resubEdge
Resubstitution classification edge for multiclass error-correcting output codes (ECOC) model
Description
returns the resubstitution classification edge
(e
= resubEdge(Mdl
)e
) for the multiclass error-correcting output codes (ECOC) model
Mdl
using the training data stored in Mdl.X
and
the corresponding class labels stored in Mdl.Y
.
The classification edge is a scalar value that represents the weighted mean of the classification margins.
computes the resubstitution classification edge with additional options specified by one or
more name-value pair arguments. For example, you can specify a decoding scheme, binary
learner loss function, and verbosity level.e
= resubEdge(Mdl
,Name,Value
)
Examples
Resubstitution Edge of ECOC Model
Compute the resubstitution edge for an ECOC model with SVM binary learners.
Load Fisher's iris data set. Specify the predictor data X
and the response data Y
.
load fisheriris
X = meas;
Y = species;
Train an ECOC model using SVM binary classifiers. Standardize the predictors using an SVM template, and specify the class order.
t = templateSVM('Standardize',true);
classOrder = unique(Y)
classOrder = 3x1 cell
{'setosa' }
{'versicolor'}
{'virginica' }
Mdl = fitcecoc(X,Y,'Learners',t,'ClassNames',classOrder);
t
is an SVM template object. During training, the software uses default values for empty properties in t
. Mdl
is a ClassificationECOC
model.
Compute the resubstitution edge, which is the mean of the training-sample margins.
e = resubEdge(Mdl)
e = 0.7440
Select ECOC Model Features by Comparing Training-Sample Edges
Perform feature selection by comparing training-sample edges from multiple models. Based solely on this comparison, the classifier with the greatest edge is the best classifier.
Load Fisher's iris data set. Define two data sets:
fullX
contains all four predictors.partX
contains the sepal measurements only.
load fisheriris
X = meas;
fullX = X;
partX = X(:,1:2);
Y = species;
Train an ECOC model using SVM binary learners for each predictor set. Standardize the predictors using an SVM template, specify the class order, and compute the posterior probabilities.
t = templateSVM('Standardize',true);
classOrder = unique(Y)
classOrder = 3x1 cell
{'setosa' }
{'versicolor'}
{'virginica' }
FullMdl = fitcecoc(fullX,Y,'Learners',t,'ClassNames',classOrder,... 'FitPosterior',true); PartMdl = fitcecoc(partX,Y,'Learners',t,'ClassNames',classOrder,... 'FitPosterior',true);
The default SVM score is the distance from the decision boundary. If you specify to compute posterior probabilities, then the software uses posterior probabilities as scores.
Compute the resubstitution edge for each classifier. The quadratic loss function operates on scores in the domain [0,1]. Specify to use quadratic loss when aggregating the binary learners for both models.
fullEdge = resubEdge(FullMdl,'BinaryLoss','quadratic')
fullEdge = 0.9896
partEdge = resubEdge(PartMdl,'BinaryLoss','quadratic')
partEdge = 0.5059
The edge for the classifier trained on the complete data set is greater, suggesting that the classifier trained with all the predictors has a better training-sample fit.
Input Arguments
Mdl
— Full, trained multiclass ECOC model
ClassificationECOC
model
Full, trained multiclass ECOC model, specified as a ClassificationECOC
model trained with fitcecoc
.
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: resubEdge(Mdl,'BinaryLoss','quadratic')
specifies a quadratic
binary learner loss function.
BinaryLoss
— Binary learner loss function
"hamming"
| "linear"
| "logit"
| "exponential"
| "binodeviance"
| "hinge"
| "quadratic"
| function handle
Binary learner loss function, specified as 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 handleBinaryLoss=@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 or linear or kernel classification models of SVM learners. | "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
"lossweighted"
or "lossbased"
. For more
information, see Binary Loss.
Example: Decoding="lossbased"
Data Types: char
| string
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
More About
Classification Edge
The classification edge is the weighted mean of the classification margins.
One way to choose among multiple classifiers, for example to perform feature selection, is to choose the classifier that yields the greatest edge.
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 resubLoss
and
resubPredict
object functions), which measures how well an ECOC
classifier performs as a whole.
Tips
To compare the margins or edges of several ECOC classifiers, use template objects to specify a common score transform function among the classifiers during training.
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
ClassificationECOC
| resubMargin
| edge
| predict
| resubPredict
| fitcecoc
| resubLoss
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