rocmetrics
Receiver operating characteristic (ROC) curve and performance metrics for binary and multiclass classifiers
Since R2022b
Description
Create a rocmetrics
object to evaluate the performance of a classification model using receiver operating characteristic (ROC) curves or other performance metrics. rocmetrics
supports both binary and multiclass problems.
For each class, rocmetrics
computes performance metrics for a one-versus-all ROC curve. You can compute metrics for an average ROC curve by
using the average
function. After
computing metrics for ROC curves, you can plot them by using the plot
function.
By default, rocmetrics
computes the false positive rates (FPR) and the true
positive rates (TPR) to obtain a ROC curve. You can compute additional metrics by specifying
the AdditionalMetrics
name-value argument when you create an object or by calling the addMetrics
function
after you create an object. A rocmetrics
object stores the computed metrics
in the Metrics
properties.
In R2024b: You can find the area under the ROC curve (AUC) using the auc
function.
rocmetrics
computes pointwise confidence intervals for the performance
metrics when you set the NumBootstraps
value to
a positive integer or when you specify cross-validated data for the true class labels
(Labels
), classification
scores (Scores
), and
observation weights (Weights
). For details,
see Pointwise Confidence Intervals.
Using confidence intervals
requires Statistics and Machine Learning Toolbox™.
Creation
Description
creates a rocObj
= rocmetrics(Labels
,Scores
,ClassNames
)rocmetrics
object using the true class labels in
Labels
and the classification scores in
Scores
. Specify Labels
as a vector of length n,
and specify Scores
as a matrix of size
n
-by-K
, where n
is the number
of observations, and K
is the number of classes.
ClassNames
specifies the column order in
Scores
.
The Metrics
property
contains the performance metrics for each class for which you specify
Scores
and ClassNames
.
If you specify cross-validated data in Labels
and
Scores
as cell arrays, then rocmetrics
computes
confidence intervals for the performance metrics. Using cross-validated data
requires Statistics and Machine Learning Toolbox.
specifies options using one or more name-value arguments in addition to any of the input
argument combinations in the previous syntaxes. For example, rocObj
= rocmetrics(___,Name=Value
)Prior="uniform"
sets all class probabilities to be
equal.
Input Arguments
Labels
— True class labels
numeric vector | logical vector | categorical vector | character array | string array | cell array
True class labels, specified as a numeric vector, logical vector, categorical vector, character array, string array, or cell array of character vectors. You can also specify Labels
as a cell array of one of these types for cross-validated data.
For data that is not cross-validated, the length of
Labels
and the number of rows inScores
must be equal.For cross-validated data, you must specify
Labels
,Scores
, andWeights
as cell arrays with the same number of elements.rocmetrics
treats an element in the cell arrays as data from one cross-validation fold and computes pointwise confidence intervals for the performance metrics. The length ofLabels{i}
and the number of rows inScores{i}
must be equal. Using cross-validated data requires Statistics and Machine Learning Toolbox.
Each row of Labels
or Labels{i}
represents the true label of one observation.
This argument sets the Labels
property.
Data Types: single
| double
| logical
| char
| string
| cell
Scores
— Classification scores
numeric matrix | cell array of numeric matrices
Classification scores, specified as a numeric matrix or a cell array of numeric matrices.
Each row of the matrix in Scores
contains the classification scores of
one observation for all classes specified in ClassNames
. The
column order of Scores
must match the class order in
ClassNames
.
For a matrix input,
Score(j,k)
is the classification score of observationj
for classClassNames(k)
. For example,predict
returns predicted class scores as an n-by-K matrix, where n is the number of observations and K is the number classes. Pass the output torocmetrics
.The number of rows in
Scores
and the length ofLabels
must be equal.rocmetrics
adjusts scores for each class relative to the scores for the rest of the classes. For details, see Adjusted Scores for Multiclass Classification Problem.For a vector input,
Score(j)
is the classification score of observationj
for the class specified inClassNames
.ClassNames
must contain only one class.Prior
must be a two-element vector withPrior(1)
representing the prior probability for the specified class.Cost
must be a2
-by-2
matrix containing[Cost(P|P),Cost(N|P);Cost(P|N),Cost(N|N)]
, whereP
is a positive class (the class for which you specify classification scores), andN
is a negative class.The length of
Scores
and the length ofLabels
must be equal.
If you want to display the model operating point when you plot the ROC curve using the
plot
function, the values inScore(j)
must be the posterior probability. This restriction applies only to a vector input.For cross-validated data, you must specify
Labels
,Scores
, andWeights
as cell arrays with the same number of elements.rocmetrics
treats an element in the cell arrays as data from one cross-validation fold and computes pointwise confidence intervals for the performance metrics.Score{i}(j,k)
is the classification score of observationj
in elementi
for classClassNames(k)
. The number of rows inScores{i}
and the length ofLabels{i}
must be equal. Using cross-validated data requires Statistics and Machine Learning Toolbox.
For more information, see Classification Score Input for rocmetrics.
This argument sets the Scores
property.
Data Types: single
| double
| cell
ClassNames
— Class names
numeric vector | logical vector | categorical vector | character array | string array | cell array of character vectors
Class names, specified as a numeric vector, logical vector, categorical vector, character
array, string array, or cell array of character vectors. ClassNames
must have the same data type as the true labels in Labels
. The values
in ClassNames
must appear in Labels
.
This argument sets the ClassNames
property.
Data Types: single
| double
| logical
| cell
| categorical
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: FixedMetric="FalsePositiveRate",FixedMetricValues=0:0.01:1
holds the FPR values fixed at 0:0.01:1
.
AdditionalMetrics
— Additional model performance metrics
[]
(default) | character vector | string array | function handle | cell array
Additional model performance metrics to compute, specified as a character vector or string
scalar of the built-in metric name, string array of names, function handle
(@metricName
), or cell array of names or function handles. A
rocmetrics
object always computes the false positive rates (FPR) and
the true positive rates (TPR) to obtain a ROC curve. Therefore, you do not have to specify
to compute FPR and TPR.
Built-in metrics — Specify one of the following built-in metric names by using a character vector or string scalar. You can specify more than one by using a string array.
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)
"FalseNegativeRate"
,"fnr"
, or"miss"
False negative rate (FNR), or miss rate, FN/(TP+FN)
"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)
"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."f1score"
F1 score, 2*TP/(2*TP+FP+FN)
You can obtain all of the previous metrics by specifying "all"
. You cannot specify"all"
in conjunction with any other metric.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 — Specify a 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 software does not support cross-validation for a custom metric. Instead, you can specify to use bootstrap when you create a
rocmetrics
object.
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: AdditionalMetrics=["Accuracy","PositivePredictiveValue"]
Example: AdditionalMetrics={"Accuracy",@m1,@m2}
specifies the
accuracy metric and the custom metrics m1
and
m2
as additional metrics. rocmetrics
stores
the custom metric values as variables named CustomMetric1
and
CustomMetric2
in the Metrics
property.
Data Types: char
| string
| cell
| function_handle
FixedMetric
— Fixed metric
"Thresholds"
(default) | "FalsePositiveRate"
| "TruePositiveRate"
| metric specified by AdditionalMetrics
Fixed metric, specified as "Thresholds"
,
"FalsePositiveRate"
(or "fpr"
),
"TruePositiveRate"
(or "tpr"
), or a metric
specified by the AdditionalMetrics
name-value argument. To hold a custom metric fixed, specify
FixedMetric
as "CustomMetricN"
, where
N
is the number that refers to the custom metric. For example,
specify "CustomMetric1"
to use the first custom metric specified by
AdditionalMetrics
as the fixed metric.
rocmetrics
finds the ROC curves and other metric values that correspond to
the fixed values (FixedMetricValues
)
of the fixed metric (FixedMetric
), and stores the values in the
Metrics
property as
a table. For more details, see Thresholds, Fixed Metric, and Fixed Metric Values.
If rocmetrics
computes confidence intervals, it uses one of two methods for
the computation, depending on the FixedMetric
value:
If
FixedMetric
is"Thresholds"
(default),rocmetrics
uses threshold averaging.If
FixedMetric
is a nondefault value,rocmetrics
uses vertical averaging.
For details, see Pointwise Confidence Intervals.
Using confidence intervals requires Statistics and Machine Learning Toolbox.
Example: FixedMetric="TruePositiveRate"
Data Types: char
| string
FixedMetricValues
— Values for fixed metric
"all"
(default) | numeric vector
Values for the fixed metric (FixedMetric
),
specified as "all"
or a numeric vector.
rocmetrics
finds the ROC curves and other metric values that correspond to
the fixed values (FixedMetricValues
) of the fixed metric
(FixedMetric
), and stores the values in the Metrics
property as
a table.
The default FixedMetric
value is "Thresholds"
, and the
default FixedMetricValues
value is "all"
. For
each class, rocmetrics
uses all distinct adjusted score values as
threshold values and computes the performance metrics using the threshold values.
Depending on the UseNearestNeighbor
setting, rocmetrics
uses the exact threshold values corresponding to
the fixed values or the nearest threshold values. For more details, see Thresholds, Fixed Metric, and Fixed Metric Values.
If rocmetrics
computes confidence intervals, it holds FixedMetric
fixed at FixedMetricValues
.
FixedMetric
value is"Thresholds"
, andFixedMetricValues
is"all"
—rocmetrics
computes confidence intervals at the values corresponding to all distinct threshold values.FixedMetric
value is a performance metric, andFixedMetricValues
is"all"
—rocmetrics
finds the metric values corresponding to all distinct threshold values, and computes confidence intervals at the values corresponding to the metric values.
For details, see Pointwise Confidence Intervals. Using confidence intervals requires Statistics and Machine Learning Toolbox.
Example: FixedMetricValues=0:0.01:1
Data Types: single
| double
NaNFlag
— NaN
condition
"omitnan"
(default) | "includenan"
NaN condition, specified as "omitnan"
or "includenan"
.
"omitnan"
—rocmetrics
ignores allNaN
score values in the inputScores
and the corresponding values inLabels
andWeights
."includenan"
—rocmetrics
uses theNaN
score values in the inputScores
for the calculation. The function adds the observations withNaN
scores to false classification counts in the respective class. That is, the function counts observations withNaN
scores from the positive class as false negative (FN), and counts observations withNaN
scores from the negative class as false positive (FP).
For more details, see NaN Score Values.
Example: NaNFlag="includenan"
Data Types: char
| string
UseNearestNeighbor
— Indicator to use nearest metric values
false
or 0
| true
or 1
Indicator to use the nearest metric values, specified as a numeric or logical
0
(false
) or 1
(true
).
logical
0
(false
) —rocmetrics
uses the exact threshold values corresponding to the specified fixed metric values inFixedMetricValues
forFixedMetric
.logical
1
(true
) — Among the adjusted input scores,rocmetrics
finds a value that is the nearest to the threshold value corresponding to each specified fixed metric value.
For more details, see Thresholds, Fixed Metric, and Fixed Metric Values.
The UseNearestNeighbor
value must be false
if
rocmetrics
computes confidence intervals. Otherwise, the default
value is true
.
Using confidence intervals requires Statistics and Machine Learning Toolbox.
Example: UseNearestNeighbor=false
Data Types: single
| double
| logical
ApplyCostToScores
— Flag to apply misclassification costs to scores
false
or 0
(default) | true
or 1
Since R2024a
Flag to apply misclassification costs to scores for appropriate models, specified as a
numeric or logical 0
(false
) or
1
(true
). Set
ApplyCostToScores
to true
only when you
specify scores for a k-nearest neighbor (KNN), discriminant analysis,
or naive Bayes model with nondefault misclassification costs. These models use expected
classification costs rather than scores to predict labels.
If you specify ApplyCostToScores
as true
, the
software changes the scores to S*(-C)
, where the scores
S
are specified by the Scores
argument,
and the misclassification cost matrix C
is specified by the Cost
name-value
argument. The rocmetrics
object stores the transformed scores in the
Scores
property.
If you specify ApplyCostToScores
as false
, the
software stores the untransformed scores in the Scores
property of
the rocmetrics
object.
Example: ApplyCostToScores=true
Data Types: single
| double
| logical
Cost
— Misclassification cost
square matrix
Misclassification cost, specified as a K-by-K square
matrix C, where K is the number of unique classes
in Labels
.
C(i,j)
is the cost of classifying a point into class
j
if its true class is i
(that is, the rows
correspond to the true class and the columns correspond to the predicted class).
ClassNames
specifies the order of the classes.
rocmetrics
converts the K
-by-K
matrix
to a 2-by-2 matrix for each one-versus-all binary problem. For details, see Misclassification Cost Matrix.
If you specify classification scores for only one class in Scores
, the
Cost
value must be a
2
-by-2
matrix containing
[0,cost(N|P);cost(P|N),0]
, where P
is a
positive class (the class for which you specify classification scores), and
N
is a negative class. cost(N|P)
is the cost
of misclassifying a positive class as a negative class, and cost(P|N)
is the cost of misclassifying a negative class as a positive class.
The default value is C(i,j)=1
if i~=j
, and C(i,j)=0
if i=j
. The diagonal entries of a cost matrix must be zero.
This argument sets the Cost
property.
Note
If you specify a misclassification cost
matrix when you use scores for a KNN, discriminant analysis, or naive Bayes model,
set ApplyCostToScores
to
true
. These models use expected classification costs rather
than scores to predict labels. (since R2024a)
Example: Cost=[0 2;1 0]
Data Types: single
| double
Prior
— Prior class probabilities
"empirical"
(default) | "uniform"
| vector of scalar values
Prior class probabilities, specified as one of the following:
"empirical"
determines class probabilities from class frequencies in the true class labelsLabels
. If you pass observation weights (Weights
),rocmetrics
also uses the weights to compute the class probabilities."uniform"
sets all class probabilities to be equal.Vector of scalar values, with one scalar value for each class.
ClassNames
specifies the order of the classes.If you specify classification scores for only one class in
Scores
, thePrior
value must be a two-element vector withPrior(1)
representing the prior probability for the specified class.
This argument sets the Prior
property.
Example: Prior="uniform"
Data Types: single
| double
| char
| string
Weights
— Observation weights
numeric vector of positive values | cell array containing numeric vectors of positive values
Observation weights, specified as a numeric vector of positive values or a cell array containing numeric vectors of positive values.
For data that is not cross-validated, specify
Weights
as a numeric vector that has the same length asLabels
.For cross-validated data, you must specify
Labels
,Scores
, andWeights
as cell arrays with the same number of elements.rocmetrics
treats an element in the cell arrays as data from one cross-validation fold and computes pointwise confidence intervals for the performance metrics. The length ofWeights{i}
and the length ofLabels{i}
must be equal. Using cross-validated data requires Statistics and Machine Learning Toolbox.
rocmetrics
weighs the observations in Labels
and
Scores
with the corresponding values in
Weights
. If you set the NumBootstraps
value
to a positive integer, rocmetrics
draws samples with replacement, using
the weights as multinomial sampling probabilities. Using the
NumBootstraps
name-value argument requires Statistics and Machine Learning Toolbox.
By default, Weights
is a vector of ones or a cell array
containing vectors of ones.
This argument sets the Weights
property.
Data Types: single
| double
| cell
Alpha
— Significance level
0.05 (default) | scalar in the range (0,1)
Significance level for the pointwise confidence intervals, specified as a scalar in the range (0,1)
.
If you specify Alpha
as α, then
rocmetrics
computes 100×(1 – α)% pointwise confidence intervals for the performance metrics.
This argument is related to computing confidence intervals. Therefore, it is valid only when
you specify cross-validated data for Labels
, Scores
, and
Weights
, or when
you set the NumBootstraps
value
to a positive integer.
This option requires Statistics and Machine Learning Toolbox.
Example: Alpha=0.01
specifies 99% confidence intervals.
Data Types: single
| double
BootstrapOptions
— Bootstrap options for parallel computation
statset("rocmetrics")
(default) | structure
Bootstrap options for parallel computation, specified as a structure.
You can specify options for computing bootstrap iterations in parallel and setting random numbers during the bootstrap sampling. Create the BootstrapOptions
structure with statset
(Statistics and Machine Learning Toolbox). This table lists the option fields and their values.
Field Name | Field Value | Default |
---|---|---|
UseParallel | Set this value to | false |
UseSubstreams | Set this value to To compute reproducibly, set | false |
Streams | Specify this value as a | If you do not specify |
This argument is valid only when you specify NumBootstraps
as a
positive integer to compute confidence intervals using bootstrapping.
This option requires Statistics and Machine Learning Toolbox, and parallel computation requires Parallel Computing Toolbox™.
Example: BootstrapOptions=statset(UseParallel=true)
Data Types: struct
BootstrapType
— Bootstrap confidence interval type
"bca"
(default) | "corrected percentile"
| "normal"
| "percentile"
| "student"
Bootstrap confidence interval type, specified as one of the values in this table.
Value | Description |
---|---|
"bca" | Bias corrected and accelerated percentile method [8][9]. This method Involves a z0 factor computed using the proportion of bootstrap values that are less than the original sample value. To produce reasonable results when the sample is lumpy, the software computes z0 by including half of the bootstrap values that are the same as the original sample value. |
"corrected percentile" or
"cper" | Bias corrected percentile method [10] |
"normal" or "norm" | Normal approximated interval with bootstrapped bias and standard error [11] |
"percentile" or "per" | Basic percentile method |
"student" or "stud" | Studentized confidence interval [8] |
This argument is valid only when you specify NumBootstraps
as a
positive integer to compute confidence intervals using bootstrapping.
This option requires Statistics and Machine Learning Toolbox.
Example: BootstrapType="student"
Data Types: char
| string
NumBootstraps
— Number of bootstrap samples to draw
0
(default) | nonnegative integer scalar
Number of bootstrap samples to draw for computing pointwise confidence intervals, specified as a nonnegative integer scalar.
If you specify NumBootstraps
as a positive integer, then
rocmetrics
uses NumBootstraps
bootstrap
samples. To create each bootstrap sample, the function randomly selects
n
out of the n
rows of input data with
replacement. The default value 0
implies that
rocmetrics
does not use bootstrapping.
rocmetrics
computes confidence intervals by using either
cross-validated data or bootstrap samples. Therefore, if you specify cross-validated
data for Labels
, Scores
, and
Weights
, then
NumBootstraps
must be 0
.
For details, see Pointwise Confidence Intervals.
This option requires Statistics and Machine Learning Toolbox.
Example: NumBootstraps=500
Data Types: single
| double
NumBootstrapsStudentizedSE
— Number of bootstrap samples to draw for studentized standard error estimate
100
(default) | positive integer scalar
Number of bootstrap samples to draw for the studentized standard error estimate, specified as a positive integer scalar.
This argument is valid only when you specify NumBootstraps
as a
positive integer and BootstrapType
as
"student"
to compute studentized bootstrap confidence intervals.
rocmetrics
estimates the studentized standard error estimate by
using NumBootstrapsStudentizedSE
bootstrap data samples.
This option requires Statistics and Machine Learning Toolbox.
Example: NumBootstrapsStudentizedSE=500
Data Types: single
| double
Properties
Performance Metrics
Metrics
— Performance metrics
table
This property is read-only.
Performance metrics, specified as a table.
The table contains performance metric values for all classes, vertically concatenated
according to the class order in ClassNames
. The
table has a row for each unique threshold value for each class.
rocmetrics
determines the threshold values to use based on the
value of FixedMetric
,
FixedMetricValues
,
and UseNearestNeighbor
.
For details, see Thresholds, Fixed Metric, and Fixed Metric Values.
The number of rows for each class in the table is the number of unique threshold values.
Each row of the table contains these variables: ClassName
,
Threshold
, FalsePositiveRate
, and
TruePositiveRate
, as well as a variable for each additional
metric specified in AdditionalMetrics
.
If you specify a custom metric, rocmetrics
names the metric
"CustomMetricN"
, where N
is the number that
refers to the custom metric. For example, "CustomMetric1"
corresponds
to the first custom metric specified by AdditionalMetrics
.
Each variable in the Metrics
table contains a vector or a three-column matrix.
If
rocmetrics
does not compute confidence intervals, each variable contains a vector.If
rocmetrics
computes confidence intervals, bothClassName
and the variable forFixedMetric
(Threshold
,FalsePositiveRate
,TruePositiveRate
, or an additional metric) contain a vector, and the other variables contain a three-column matrix. The first column of the matrix corresponds to the metric values, and the second and third columns correspond to the lower and upper bounds, respectively.Using confidence intervals requires Statistics and Machine Learning Toolbox.
Data Types: table
Classification Model Properties
You can specify the following properties when creating a rocmetrics
object.
ClassNames
— Class names
numeric vector | logical vector | categorical vector | cell array of character vectors
This property is read-only.
Class names, specified as a numeric vector, logical vector, categorical vector, or cell array of character vectors.
For details, see the input argument ClassNames
, which
sets this property. (The software treats character or string arrays as cell arrays of character vectors.)
Data Types: single
| double
| logical
| cell
| categorical
Cost
— Misclassification cost
square matrix
This property is read-only.
Misclassification cost, specified as a square matrix.
For details, see the Cost
name-value
argument, which sets this property.
Data Types: single
| double
Labels
— True class labels
numeric vector | logical vector | categorical vector | cell array
This property is read-only.
True class labels, specified as a numeric vector, logical vector, categorical vector, cell array of character vectors, or cell array of one of these types for cross-validated data.
For details, see the input argument Labels
, which sets
this property. (The software treats character or string arrays as cell arrays of character vectors.)
Data Types: single
| double
| logical
| cell
| categorical
Prior
— Prior class probabilities
numeric vector
This property is read-only.
Prior class probabilities, specified as a numeric vector.
For details, see the Prior
name-value
argument, which sets this property. If you specify this argument as a character vector
or string scalar ("empirical"
or "uniform"
),
rocmetrics
computes the prior probabilities and stores the
Prior
property as a numeric vector.
Data Types: single
| double
Scores
— Classification scores
numeric matrix | cell array of numeric matrices
This property is read-only.
Classification scores, specified as a numeric matrix or a cell array of numeric matrices.
For details, see the input argument Scores
, which sets
this property.
Note
If you specify the ApplyCostToScores
name-value argument as true
, the software stores the transformed
scores S*(-C)
, where the scores S
are
specified by the Scores
argument, and the misclassification
cost matrix C
is specified by the Cost
name-value
argument. (since R2024a)
Data Types: single
| double
| cell
Weights
— Observation weights
numeric vector of positive values | cell array containing numeric vectors of positive values
This property is read-only.
Observation weights, specified as a numeric vector of positive values or a cell array containing numeric vectors of positive values.
For details, see the Weights
name-value
argument, which sets this property.
Data Types: single
| double
| cell
Object Functions
addMetrics | Compute additional classification performance metrics |
auc | Area under the ROC curve or area under the PR (precision-recall) curve |
average | Compute performance metrics for average receiver operating characteristic (ROC) curve in multiclass problem |
modelOperatingPoint | Operating point of rocmetrics object |
plot | Plot receiver operating characteristic (ROC) curves and other performance curves |
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=[])
Compute Confidence Intervals Using Bootstrapping
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;
predLabels = flowersData.predictedLabels;
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);
Find the rows for the second class in the table of the Metrics
property, and display the first eight rows.
idx = rocObj.Metrics.ClassName ==classNames(2); head(rocObj.Metrics(idx,:))
ClassName Threshold FalsePositiveRate TruePositiveRate _________ _________ _________________ _____________________________ dandelion 1 0 0 0 0 0 0 dandelion 1 0 0 0 0.23889 0.17858 0.31326 dandelion 1 0 0 0 0.26111 0.20107 0.34007 dandelion 1 0 0 0 0.27222 0.21829 0.35778 dandelion 1 0 0 0 0.28889 0.22739 0.36583 dandelion 1 0 0 0 0.29444 0.23682 0.41685 dandelion 1 0 0 0 0.3 0.24296 0.42567 dandelion 1 0 0 0 0.31111 0.24964 0.42614
Each row of the table contains the metric value and its confidence intervals for FPR and TPR for a fixed threshold value. The Threshold
variable is a column vector, and the FalsePositiveRate
and TruePositiveRate
variables are three-column matrices. The first column of the matrices corresponds to the metric values, and the second and third columns correspond to the lower and upper bounds, respectively.
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 the ROC curve indicates the confidence intervals. The confidence intervals represent the uncertainty of the curve due to the variance in the data set for the trained model.
Specify one class to plot by using the ClassNames
name-value argument.
plot(rocObj,ShowConfidenceIntervals=true,ClassNames="daisy")
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.
Model Operating Point
The model operating point represents the FPR and TPR corresponding to the typical threshold value.
The typical threshold value depends on the input format of the Scores
argument (classification scores) specified when you create a
rocmetrics
object:
If you specify
Scores
as a matrix,rocmetrics
assumes that the values inScores
are the scores for a multiclass classification problem and uses adjusted score values. A multiclass classification model classifies an observation into a class that yields the largest score, which corresponds to a nonnegative score in the adjusted scores. Therefore, the threshold value is0
.If you specify
Scores
as a column vector,rocmetrics
assumes that the values inScores
are posterior probabilities of the class specified inClassNames
. A binary classification model classifies an observation into a class that yields a higher posterior probability, that is, a posterior probability greater than0.5
. Therefore, the threshold value is0.5
.
For a binary classification problem, you can specify Scores
as a
two-column matrix or a column vector. However, if the classification scores are not
posterior probabilities, you must specify Scores
as a matrix. A binary
classifier classifies an observation into a class that yields a larger score, which is
equivalent to a class that yields a nonnegative adjusted score. Therefore, if you specify
Scores
as a matrix for a binary classifier,
rocmetrics
can find a correct model operating point using the same
scheme that it applies to a multiclass classifier. If you specify classification scores that
are not posterior probabilities as a vector, rocmetrics
cannot identify a
correct model operating point because it always uses 0.5
as a threshold
for the model operating point.
The plot
function displays a filled circle marker at the model
operating point for each ROC curve (see ShowModelOperatingPoint
). The function chooses a point corresponding to the
typical threshold value. If the curve does not have a data point for the typical threshold
value, the function finds a point that has the smallest threshold value greater than the
typical threshold. The point on the curve indicates identical performance to the performance
of the typical threshold value.
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] Fawcett, T. “ROC Graphs: Notes and Practical Considerations for Researchers”, Machine Learning 31, no. 1 (2004): 1–38.
[2] Zweig, M., and G. Campbell. “Receiver-Operating Characteristic (ROC) Plots: A Fundamental Evaluation Tool in Clinical Medicine.” Clinical Chemistry 39, no. 4 (1993): 561–577.
[3] Davis, J., and M. Goadrich. “The Relationship Between Precision-Recall and ROC Curves.” Proceedings of ICML ’06, 2006, pp. 233–240.
[4] Moskowitz, C. S., and M. S. Pepe. “Quantifying and Comparing the Predictive Accuracy of Continuous Prognostic Factors for Binary Outcomes.” Biostatistics 5, no. 1 (2004): 113–27.
[5] Huang, Y., M. S. Pepe, and Z. Feng. “Evaluating the Predictiveness of a Continuous Marker.” U. Washington Biostatistics Paper Series, 2006, 250–61.
[6] Briggs, W. M., and R. Zaretzki. “The Skill Plot: A Graphical Technique for Evaluating Continuous Diagnostic Tests.” Biometrics 64, no. 1 (2008): 250–256.
[7] Bettinger, R. “Cost-Sensitive Classifier Selection Using the ROC Convex Hull Method.” SAS Institute, 2003.
[8] DiCiccio, Thomas J., and Bradley Efron. “Bootstrap Confidence Intervals.” Statistical Science 11, no. 3 (1996): 189–228.
[9] Efron, Bradley, and Robert J. Tibshirani. An Introduction to the Bootstrap. New York: Chapman & Hall, 1993.
[10] Efron, Bradley. The Jackknife, the Bootstrap and Other Resampling Plans. Philadelphia: The Society for Industrial and Applied Mathematics, 1982.
[11] Davison, A. C., and D. V. Hinkley. Bootstrap Methods and Their Applications. Cambridge University Press, 1997.
Version History
Introduced in R2022bR2024b: Use updates and extensions to rocmetrics
and its object functions
rocmetrics
has several changes and extensions:
The new
auc
function computes the AUC of some named curves. Arocmetrics
object no longer has anAUC
property.The new
modelOperatingPoint
function returns the model performance for each class.The
AverageROCType
name-value argument of theplot
function is renamedAverageCurveType
, and applies to non-ROC curves as well as ROC curves.The model operating point can be plotted using the
ShowModelOperatingPoint
name-value argument of theplot
function. The operating point is displayed for averaged curves as well as nonaveraged curves.The
average
function is extended to compute the average of any two metrics.The
AdditionalMetrics
name-value argument ofrocmetrics
has new values:'f1score'
, which computes the F1 score;'precision'
, which is the same as'ppv'
and'prec'
; and'all'
, which computes all supported metrics.The
metrics
input argument of theaddMetrics
function takes the same new values as theAdditionalMetrics
name-value argument ofrocmetrics
.
R2024a: Apply misclassification costs to scores for k-nearest neighbor (KNN), discriminant analysis, and naive Bayes models
If you use nondefault misclassification costs by specifying the Cost
name-value argument,
and you use scores for a KNN, discriminant analysis, or naive Bayes model, set the ApplyCostToScores
name-value
argument to true
. Because these models use expected classification costs
rather than scores to predict labels, this setting enables the function to transform the
scores appropriately.
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