Calculating and Visualizing ROC and PR Curves Across Multi-Class Classifications
The receiver operating characteristic (ROC) and precision recall (PR) is an extensively utilized method for comparing binary classifiers in various areas. However, many real-world problems are designed to multiple classes (e.g., tumor, node, and metastasis staging system of cancer), which require an evaluation strategy to assess multiclass classifiers. This package aims to fill the gap by enabling the calculation of multiclass ROC-AUC and PR-AUC with confidence intervals and the generation of publication-quality figures of multiclass ROC curves and PR curves.
A user-friendly website is available at https://metabolomics.cc.hawaii.edu/software/multiROC/.
Please cite our paper once it is published: (Submitted).
Install multiROC from GitHub:
install.packages('devtools')
require(devtools)
install_github("WandeRum/multiROC")
require(multiROC)
Install multiROC from CRAN:
install.packages('multiROC')
require(multiROC)
This demo is about the comparison between random forest and multinomial logistic regression based on Iris data.
require(multiROC) data(iris) head(iris)3.2 60% training data and 40% testing data
set.seed(123456) total_number <- nrow(iris) train_idx <- sample(total_number, round(total_number*0.6)) train_df <- iris[train_idx, ] test_df <- iris[-train_idx, ]
rf_res <- randomForest::randomForest(Species~., data = train_df, ntree = 100) rf_pred <- predict(rf_res, test_df, type = 'prob') rf_pred <- data.frame(rf_pred) colnames(rf_pred) <- paste(colnames(rf_pred), "_pred_RF")3.4 Multinomial logistic regression
mn_res <- nnet::multinom(Species ~., data = train_df) mn_pred <- predict(mn_res, test_df, type = 'prob') mn_pred <- data.frame(mn_pred) colnames(mn_pred) <- paste(colnames(mn_pred), "_pred_MN")3.5 Merge true labels and predicted values
true_label <- dummies::dummy(test_df$Species, sep = ".")
true_label <- data.frame(true_label)
colnames(true_label) <- gsub(".*?\\.", "", colnames(true_label))
colnames(true_label) <- paste(colnames(true_label), "_true")
final_df <- cbind(true_label, rf_pred, mn_pred)
roc_res <- multi_roc(final_df, force_diag=T) pr_res <- multi_pr(final_df, force_diag=T)
plot_roc_df <- plot_roc_data(roc_res)
plot_pr_df <- plot_pr_data(pr_res)
require(ggplot2)
ggplot(plot_roc_df, aes(x = 1-Specificity, y=Sensitivity)) +
geom_path(aes(color = Group, linetype=Method), size=1.5) +
geom_segment(aes(x = 0, y = 0, xend = 1, yend = 1),
colour='grey', linetype = 'dotdash') +
theme_bw() +
theme(plot.title = element_text(hjust = 0.5),
legend.justification=c(1, 0), legend.position=c(.95, .05),
legend.title=element_blank(),
legend.background = element_rect(fill=NULL, size=0.5,
linetype="solid", colour ="black"))
ggplot(plot_pr_df, aes(x=Recall, y=Precision)) +
geom_path(aes(color = Group, linetype=Method), size=1.5) +
theme_bw() +
theme(plot.title = element_text(hjust = 0.5),
legend.justification=c(1, 0), legend.position=c(.95, .05),
legend.title=element_blank(),
legend.background = element_rect(fill=NULL, size=0.5,
linetype="solid", colour ="black"))
library(multiROC) data(test_data) head(test_data)
## G1_true G2_true G3_true G1_pred_m1 G2_pred_m1 G3_pred_m1 G1_pred_m2 G2_pred_m2 G3_pred_m2
## 1 1 0 0 0.8566867 0.1169520 0.02636133 0.4371601 0.1443851 0.41845482
## 2 1 0 0 0.8011788 0.1505448 0.04827643 0.3075236 0.5930025 0.09947397
## 3 1 0 0 0.8473608 0.1229815 0.02965766 0.3046363 0.4101367 0.28522698
## 4 1 0 0 0.8157730 0.1422322 0.04199482 0.2378494 0.5566147 0.20553591
## 5 1 0 0 0.8069553 0.1472971 0.04574766 0.4067347 0.2355822 0.35768312
## 6 1 0 0 0.6894488 0.2033285 0.10722271 0.1063048 0.4800507 0.41364450
This example dataset contains two classifiers (m1, m2), and three groups (G1, G2, G3).
4.1 multi_roc and multi_pr functionroc_res <- multi_roc(test_data, force_diag=T) pr_res <- multi_pr(test_data, force_diag=T)
The function multi_roc and multi_pr are core functions for calculating multiclass ROC-AUC and PR-AUC.
Arguments of multi_roc and multi_pr:
data is the dataset contains both of true labels and corresponding predicted scores. True labels (0 - Negative, 1 - Positive) columns should be named as XX_true (e.g., S1_true, S2_true) and predictive scores (continuous) columns should be named as XX_pred_YY (e.g., S1_pred_SVM, S2_pred_RF). Predictive scores can be probabilities among [0, 1] or other continuous values. For each classifier, the number of columns should be equal to the number of groups of true labels.
If force_diag equals TRUE, true positive rate (TPR) and false positive rate (FPR) will be forced to across (0, 0) and (1, 1).
Outputs of multi_roc:
Specificity contains a list of specificities for each group of different classifiers.
Sensitivity contains a list of sensitivities for each group of different classifiers.
AUC contains a list of AUC for each group of different classifiers. Micro-average ROC-AUC was calculated by stacking all groups together, thus converting the multi-class classification into binary classification. Macro-average ROC-AUC was calculated by averaging all groups results (one vs rest) and linear interpolation was used between points of ROC.
Methods shows names of different classifiers.
Groups shows names of different groups.
Outputs of multi_pr:
Recall contains a list of recalls for each group of different classifiers.
Precision contains a list of precisions for each group of different classifiers.
AUC contains a list of AUC for each group of different classifiers. Micro-average PR-AUC was calculated by stacking all groups together, thus converting the multi-class classification into binary classification. Macro-average PR-AUC was calculated by averaging all groups results (one vs rest) and linear interpolation was used between points of ROC.
Methods shows names of different classifiers.
Groups shows names of different groups.
## m1.G1 m1.G2 m1.G3 m1.macro m1.micro m2.G1 m2.G2 m2.G3 m2.macro m2.micro
## 0.7233607 0.5276190 0.9751462 0.7420609 0.8824221 0.3237705 0.3723810 0.4020468 0.3665670 0.4174394
This list shows the following AUC information:
roc_ci_res <- roc_ci(test_data, conf= 0.95, type='basic', R = 100, index = 4) pr_ci_res <- pr_ci(test_data, conf= 0.95, type='basic', R = 100, index = 4)
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 100 bootstrap replicates
##
## CALL :
## boot.ci(boot.out = res_boot, conf = conf, type = type, index = index)
##
## Intervals :
## Level BCa
## 95% ( 0.649, 0.861 )
## Calculations and Intervals on Original Scale
## Some BCa intervals may be unstable
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 100 bootstrap replicates
##
## CALL :
## boot.ci(boot.out = res_boot, conf = conf, type = type, index = index)
##
## Intervals :
## Level BCa
## 95% ( 0.4242, 0.6547 )
## Calculations and Intervals on Original Scale
## Warning : BCa Intervals used Extreme Quantiles
## Some BCa intervals may be unstable
The function roc_ci and pr_ci are used to calculate confidence intervals of multiclass ROC-AUC and PR-AUC.
Arguments of roc_ci and pr_ci:
data is the dataset contains both of true labels and corresponding predicted scores. True labels (0 - Negative, 1 - Positive) columns should be named as XX_true (e.g., S1_true, S2_true) and predictive scores (continuous) columns should be named as XX_pred_YY (e.g., S1_pred_SVM, S2_pred_RF). Predictive scores can be probabilities among [0, 1] or other continuous values. For each classifier, the number of columns should be equal to the number of groups of true labels.
conf contains the required level of confidence intervals, and the default number is 0.95.
type includes five different types of equi-tailed two-sided nonparametric confidence intervals (e.g., "norm","basic", "stud", "perc", "bca", "all").
R is the number of bootstrap replicates, the default number is 100.
index is the position of the list of AUC results in 3.2.1.
Here, we set index = 4 to calculate 95% CI of AUC of Macro in the classifier m1 based on 1000 bootstrap replicates as an example.
roc_auc_with_ci_res <- roc_auc_with_ci(test_data, conf= 0.95, type='bca', R = 100) roc_auc_with_ci_res pr_auc_with_ci_res <- pr_auc_with_ci(test_data, conf= 0.95, type='bca', R = 100) pr_auc_with_ci_res
## Var AUC lower CI higher CI
## 1 m1.G1 0.7233607 0.5555556 0.8406849
## 2 m1.G2 0.5276190 0.3141490 0.6991112
## 3 m1.G3 0.9751462 0.9156118 0.9969245
## 4 m1.macro 0.7420420 0.6162905 0.8469999
## 5 m1.micro 0.8824221 0.7942627 0.9318145
## 6 m2.G1 0.3237705 0.2039669 0.4888149
## 7 m2.G2 0.3723810 0.2322795 0.5126755
## 8 m2.G3 0.4020468 0.2266853 0.5944778
## 9 m2.macro 0.3665214 0.2796633 0.4970809
## 10 m2.micro 0.4174394 0.3449170 0.5036827
## Var AUC lower CI higher CI
## 1 m1.G1 0.81104090 0.69394085 0.9219133
## 2 m1.G2 0.18898097 0.09755974 0.3404294
## 3 m1.G3 0.67479141 0.34789377 0.9871966
## 4 m1.macro 0.54968868 0.43208030 0.6663112
## 5 m1.micro 0.75125213 0.61651803 0.8635095
## 6 m2.G1 0.60633468 0.49548427 0.7510816
## 7 m2.G2 0.13298786 0.06840618 0.2092138
## 8 m2.G3 0.08150105 0.03931745 0.1388464
## 9 m2.macro 0.27320882 0.23863708 0.3009619
## 10 m2.micro 0.27540471 0.23380391 0.3087388
The function roc_auc_with_ci and pr_auc_with_ci are used to calculate confidence intervals of multiclass ROC-AUC, PR-AUC, and output a dataframe with AUCs, lower CIs, and higher CIs of all methods and groups.
Arguments of roc_auc_with_ci and pr_auc_with_ci:
data is the dataset contains both of true labels and corresponding predicted scores. True labels (0 - Negative, 1 - Positive) columns should be named as XX_true (e.g., S1_true, S2_true) and predictive scores (continuous) columns should be named as XX_pred_YY (e.g., S1_pred_SVM, S2_pred_RF). Predictive scores can be probabilities among [0, 1] or other continuous values. For each classifier, the number of columns should be equal to the number of groups of true labels.
conf contains the required level of confidence intervals, and the default number is 0.95.
type includes five different types of equi-tailed two-sided nonparametric confidence intervals (e.g., "norm","basic", "stud", "perc", "bca").
R is the number of bootstrap replicates, the default number is 100.
plot_roc_df <- plot_roc_data(roc_res) plot_pr_df <- plot_pr_data(pr_res)
ggplot(plot_roc_df, aes(x = 1-Specificity, y=Sensitivity)) + geom_path(aes(color = Group, linetype=Method)) + geom_segment(aes(x = 0, y = 0, xend = 1, yend = 1), colour='grey', linetype = 'dotdash') + theme_bw() + theme(plot.title = element_text(hjust = 0.5), legend.justification=c(1, 0), legend.position=c(.95, .05), legend.title=element_blank(), legend.background = element_rect(fill=NULL, size=0.5, linetype="solid", colour ="black"))
ggplot(plot_pr_df, aes(x=Recall, y=Precision)) + geom_path(aes(color = Group, linetype=Method), size=1.5) + theme_bw() + theme(plot.title = element_text(hjust = 0.5), legend.justification=c(1, 0), legend.position=c(.95, .05), legend.title=element_blank(), legend.background = element_rect(fill=NULL, size=0.5, linetype="solid", colour ="black"))
For sending comments, suggestions, bug reports of multiROC, please email to Runmin Wei (wander1021@gmail.com) or report it via thus URL: https://github.com/WandeRum/multiROC/issues
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