaluate_1.0.3 grid_4.5.0 RColorBrewer_1.1-3 fastmap_1.2.0
[13] rprojroot_2.0.4 jsonlite_2.0.0 processx_3.8.6 whisker_0.4.1
[17] ps_1.9.1 promises_1.3.3 httr_1.4.7 scales_1.4.0
[21] jquerylib_0.1.4 cli_3.6.5 rlang_1.1.6 withr_3.0.2
[25] cachem_1.1.0 yaml_2.3.10 tools_4.5.0 tzdb_0.5.0
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[33] git2r_0.36.2 fs_1.6.6 pkgconfig_2.0.3 callr_3.7.6
[37] pillar_1.10.2 bslib_0.9.0 later_1.4.2 gtable_0.3.6
[41] glue_1.8.0 Rcpp_1.0.14 xfun_0.52 tidyselect_1.2.1
[45] rstudioapi_0.17.1 knitr_1.50 farver_2.1.2 htmltools_0.5.8.1
[49] rmarkdown_2.29 compiler_4.5.0 getPass_0.2-4