edge
Description
returns the Classification Edge (e
= edge(Mdl
,Tbl
,ResponseVarName
)e
)
for the generalized additive model Mdl
using the predictor data in
Tbl
and the true class labels in
Tbl.ResponseVarName
.
specifies options using one or more name-value arguments in addition to any of the input
argument combinations in previous syntaxes. For example, you can specify observation weights
and whether to include interaction terms in computations.e
= edge(___,Name,Value
)
Examples
Estimate Test Sample Classification Margins and Edge
Estimate the test sample classification margins and edge of a generalized additive model. The test sample margins are the observed true class scores minus the false class scores, and the test sample edge is the mean of the margins.
Load the fisheriris
data set. Create X
as a numeric matrix that contains two sepal and two petal measurements for versicolor and virginica irises. Create Y
as a cell array of character vectors that contains the corresponding iris species.
load fisheriris inds = strcmp(species,'versicolor') | strcmp(species,'virginica'); X = meas(inds,:); Y = species(inds,:);
Randomly partition observations into a training set and a test set with stratification, using the class information in Y
. Specify a 30% holdout sample for testing.
rng('default') % For reproducibility cv = cvpartition(Y,'HoldOut',0.30);
Extract the training and test indices.
trainInds = training(cv); testInds = test(cv);
Specify the training and test data sets.
XTrain = X(trainInds,:); YTrain = Y(trainInds); XTest = X(testInds,:); YTest = Y(testInds);
Train a GAM using the predictors XTrain
and class labels YTrain
. A recommended practice is to specify the class names.
Mdl = fitcgam(XTrain,YTrain,'ClassNames',{'versicolor','virginica'});
Mdl
is a ClassificationGAM
model object.
Estimate the test sample classification margins and edge.
m = margin(Mdl,XTest,YTest); e = edge(Mdl,XTest,YTest)
e = 0.8000
Display the histogram of the test sample classification margins.
histogram(m,length(unique(m)),'Normalization','probability') xlabel('Test Sample Margins') ylabel('Probability') title('Probability Distribution of the Test Sample Margins')
Estimate Test Sample Weighted Edge
Estimate the test sample weighted edge (the weighted average of margins) of a generalized additive model.
Load the fisheriris
data set. Create X
as a numeric matrix that contains two sepal and two petal measurements for versicolor and virginica irises. Create Y
as a cell array of character vectors that contains the corresponding iris species.
load fisheriris idx1 = strcmp(species,'versicolor') | strcmp(species,'virginica'); X = meas(idx1,:); Y = species(idx1,:);
Suppose that the quality of some measurements is lower because they were measured with older technology. To simulate this effect, add noise to a random subset of 20 measurements.
rng('default') % For reproducibility idx2 = randperm(size(X,1),20); X(idx2,:) = X(idx2,:) + 2*randn(20,size(X,2));
Randomly partition observations into a training set and a test set with stratification, using the class information in Y
. Specify a 30% holdout sample for testing.
cv = cvpartition(Y,'HoldOut',0.30);
Extract the training and test indices.
trainInds = training(cv); testInds = test(cv);
Specify the training and test data sets.
XTrain = X(trainInds,:); YTrain = Y(trainInds); XTest = X(testInds,:); YTest = Y(testInds);
Train a GAM using the predictors XTrain
and class labels YTrain
. A recommended practice is to specify the class names.
Mdl = fitcgam(XTrain,YTrain,'ClassNames',{'versicolor','virginica'});
Mdl
is a ClassificationGAM
model object.
Estimate the test sample edge.
e = edge(Mdl,XTest,YTest)
e = 0.8000
The average margin is approximately 0.80.
One way to reduce the effect of the noisy measurements is to assign them less weight than the other observations. Define a weight vector that gives the higher quality observations twice the weight of the other observations.
n = size(X,1); weights = ones(size(X,1),1); weights(idx2) = 0.5; weightsTrain = weights(trainInds); weightsTest = weights(testInds);
Train a GAM using the predictors XTrain
, class labels YTrain
, and weights weightsTrain
.
Mdl_W = fitcgam(XTrain,YTrain,'Weights',weightsTrain,... 'ClassNames',{'versicolor','virginica'});
Estimate the test sample weighted edge using the weighting scheme.
e_W = edge(Mdl_W,XTest,YTest,'Weights',weightsTest)
e_W = 0.8770
The weighted average margin is approximately 0.88. This result indicates that, on average, the labels from weighted classifier labels have higher confidence.
Compare GAMs by Examining Test Sample Margins and Edge
Compare a GAM with linear terms to a GAM with both linear and interaction terms by examining the test sample margins and edge. Based solely on this comparison, the classifier with the highest margins and edge is the best model.
Load the ionosphere
data set. This data set has 34 predictors and 351 binary responses for radar returns, either bad ('b'
) or good ('g'
).
load ionosphere
Randomly partition observations into a training set and a test set with stratification, using the class information in Y
. Specify a 30% holdout sample for testing.
rng('default') % For reproducibility cv = cvpartition(Y,'Holdout',0.30);
Extract the training and test indices.
trainInds = training(cv); testInds = test(cv);
Specify the training and test data sets.
XTrain = X(trainInds,:); YTrain = Y(trainInds); XTest = X(testInds,:); YTest = Y(testInds);
Train a GAM that contains both linear and interaction terms for predictors. Specify to include all available interaction terms whose p-values are not greater than 0.05.
Mdl = fitcgam(XTrain,YTrain,'Interactions','all','MaxPValue',0.05)
Mdl = ClassificationGAM ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'b' 'g'} ScoreTransform: 'logit' Intercept: 3.0398 Interactions: [561x2 double] NumObservations: 246
Mdl
is a ClassificationGAM
model object. Mdl
includes all available interaction terms.
Estimate the test sample margins and edge for Mdl
.
M = margin(Mdl,XTest,YTest); E = edge(Mdl,XTest,YTest)
E = 0.7848
Estimate the test sample margins and edge for Mdl
without including interaction terms.
M_nointeractions = margin(Mdl,XTest,YTest,'IncludeInteractions',false); E_nointeractions = edge(Mdl,XTest,YTest,'IncludeInteractions',false)
E_nointeractions = 0.7871
Display the distributions of the margins using box plots.
boxplot([M M_nointeractions],'Labels',{'Linear and Interaction Terms','Linear Terms Only'}) title('Box Plots of Test Sample Margins')
The margins M
and M_nointeractions
have a similar distribution, but the test sample edge of the classifier with only linear terms is larger. Classifiers that yield relatively large margins are preferred.
Input Arguments
Mdl
— Generalized additive model
ClassificationGAM
model object | CompactClassificationGAM
model object
Generalized additive model, specified as a ClassificationGAM
or CompactClassificationGAM
model object.
Tbl
— Sample data
table
Sample data, specified as a table. Each row of Tbl
corresponds to one observation, and each column corresponds to one predictor variable. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed.
Tbl
must contain all the predictors used to train
Mdl
. Optionally, Tbl
can contain a column
for the response variable and a column for the observation weights.
The response variable must have the same data type as
Mdl.Y
. (The software treats string arrays as cell arrays of character vectors.) If the response variable inTbl
has the same name as the response variable used to trainMdl
, then you do not need to specifyResponseVarName
.The weight values must be a numeric vector. You must specify the observation weights in
Tbl
by using'Weights'
.
If you trained Mdl
using sample data contained in a table, then the input data for edge
must also be in a table.
Data Types: table
ResponseVarName
— Response variable name
name of variable in Tbl
Response variable name, specified as a character vector or string scalar containing the name
of the response variable in Tbl
. For example, if the response
variable Y
is stored in Tbl.Y
, then specify it as
'Y'
.
Data Types: char
| string
Y
— Class labels
categorical array | character array | string array | logical vector | numeric vector | cell array of character vectors
Class labels, specified as a categorical, character, or string array, a logical or
numeric vector, or a cell array of character vectors. Each row of Y
represents the classification of the corresponding row of X
or
Tbl
.
Y
must have the same data type as Mdl.Y
. (The software treats string arrays as cell arrays of character
vectors.)
Data Types: single
| double
| categorical
| logical
| char
| string
| cell
X
— Predictor data
numeric matrix
Predictor data, specified as a numeric matrix. Each row of X
corresponds to one observation, and each column corresponds to one predictor variable.
If you trained Mdl
using sample data contained in a matrix, then the input data for edge
must also be in a matrix.
Data Types: single
| double
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: 'IncludeInteractions',false,'Weights',w
specifies to exclude
interaction terms from the model and to use the observation weights
w
.
IncludeInteractions
— Flag to include interaction terms
true
| false
Flag to include interaction terms of the model, specified as true
or
false
.
The default 'IncludeInteractions'
value is true
if Mdl
contains interaction terms. The value must be false
if the model does not contain interaction terms.
Example: 'IncludeInteractions',false
Data Types: logical
Weights
— Observation weights
ones(size(X,1),1)
(default) | vector of scalar values | name of variable in Tbl
Observation weights, specified as a vector of scalar values or the name of a variable in Tbl
. The software weights the observations in each row of X
or Tbl
with the corresponding value in Weights
. The size of Weights
must equal the number of rows in X
or Tbl
.
If you specify the input data as a table Tbl
, then
Weights
can be the name of a variable in Tbl
that contains a numeric vector. In this case, you must specify
Weights
as a character vector or string scalar. For example, if
the weights vector W
is stored in Tbl.W
, then
specify it as 'W'
.
edge
normalizes the weights in each class to add up to the value of the prior probability of the respective class.
Data Types: single
| double
| char
| string
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 for binary classification is, for each observation, the difference between the classification score for the true class and the classification score for the false class.
If the margins are on the same scale (that is, the score values are based on the same score transformation), then they serve as a classification confidence measure. Among multiple classifiers, those that yield greater margins are better.
Version History
Introduced in R2021a
See Also
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