kfoldMargin
Classification margins for cross-validated ECOC model
Description
returns classification margins obtained by the
cross-validated ECOC model (margin
= kfoldMargin(CVMdl
)ClassificationPartitionedECOC
)
CVMdl
. For every fold, kfoldMargin
computes classification margins for validation-fold observations using an ECOC model
trained on training-fold observations. CVMdl.X
contains both sets
of observations.
returns classification margins with additional options specified by one or more
name-value pair arguments. For example, specify the binary learner loss function,
decoding scheme, or verbosity level.margin
= kfoldMargin(CVMdl
,Name,Value
)
Examples
Estimate k-Fold Cross-Validation Margins
Load Fisher's iris data set. Specify the predictor data X
, the response data Y
, and the order of the classes in Y
.
load fisheriris X = meas; Y = categorical(species); classOrder = unique(Y); rng(1); % For reproducibility
Train and cross-validate an ECOC model using support vector machine (SVM) binary classifiers. Standardize the predictor data using an SVM template, and specify the class order.
t = templateSVM('Standardize',1); CVMdl = fitcecoc(X,Y,'CrossVal','on','Learners',t,'ClassNames',classOrder);
CVMdl
is a ClassificationPartitionedECOC
model. By default, the software implements 10-fold cross-validation. You can specify a different number of folds using the 'KFold'
name-value pair argument.
Estimate the margins for validation-fold observations. Display the distribution of the margins using a box plot.
margin = kfoldMargin(CVMdl);
boxplot(margin)
title('Distribution of Margins')
Select ECOC Model Features by Comparing Cross-Validation Margins
One way to perform feature selection is to compare cross-validation margins from multiple models. Based solely on this criterion, the classifier with the greatest margins is the best classifier.
Load Fisher's iris data set. Specify the predictor data X
, the response data Y
, and the order of the classes in Y
.
load fisheriris X = meas; Y = categorical(species); classOrder = unique(Y); % Class order rng(1); % For reproducibility
Define the following two data sets.
fullX
contains all the predictors.partX
contains the petal dimensions.
fullX = X; partX = X(:,3:4);
For each predictor set, train and cross-validate an ECOC model using SVM binary classifiers. Standardize the predictors using an SVM template, and specify the class order.
t = templateSVM('Standardize',1); CVMdl = fitcecoc(fullX,Y,'CrossVal','on','Learners',t,... 'ClassNames',classOrder); PCVMdl = fitcecoc(partX,Y,'CrossVal','on','Learners',t,... 'ClassNames',classOrder);
CVMdl
and PCVMdl
are ClassificationPartitionedECOC
models. By default, the software implements 10-fold cross-validation.
Estimate the margins for each classifier. Use loss-based decoding for aggregating the binary learner results. For each model, display the distribution of the margins using a boxplot.
fullMargins = kfoldMargin(CVMdl,'Decoding','lossbased'); partMargins = kfoldMargin(PCVMdl,'Decoding','lossbased'); boxplot([fullMargins partMargins],'Labels',{'All Predictors','Two Predictors'}) title('Distributions of Margins')
The margin distributions are approximately the same.
Input Arguments
CVMdl
— Cross-validated ECOC model
ClassificationPartitionedECOC
model
Cross-validated ECOC model, specified as a ClassificationPartitionedECOC
model. You can create a
ClassificationPartitionedECOC
model in two ways:
Pass a trained ECOC model (
ClassificationECOC
) tocrossval
.Train an ECOC model using
fitcecoc
and specify any one of these cross-validation name-value pair arguments:'CrossVal'
,'CVPartition'
,'Holdout'
,'KFold'
, or'Leaveout'
.
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.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: kfoldMargin(CVMdl,'Verbose',1)
specifies to display
diagnostic messages in the Command Window.
BinaryLoss
— Binary learner loss function
'hamming'
| 'linear'
| 'logit'
| 'exponential'
| 'binodeviance'
| 'hinge'
| 'quadratic'
| function handle
Binary learner loss function, specified as the comma-separated pair consisting of
'BinaryLoss'
and a built-in loss function name or function handle.
This table describes the built-in functions, where yj is the class label for a particular binary learner (in the set {–1,1,0}), sj is the score for observation j, and g(yj,sj) is the binary loss formula.
Value Description Score Domain g(yj,sj) "binodeviance"
Binomial deviance (–∞,∞) log[1 + exp(–2yjsj)]/[2log(2)] "exponential"
Exponential (–∞,∞) exp(–yjsj)/2 "hamming"
Hamming [0,1] or (–∞,∞) [1 – sign(yjsj)]/2 "hinge"
Hinge (–∞,∞) max(0,1 – yjsj)/2 "linear"
Linear (–∞,∞) (1 – yjsj)/2 "logit"
Logistic (–∞,∞) log[1 + exp(–yjsj)]/[2log(2)] "quadratic"
Quadratic [0,1] [1 – yj(2sj – 1)]2/2 The software normalizes binary losses so that the loss is 0.5 when yj = 0. Also, the software calculates the mean binary loss for each class [1].
For a custom binary loss function, for example
customFunction
, specify its function handle'BinaryLoss',@customFunction
.customFunction
has this form:bLoss = customFunction(M,s)
M
is the K-by-B coding matrix stored inMdl.CodingMatrix
.s
is the 1-by-B row vector of classification scores.bLoss
is the classification loss. This scalar aggregates the binary losses for every learner in a particular class. For example, you can use the mean binary loss to aggregate the loss over the learners for each class.K is the number of classes.
B is the number of binary learners.
For an example of passing a custom binary loss function, see Predict Test-Sample Labels of ECOC Model Using Custom Binary Loss Function.
This table identifies the default BinaryLoss
value, which depends on the
score ranges returned by the binary learners.
Assumption | Default Value |
---|---|
All binary learners are any of the following:
| 'quadratic' |
All binary learners are SVMs. | 'hinge' |
All binary learners are ensembles trained by
AdaboostM1 or
GentleBoost . | 'exponential' |
All binary learners are ensembles trained by
LogitBoost . | 'binodeviance' |
You specify to predict class posterior probabilities by setting
'FitPosterior',true in fitcecoc . | 'quadratic' |
Binary learners are heterogeneous and use different loss functions. | 'hamming' |
To check the default value, use dot notation to display the BinaryLoss
property of the trained model at the command line.
Example: 'BinaryLoss','binodeviance'
Data Types: char
| string
| function_handle
Decoding
— Decoding scheme
'lossweighted'
(default) | 'lossbased'
Decoding scheme that aggregates the binary losses, specified as the comma-separated pair
consisting of 'Decoding'
and 'lossweighted'
or
'lossbased'
. For more information, see Binary Loss.
Example: 'Decoding','lossbased'
Options
— Estimation options
[]
(default) | structure array
Estimation options, specified as a structure array as returned by statset
.
To invoke parallel computing you need a Parallel Computing Toolbox™ license.
Example: Options=statset(UseParallel=true)
Data Types: struct
Verbose
— Verbosity level
0
(default) | 1
Verbosity level, specified as 0
or 1
.
Verbose
controls the number of diagnostic messages that the
software displays in the Command Window.
If Verbose
is 0
, then the software does not display
diagnostic messages. Otherwise, the software displays diagnostic messages.
Example: Verbose=1
Data Types: single
| double
Output Arguments
margin
— Classification margins
numeric vector
Classification
margins, returned as a numeric vector.
margin
is an n-by-1 vector,
where each row is the margin of the corresponding observation and
n is the number of observations
(size(CVMdl.X,1)
).
More About
Classification Margin
The classification margin is, for each observation, the difference between the negative loss for the true class and the maximal negative loss among the false classes. If the margins are on the same scale, then they serve as a classification confidence measure. Among multiple classifiers, those that yield greater margins are better.
Binary Loss
The binary loss is a function of the class and classification score that determines how well a binary learner classifies an observation into the class. The decoding scheme of an ECOC model specifies how the software aggregates the binary losses and determines the predicted class for each observation.
Assume the following:
mkj is element (k,j) of the coding design matrix M—that is, the code corresponding to class k of binary learner j. M is a K-by-B matrix, where K is the number of classes, and B is the number of binary learners.
sj is the score of binary learner j for an observation.
g is the binary loss function.
is the predicted class for the observation.
The software supports two decoding schemes:
Loss-based decoding [2] (
Decoding
is"lossbased"
) — The predicted class of an observation corresponds to the class that produces the minimum average of the binary losses over all binary learners.Loss-weighted decoding [3] (
Decoding
is"lossweighted"
) — The predicted class of an observation corresponds to the class that produces the minimum average of the binary losses over the binary learners for the corresponding class.The denominator corresponds to the number of binary learners for class k. [1] suggests that loss-weighted decoding improves classification accuracy by keeping loss values for all classes in the same dynamic range.
The predict
, resubPredict
, and
kfoldPredict
functions return the negated value of the objective
function of argmin
as the second output argument
(NegLoss
) for each observation and class.
This table summarizes the supported binary loss functions, where yj is a class label for a particular binary learner (in the set {–1,1,0}), sj is the score for observation j, and g(yj,sj) is the binary loss function.
Value | Description | Score Domain | g(yj,sj) |
---|---|---|---|
"binodeviance" | Binomial deviance | (–∞,∞) | log[1 + exp(–2yjsj)]/[2log(2)] |
"exponential" | Exponential | (–∞,∞) | exp(–yjsj)/2 |
"hamming" | Hamming | [0,1] or (–∞,∞) | [1 – sign(yjsj)]/2 |
"hinge" | Hinge | (–∞,∞) | max(0,1 – yjsj)/2 |
"linear" | Linear | (–∞,∞) | (1 – yjsj)/2 |
"logit" | Logistic | (–∞,∞) | log[1 + exp(–yjsj)]/[2log(2)] |
"quadratic" | Quadratic | [0,1] | [1 – yj(2sj – 1)]2/2 |
The software normalizes binary losses so that the loss is 0.5 when yj = 0, and aggregates using the average of the binary learners [1].
Do not confuse the binary loss with the overall classification loss (specified by the
LossFun
name-value argument of the kfoldLoss
and
kfoldPredict
object functions), which measures how well an ECOC
classifier performs as a whole.
References
[1] Allwein, E., R. Schapire, and Y. Singer. “Reducing multiclass to binary: A unifying approach for margin classifiers.” Journal of Machine Learning Research. Vol. 1, 2000, pp. 113–141.
[2] Escalera, S., O. Pujol, and P. Radeva. “Separability of ternary codes for sparse designs of error-correcting output codes.” Pattern Recog. Lett. Vol. 30, Issue 3, 2009, pp. 285–297.
[3] Escalera, S., O. Pujol, and P. Radeva. “On the decoding process in ternary error-correcting output codes.” IEEE Transactions on Pattern Analysis and Machine Intelligence. Vol. 32, Issue 7, 2010, pp. 120–134.
Extended Capabilities
Automatic Parallel Support
Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.
To run in parallel, specify the Options
name-value argument in the call to
this function and set the UseParallel
field of the
options structure to true
using
statset
:
Options=statset(UseParallel=true)
For more information about parallel computing, see Run MATLAB Functions with Automatic Parallel Support (Parallel Computing Toolbox).
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced in R2014b
See Also
ClassificationPartitionedECOC
| ClassificationECOC
| kfoldEdge
| margin
| kfoldPredict
| fitcecoc
| statset
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