plot
Plot receiver operating characteristic (ROC) curves and other performance curves
Since R2022b
Syntax
Description
plot(
creates
a receiver operating characteristic (ROC) curve, which is a plot of the true positive
rate (TPR) versus the false positive rate (FPR), for each class in the rocObj
)ClassNames
property of the
rocmetrics
object
rocObj
. The function marks the model operating point for each
curve, and displays the value of the area under the ROC curve (AUC) and the class name for the curve in the legend.
plot(___,
specifies
additional options using one or more name-value arguments in addition to any of the input
argument combinations in the previous syntaxes. For example,
Name=Value
)AverageCurveType="macro",ClassNames=[]
computes the average
performance metrics using the macro-averaging method and plots the average ROC curve
only.
[
also returns graphics objects for the model operating points and diagonal line.curveObj
,graphicsObjs
] = plot(___)
Examples
Plot ROC Curve
Load a sample of predicted classification scores and true labels for a classification problem.
load('flowersDataResponses.mat')
trueLabels
is the true labels for an image classification problem and scores
is the softmax prediction scores. scores
is an N-by-K array where N is the number of observations and K is the number of classes.
trueLabels = flowersData.trueLabels; scores = flowersData.scores;
Load the class names. The column order of scores
follows the class order stored in classNames
.
classNames = flowersData.classNames;
Create a rocmetrics
object by using the true labels in trueLabels
and the classification scores in scores
. Specify the column order of scores
using classNames
.
rocObj = rocmetrics(trueLabels,scores,classNames);
rocObj
is a rocmetrics
object that stores performance metrics for each class in the property. Compute the AUC
for all the model classes by calling auc
on the object.
a = auc(rocObj)
a = 1x5 single row vector
0.9781 0.9889 0.9728 0.9809 0.9732
Plot the ROC curve for each class. The plot
function also returns the AUC values for the classes.
plot(rocObj)
The filled circle markers indicate the model operating points. The legend displays the class name and AUC value for each curve.
Plot the macro average ROC curve.
plot(rocObj,AverageCurveType=["macro"],ClassNames=[])
Plot Precision-Recall Curve and Detection Error Tradeoff (DET) Graph
Create a rocmetrics
object and plot performance curves by using the plot
function. Specify the XAxisMetric
and YAxisMetric
name-value arguments of the plot
function to plot different types of performance curves other than the ROC curve. If you specify new metrics when you call the plot
function, the function computes the new metrics and then uses them to plot the curve.
Load a sample of true labels and the prediction scores for a classification problem. For this example, there are five classes: daisy, dandelion, roses, sunflowers, and tulips. The class names are stored in classNames
. The scores are the softmax prediction scores generated using the predict
function. scores
is an N-by-K array where N is the number of observations and K is the number of classes. The column order of scores
follows the class order stored in classNames
.
load('flowersDataResponses.mat')
scores = flowersData.scores;
trueLabels = flowersData.trueLabels;
classNames = flowersData.classNames;
Create a rocmetrics
object. The rocmetrics
function computes the FPR and TPR at different thresholds.
rocObj = rocmetrics(trueLabels,scores,classNames);
Plot the precision-recall curve for the first class. Specify the y-axis metric as precision (or positive predictive value) and the x-axis metric as recall (or true positive rate). The plot
function computes the new metric values and plots the curve.
curveObj = plot(rocObj,ClassNames=classNames(1), ... YAxisMetric="PositivePredictiveValue",XAxisMetric="TruePositiveRate");
Plot the detection error tradeoff (DET) graph for the first class. Specify the y-axis metric as the false negative rate and the x-axis metric as the false positive rate. Use a log scale for the x-axis and y-axis.
f = figure; plot(rocObj,ClassNames=classNames(1), ... YAxisMetric="FalseNegativeRate",XAxisMetric="FalsePositiveRate") f.CurrentAxes.XScale = "log"; f.CurrentAxes.YScale = "log"; title("DET Graph")
Plot Confidence Intervals
Compute the confidence intervals for FPR and TPR for fixed threshold values by using bootstrap samples, and plot the confidence intervals for TPR on the ROC curve by using the plot
function. This examples requires Statistics and Machine Learning Toolbox™.
Load a sample of true labels and the prediction scores for a classification problem. For this example, there are five classes: daisy, dandelion, roses, sunflowers, and tulips. The class names are stored in classNames
. The scores are the softmax prediction scores generated using the predict
function. scores
is an N-by-K array where N is the number of observations and K is the number of classes. The column order of scores
follows the class order stored in classNames
.
load('flowersDataResponses.mat')
scores = flowersData.scores;
trueLabels = flowersData.trueLabels;
classNames = flowersData.classNames;
Create a rocmetrics
object by using the true labels in trueLabels
and the classification scores in scores
. Specify the column order of scores
using classNames
. Specify NumBootstraps
as 100 to use 100 bootstrap samples to compute the confidence intervals.
rocObj = rocmetrics(trueLabels,scores,classNames,NumBootstraps=100);
Plot the ROC curve and the confidence intervals for TPR. Specify ShowConfidenceIntervals=true
to show the confidence intervals.
plot(rocObj,ShowConfidenceIntervals=true)
The shaded area around each curve indicates the confidence intervals. rocmetrics
computes the ROC curves using the scores. The confidence intervals represent the estimates of uncertainty for the curve.
Specify one class to plot by using the ClassNames
name-value argument.
plot(rocObj,ShowConfidenceIntervals=true,ClassNames="daisy")
Input Arguments
rocObj
— Object evaluating classification performance
rocmetrics
object
Object evaluating classification performance, specified as a rocmetrics
object.
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Example: plot(rocObj,YAxisMetric="PositivePredictiveValue",XAxisMetric="TruePositiveRate")
plots the precision (positive predictive value) versus the recall (true positive rate),
which represents a precision-recall curve.
AverageCurveType
— Method for averaging ROC or other performance curves
"none"
(default) | "micro"
| "macro"
| "weighted"
| string array | cell array of character vectors
Since R2024b
Method for averaging ROC or other performance curves, specified as
"none"
, "micro"
, "macro"
,
"weighted"
, a string array of method names, or a cell array of
method names.
If you specify
"none"
(default), theplot
function does not create the average performance curve.If you specify multiple methods as a string array or a cell array of character vectors, then the
plot
function plots multiple average performance curves using the specified methods.If you specify one or more averaging methods and specify
ClassNames=[]
, then theplot
function plots only the average performance curves.
plot
computes the averages of performance metrics for a
multiclass classification problem, and plots the average performance curves using these
methods:
"micro"
(micro-averaging) —plot
finds the average performance metrics by treating all one-versus-all binary classification problems as one binary classification problem. The function computes the confusion matrix components for the combined binary classification problem, and then computes the average metrics (as specified by theXAxisMetric
andYAxisMetric
name-value arguments) using the values of the confusion matrix."macro"
(macro-averaging) —plot
computes the average values for the metrics by averaging the values of all one-versus-all binary classification problems."weighted"
(weighted macro-averaging) —plot
computes the weighted average values for the metrics using the macro-averaging method and using the prior class probabilities (thePrior
property ofrocObj
) as weights.
The algorithm type determines the length of the vectors in the XData
, YData
, and
Thresholds
properties of a ROCCurve
object, returned by plot
,
for the average performance curve. For more details, see Average of Performance Metrics.
Example: AverageCurveType="macro"
Example: AverageCurveType=["micro","macro"]
Data Types: char
| string
| cell
ClassNames
— Class labels to plot
rocObj.ClassNames
(default) | categorical array | character array | string array | logical vector | numeric vector | cell array of character vectors
Class labels to plot, specified as a categorical, character, or string array, logical or
numeric vector, or cell array of character vectors. The values and data types in
ClassNames
must match those of the class names in the ClassNames
property
of rocObj
. (The software treats character or string arrays as cell arrays of character vectors.)
If you specify multiple class labels, the
plot
function plots a ROC curve for each class.If you specify
ClassNames=[]
and specify one or more averaging methods usingAverageCurveType
, then theplot
function plots only the average ROC curves.
Example: ClassNames=["red","blue"]
Data Types: single
| double
| logical
| char
| string
| cell
| categorical
ShowConfidenceIntervals
— Flag to show confidence intervals of y-axis metric
false
or 0
(default) | true
or 1
Flag to show the confidence intervals of the y-axis metric
(YAxisMetric
), specified as a numeric or logical
0
(false
) or 1
(true
).
The ShowConfidenceIntervals
value can be true
only if
the Metrics
property of
rocObj
contains the confidence intervals for the
y-axis metric.
Example: ShowConfidenceIntervals=true
Using confidence intervals requires Statistics and Machine Learning Toolbox™.
Data Types: single
| double
| logical
ShowDiagonalLine
— Flag to show diagonal line
true
or 1
| false
or 0
Flag to show the diagonal line that extends from [0,0]
to
[1,1]
, specified as a numeric or logical 1
(true
) or 0
(false
).
The default value is true
if you plot a ROC curve or an average ROC curve, and false
otherwise.
In the ROC curve plot, the diagonal line represents a random classifier, and the line passing through [0,0]
, [0,1]
, and [1,1]
represents a perfect classifier.
Example: ShowDiagonalLine=false
Data Types: single
| double
| logical
ShowModelOperatingPoint
— Flag to show model operating point
true
or 1
| false
or 0
Flag to show the model operating point, specified as a
numeric or logical 1
(true
) or 0
(false
).
The default value is true
for a ROC curve, and false
otherwise.
Example: ShowModelOperatingPoint=false
Data Types: single
| double
| logical
XAxisMetric
— Metric for x-axis
"FalsePositiveRate"
(default) | name of performance metric | function handle
Metric for the x-axis, specified as a character vector or string scalar of the built-in metric name or a custom metric name, or a function handle (@metricName
).
Built-in metrics — Specify one of the following built-in metric names by using a character vector or string scalar.
Name Description "TruePositives"
or"tp"
Number of true positives (TP) "FalseNegatives"
or"fn"
Number of false negatives (FN) "FalsePositives"
or"fp"
Number of false positives (FP) "TrueNegatives"
or"tn"
Number of true negatives (TN) "SumOfTrueAndFalsePositives"
or"tp+fp"
Sum of TP and FP "RateOfPositivePredictions"
or"rpp"
Rate of positive predictions (RPP), (TP+FP)/(TP+FN+FP+TN)
"RateOfNegativePredictions"
or"rnp"
Rate of negative predictions (RNP), (TN+FN)/(TP+FN+FP+TN)
"Accuracy"
or"accu"
Accuracy, (TP+TN)/(TP+FN+FP+TN)
"TruePositiveRate"
,"tpr"
, or"recall"
True positive rate (TPR), also known as recall or sensitivity, TP/(TP+FN)
"FalseNegativeRate"
,"fnr"
, or"miss"
False negative rate (FNR), or miss rate, FN/(TP+FN)
"FalsePositiveRate"
or"fpr"
False positive rate (FPR), also known as fallout or 1-specificity, FP/(TN+FP)
"TrueNegativeRate"
,"tnr"
, or"spec"
True negative rate (TNR), or specificity, TN/(TN+FP)
"PositivePredictiveValue"
,"ppv"
,"prec"
, or"precision"
Positive predictive value (PPV), or precision, TP/(TP+FP)
"NegativePredictiveValue"
or"npv"
Negative predictive value (NPV), TN/(TN+FN)
"f1score"
F1 score, 2*TP/(2*TP+FP+FN)
"ExpectedCost"
or"ecost"
Expected cost,
(TP*cost(P|P)+FN*cost(N|P)+FP*cost(P|N)+TN*cost(N|N))/(TP+FN+FP+TN)
, wherecost
is a 2-by-2 misclassification cost matrix containing[0,cost(N|P);cost(P|N),0]
.cost(N|P)
is the cost of misclassifying a positive class (P
) as a negative class (N
), andcost(P|N)
is the cost of misclassifying a negative class as a positive class.The software converts the
K
-by-K
matrix specified by theCost
name-value argument ofrocmetrics
to a 2-by-2 matrix for each one-versus-all binary problem. For details, see Misclassification Cost Matrix.The software computes the scale vector using the prior class probabilities (
Prior
) and the number of classes inLabels
, and then scales the performance metrics according to this scale vector. For details, see Performance Metrics.Custom metric stored in the
Metrics
property — Specify the name of a custom metric stored in theMetrics
property of the input objectrocObj
. Therocmetrics
function names a custom metric"CustomMetricN"
, whereN
is the number that refers to the custom metric. For example, specifyXAxisMetric="CustomMetric1"
to use the first custom metric inMetrics
as a metric for the x-axis.Custom metric — Specify a new custom metric by using a function handle. A custom function that returns a performance metric must have this form:
metric = customMetric(C,scale,cost)
The output argument
metric
is a scalar value.A custom metric is a function of the confusion matrix (
C
), scale vector (scale
), and cost matrix (cost
). The software finds these input values for each one-versus-all binary problem. For details, see Performance Metrics.C
is a2
-by-2
confusion matrix consisting of[TP,FN;FP,TN]
.scale
is a2
-by-1
scale vector.cost
is a2
-by-2
misclassification cost matrix.
The
plot
function names a custom metric"Custom Metric"
for the axis label.The software does not support cross-validation for a custom metric. Instead, you can specify to use bootstrap when you create a
rocmetrics
object.
If you specify a new metric instead of one in the Metrics
property of
the input object rocObj
, the plot
function
computes and plots the metric values. If you compute confidence intervals when you
create rocObj
, the plot
function also computes
confidence intervals for the new metric.
The plot
function ignores NaN
s in the performance metric values. Note that the positive predictive value (PPV) is
NaN
for the reject-all threshold for which TP
= FP
= 0
, and the negative predictive value (NPV) is NaN
for the
accept-all threshold for which TN
= FN
= 0
. For more details, see Thresholds, Fixed Metric, and Fixed Metric Values.
Example: XAxisMetric="FalseNegativeRate"
Data Types: char
| string
| function_handle
YAxisMetric
— Metric for y-axis
"TruePositiveRate"
(default) | name of performance metric | function handle
Metric for the y-axis, specified as a character vector or string scalar of
the built-in metric name or custom metric name, or a function handle
(@metricName
). For details, see XAxisMetric
.
Example: YAxisMetric="FalseNegativeRate"
Data Types: char
| string
| function_handle
Output Arguments
curveObj
— Object for performance curve
ROCCurve
object | array of ROCCurve
objects
Object for the performance curve, returned as a ROCCurve
object or an array of ROCCurve
objects. plot
returns a ROCCurve
object for each performance curve.
Use curveObj
to query and modify properties of the plot after creating
it. For a list of properties, see ROCCurve Properties.
graphicsObjs
— Graphics objects
graphics array
Graphics objects for the model operating points and diagonal line, returned as a graphics array containing Scatter
and Line
objects.
graphicsObjs
contains a Scatter
object for each model operating point (if
) and a ShowModelOperatingPoint
=trueLine
object for the diagonal line (if
). Use ShowDiagonalLine
=truegraphicsObjs
to query and modify properties of the model operating points and diagonal line after creating the plot. For a list of properties, see Scatter Properties and Line Properties.
More About
Receiver Operating Characteristic (ROC) Curve
A ROC curve shows the true positive rate versus the false positive rate for different thresholds of classification scores.
The true positive rate and the false positive rate are defined as follows:
True positive rate (TPR), also known as recall or sensitivity —
TP/(TP+FN)
, where TP is the number of true positives and FN is the number of false negativesFalse positive rate (FPR), also known as fallout or 1-specificity —
FP/(TN+FP)
, where FP is the number of false positives and TN is the number of true negatives
Each point on a ROC curve corresponds to a pair of TPR and FPR values for a specific
threshold value. You can find different pairs of TPR and FPR values by varying the
threshold value, and then create a ROC curve using the pairs. For each class,
rocmetrics
uses all distinct adjusted score values
as threshold values to create a ROC curve.
For a multiclass classification problem, rocmetrics
formulates a set
of one-versus-all binary
classification problems to have one binary problem for each class, and finds a ROC
curve for each class using the corresponding binary problem. Each binary problem
assumes one class as positive and the rest as negative.
For a binary classification problem, if you specify the classification scores as a
matrix, rocmetrics
formulates two one-versus-all binary
classification problems. Each of these problems treats one class as a positive class
and the other class as a negative class, and rocmetrics
finds two
ROC curves. Use one of the curves to evaluate the binary classification
problem.
For more details, see ROC Curve and Performance Metrics.
Area Under ROC Curve (AUC)
The area under a ROC curve (AUC) corresponds to the integral of a ROC curve
(TPR values) with respect to FPR from FPR
= 0
to FPR
= 1
.
The AUC provides an aggregate performance measure across all possible thresholds. The AUC
values are in the range 0
to 1
, and larger AUC values
indicate better classifier performance.
One-Versus-All (OVA) Coding Design
The one-versus-all (OVA) coding design reduces a multiclass classification
problem to a set of binary classification problems. In this coding design, each binary
classification treats one class as positive and the rest of the classes as negative.
rocmetrics
uses the OVA coding design for multiclass classification and
evaluates the performance on each class by using the binary classification that the class is
positive.
For example, the OVA coding design for three classes formulates three binary classifications:
Each row corresponds to a class, and each column corresponds to a binary
classification problem. The first binary classification assumes that class 1 is a positive
class and the rest of the classes are negative. rocmetrics
evaluates the
performance on the first class by using the first binary classification problem.
Algorithms
Adjusted Scores for Multiclass Classification Problem
For each class, rocmetrics
adjusts the classification scores (input argument
Scores
of rocmetrics
) relative to the scores for the rest
of the classes if you specify Scores
as a matrix. Specifically, the
adjusted score for a class given an observation is the difference between the score for the
class and the maximum value of the scores for the rest of the classes.
For example, if you have [s1,s2,s3] in a row of Scores
for a classification problem with
three classes, the adjusted score values are [s1-max
(s2,s3),s2-max
(s1,s3),s3-max
(s1,s2)].
rocmetrics
computes the performance metrics using the adjusted score values
for each class.
For a binary classification problem, you can specify Scores
as a
two-column matrix or a column vector. Using a two-column matrix is a simpler option because
the predict
function of a classification object returns classification
scores as a matrix, which you can pass to rocmetrics
. If you pass scores in
a two-column matrix, rocmetrics
adjusts scores in the same way that it
adjusts scores for multiclass classification, and it computes performance metrics for both
classes. You can use the metric values for one of the two classes to evaluate the binary
classification problem. The metric values for a class returned by
rocmetrics
when you pass a two-column matrix are equivalent to the
metric values returned by rocmetrics
when you specify classification scores
for the class as a column vector.
References
[1] Sebastiani, Fabrizio. "Machine Learning in Automated Text Categorization." ACM Computing Surveys 34, no. 1 (March 2002): 1–47.
Version History
Introduced in R2022bR2024b: Plot the operating point for all curves
plot(rocobj,ShowModelOperatingPoint=true)
plots the operating point for all curves in the plot, including averaged curves and non-ROC
curves. Previously, plot
indicated the operating point only for ROC curves,
and not for averaged curves.
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