ROCR: visualizing classifier performance in R"
In ROCR: Visualizing the Performance of Scoring Classifiers

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

Introduction

library(ROCR)

Pattern classification has become a central tool in bioinformatics, offering rapid insights into large data sets [@Baldi2001]. While one area of our work involves predicting phenotypic properties of HIV-1 from genotypic information [@Beerenwinkel2002;@Beerenwinkel2003;@Sing04learningmixtures], scoring or ranking predictors are also vital in a wide range of other biological problems. Examples include microarray analysis (e.g. prediction of tissue condition based on gene expression), protein structural and functional characterization (remote homology detection, prediction of post-translational modifications and molecular function annotation based on sequence or structural motifs), genome annotation (gene finding and splice site identification), protein–ligand interactions (virtual screening and molecular docking) and structure–activity relationships (predicting bioavailability or toxicity of drug compounds). In many of these cases, considerable class skew, class-specific misclassification costs, and extensive noise due to variability in experimental assays complicate predictive modelling. Thus, careful predictor validation is compulsory.

table <- data.frame(group = c("Contingency ratios",
                              "Discrete covariation measures",
                              "Information retrieval measures",
                              "Performance in ROC space",
                              "Absolute scoring performance",
                              "Cost measures"),
                    measure = c("error rate, accuracy, sensitivity, specificity, true/false positive rate, fallout, miss, precision, recall, negative predictive value, prediction-conditioned fallout/miss.",
                                "Phi/Matthews correlation coefficient, mutual information, Chi-squared test statistic, odds ratio",
                                "F-measure, lift, precision-recall break-even point",
                                "ROC convex hull, area under the ROC curve",
                                "calibration error, mean cross-entropy, root mean-squared error",
                                "expected cost, explicit cost"))
knitr::kable(table,
             caption = "***Table 1:**Performance measures in the ROCR package*",
             col.names = c("",""),
             align = "l")

The real-valued output of scoring classifiers is turned into a binary class decision by choosing a cutoff. As no cutoff is optimal according to all possible performance criteria, cutoff choice involves a trade-off among different measures. Typically, a trade-off between a pair of criteria (e.g. sensitivity versus specificity) is visualized as a cutoff-parametrized curve in the plane spanned by the two measures. Popular examples of such trade-off visualizations include receiver operating characteristic (ROC) graphs, sensitivity/specificity curves, lift charts and precision/recall plots. @Fawcett2004 provides a general introduction into evaluating scoring classifiers with a focus on ROC graphs.

Although functions for drawing ROC graphs are provided by the Bioconductor project (http://www.bioconductor.org) or by the machine learning package Weka (http://www.cs.waikato.ac.nz/ml), for example, no comprehensive evaluation suite is available to date. ROCR is a flexible evaluation package for R (https://www.r-project.org), a statistical language that is widely used in biomedical data analysis. Our tool allows for creating cutoff-parametrized performance curves by freely combining two out of more than 25 performance measures (Table 1). Curves from different cross-validation or bootstrapping runs can be averaged by various methods. Standard deviations, standard errors and box plots are available to summarize the variability across the runs. The parametrization can be visualized by printing cutoff values at the corresponding curve positions, or by coloring the curve according to the cutoff. All components of a performance plot are adjustable using a flexible mechanism for dispatching optional arguments. Despite this flexibility, ROCR is easy to use, with only three commands and reasonable default values for all optional parameters.

In the example below, we will briefly introduce ROCR's three commands—prediction, performance and plot—applied to a 10-fold cross-validation set of predictions and corresponding class labels from a study on predicting HIV coreceptor usage from the sequence of the viral envelope protein. After loading the dataset, a prediction object is created from the raw predictions and class labels.

data(ROCR.hiv)
predictions <- ROCR.hiv$hiv.svm$predictions
labels <- ROCR.hiv$hiv.svm$labels
pred <- prediction(predictions, labels)
pred

Performance measures or combinations thereof are computed by invoking the performance method on this prediction object. The resulting performance object can be visualized using the method plot. For example, an ROC curve that trades off the rate of true positives against the rate of false positives is obtained as follows:

perf <- performance(pred, "tpr", "fpr")
perf
plot(perf,
     avg="threshold",
     spread.estimate="boxplot")

The optional parameter avg selects a particular form of performance curve averaging across the validation runs; the visualization of curve variability is determined with the parameter spread.estimate.

data(ROCR.hiv)
pp.unnorm <- ROCR.hiv$hiv.svm$predictions
ll <- ROCR.hiv$hiv.svm$labels

# normalize predictions to 0..1
v <- unlist(pp.unnorm)
pp <- lapply(pp.unnorm, function(run) {approxfun(c(min(v), max(v)), c(0,1))(run)})

par(mfrow=c(1,4))
pred<- prediction(pp, ll)
perf <- performance(pred, "tpr", "fpr")

plot(perf, avg= "threshold", colorize=TRUE, lwd= 3,
     coloraxis.at=seq(0,1,by=0.2),)
plot(perf, col="gray78", add=TRUE)
plot(perf, avg= "threshold", colorize=TRUE, colorkey=FALSE,lwd= 3,,add=TRUE)
mtext(paste0("(a)"), side = 3, adj = 0.01,line = 1)

perf <- performance(pred, "acc")
plot(perf, avg= "vertical", spread.estimate="boxplot", lwd=3,col='blue',
     show.spread.at= seq(0.1, 0.9, by=0.1),)
mtext(paste0("(b)"), side = 3, adj = 0.01,line = 1)


plot(performance(pred, "cal", window.size= 10),
     avg="vertical",)
mtext(paste0("(c)"), side = 3, adj = 0.01,line = 1)

plot(0,0,type="n", xlim= c(0,1), ylim=c(0,7),
     xlab="Cutoff", ylab="Density",)
mtext(paste0("(d)"), side = 3, adj = 0.01,line = 1)
for (runi in 1:length(pred@predictions)) {
  lines(density(pred@predictions[[runi]][pred@labels[[runi]]=="-1"]), col= "red")
  lines(density(pred@predictions[[runi]][pred@labels[[runi]]=="1"]), col="green")
}

Issuing demo(ROCR) starts a demonstration of further graphical capabilities of ROCR. The command help(package=ROCR) points to the available help pages. In particular, a complete list of available performance measures can be obtained via help(performance). A reference manual can be downloaded from the ROCR website.

In conclusion, ROCR is a comprehensive tool for evaluating scoring classifiers and producing publication-quality figures. It allows for studying the intricacies inherent to many biological datasets and their implications on classifier performance.

Additional examples

Below you can find many additional examples of ROCR's features of performance measurement and the possibilites in plotting. However, this only a first taste. For more examples, please run demo(ROCR) and make sure the plotting deminsions are big enough.

ROC curves, Precision/Recall graphs and more ...

perf <- performance(pred, "tpr", "fpr")
plot(perf,
     avg= "threshold",
     colorize=TRUE,
     lwd= 3,
     main= "With ROCR you can produce standard plots\nlike ROC curves ...")
plot(perf,
     lty=3,
     col="grey78",
     add=TRUE)

perf <- performance(pred, "prec", "rec")
plot(perf,
     avg= "threshold",
     colorize=TRUE,
     lwd= 3,
     main= "... Precision/Recall graphs ...")
plot(perf,
     lty=3,
     col="grey78",
     add=TRUE)

perf <- performance(pred, "sens", "spec")
plot(perf,
     avg= "threshold",
     colorize=TRUE,
     lwd= 3,
     main="... Sensitivity/Specificity plots ...")
plot(perf,
     lty=3,
     col="grey78",
     add=TRUE)

perf <- performance(pred, "lift", "rpp")
plot(perf,
     avg= "threshold",
     colorize=TRUE,
     lwd= 3,
     main= "... and Lift charts.")
plot(perf,
     lty=3,
     col="grey78",
     add=TRUE)

Averaging over multiple predictions

Multiple batches of predictions can be analyzed at the same time.

data(ROCR.xval)
predictions <- ROCR.xval$predictions
labels <- ROCR.xval$labels
length(predictions)

pred <- prediction(predictions, labels)
perf <- performance(pred,'tpr','fpr')

This can be used for plotting averages using the avg argument.

plot(perf,
     colorize=TRUE,
     lwd=2,
     main='ROC curves from 10-fold cross-validation')

plot(perf,
     avg='vertical',
     spread.estimate='stderror',
     lwd=3,main='Vertical averaging + 1 standard error',
     col='blue')

plot(perf,
     avg='horizontal',
     spread.estimate='boxplot',
     lwd=3,
     main='Horizontal averaging + boxplots',
     col='blue')

plot(perf,
     avg='threshold',
     spread.estimate='stddev',
     lwd=2,
     main='Threshold averaging + 1 standard deviation',
     colorize=TRUE)

Cutoff stacking

plot(perf,
     print.cutoffs.at=seq(0,1,by=0.2),
     text.cex=0.8,
     text.y=lapply(as.list(seq(0,0.5,by=0.05)), function(x) { rep(x,length(perf@x.values[[1]])) } ),
     col= as.list(terrain.colors(10)),
     text.col= as.list(terrain.colors(10)), 
     points.col= as.list(terrain.colors(10)), 
     main= "Cutoff stability")

Combination of performance measures

Performance measures can be combined freely.

perf <- performance(pred,"pcmiss","lift")

plot(perf,
     colorize=TRUE,
     print.cutoffs.at=seq(0,1,by=0.1),
     text.adj=c(1.2,1.2),
     avg="threshold",
     lwd=3,
     main= "You can freely combine performance measures ...")