edge

Classification edge

Syntax

E = edge(ens,tbl,ResponseVarName)
E = edge(ens,tbl,Y)
E = edge(ens,X,Y)
E = edge(___,Name,Value)


Description

E = edge(ens,tbl,ResponseVarName) returns the classification edge for ens with data tbl and classification tbl.ResponseVarName.

E = edge(ens,tbl,Y) returns the classification edge for ens with data tbl and classification Y.

E = edge(ens,X,Y) returns the classification edge for ens with data X and classification Y.

E = edge(___,Name,Value) computes the edge with additional options specified by one or more Name,Value pair arguments, using any of the previous syntaxes.

Note

If the predictor data X or the predictor variables in tbl contain any missing values, the edge function can return NaN. For more details, see edge can return NaN for predictor data with missing values.

Input Arguments

ens	A classification ensemble constructed with fitcensemble, or a compact classification ensemble constructed with compact.
tbl	Sample data, specified as a table. Each row of tbl corresponds to one observation, and each column corresponds to one predictor variable. tbl must contain all of the predictors used to train the model. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed. If you trained ens using sample data contained in a table, then the input data for this method must also be in a table.
ResponseVarName	Response variable name, specified as the name of a variable in tbl. You must specify ResponseVarName as a character vector or string scalar. For example, if the response variable Y is stored as tbl.Y, then specify it as 'Y'. Otherwise, the software treats all columns of tbl, including Y, as predictors when training the model.
X	A matrix where each row represents an observation, and each column represents a predictor. The number of columns in X must equal the number of predictors in ens. If you trained ens using sample data contained in a matrix, then the input data for this method must also be in a matrix.
Y	Class labels of observations in tbl or X. Y should be of the same type as the classification used to train ens, and its number of elements should equal the number of rows of tbl or X.

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.

learners	Indices of weak learners in the ensemble ranging from 1 to ens.NumTrained. edge uses only these learners for calculating loss. Default: 1:NumTrained
mode	Meaning of the output E: 'ensemble' — E is a scalar value, the edge for the entire ensemble. 'individual' — E is a vector with one element per trained learner. 'cumulative' — E is a vector in which element J is obtained by using learners 1:J from the input list of learners. Default: 'ensemble'
UseObsForLearner	A logical matrix of size N-by-T, where: N is the number of rows of X. T is the number of weak learners in ens. When UseObsForLearner(i,j) is true, learner j is used in predicting the class of row i of X. Default: true(N,T)
UseParallel	Indication to perform inference in parallel, specified as false (compute serially) or true (compute in parallel). Parallel computation requires Parallel Computing Toolbox™. Parallel inference can be faster than serial inference, especially for large datasets. Parallel computation is supported only for tree learners. Default: false
weights	Observation weights, a numeric vector of length size(X,1). If you supply weights, edge computes weighted classification edge. Default: ones(size(X,1),1)

Output Arguments

E	The classification edge, a vector or scalar depending on the setting of the mode name-value pair. Classification edge is weighted average classification margin.

Examples

Find Classification Edge of Training Data

Find the classification edge for some of the data used to train a boosted ensemble classifier.

Load the ionosphere data set.

load ionosphere

Train an ensemble of 100 boosted classification trees using AdaBoostM1.

t = templateTree('MaxNumSplits',1); % Weak learner template tree object
ens = fitcensemble(X,Y,'Method','AdaBoostM1','Learners',t);

Find the classification edge for the last few rows.

E = edge(ens,X(end-10:end,:),Y(end-10:end))

E = 8.3310

More About

Margin

The classification margin is the difference between the classification score for the true class and maximal classification score for the false classes. Margin is a column vector with the same number of rows as in the matrix X.

Score (ensemble)

For ensembles, a classification score represents the confidence of a classification into a class. The higher the score, the higher the confidence.

Different ensemble algorithms have different definitions for their scores. Furthermore, the range of scores depends on ensemble type. For example:

• AdaBoostM1 scores range from –∞ to ∞.

• Bag scores range from 0 to 1.

Edge

The edge is the weighted mean value of the classification margin. The weights are the class probabilities in ens.Prior. If you supply weights in the weights name-value pair, those weights are used instead of class probabilities.

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

Usage notes and limitations:

• You cannot use UseParallel with tall arrays.

For more information, see Tall Arrays.

Automatic Parallel Support

Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.

To run in parallel, set the UseParallel name-value argument to true in the call to this function.

For more general information about parallel computing, see Run MATLAB Functions with Automatic Parallel Support (Parallel Computing Toolbox).

You cannot use UseParallel with tall or GPU arrays.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

• The edge function does not support ensembles trained using decision tree learners with surrogate splits.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

R2022a: edge returns a different value for a model with a nondefault cost matrix

If you specify a nondefault cost matrix when you train the input model object, the edge function returns a different value compared to previous releases.

The edge function uses the prior probabilities stored in the Prior property to normalize the observation weights of the input data. The way the function uses the Prior property value has not changed. However, the property value stored in the input model object has changed for a model with a nondefault cost matrix, so the function can return a different value.

For details about the property value change, see Cost property stores the user-specified cost matrix.

If you want the software to handle the cost matrix, prior probabilities, and observation weights as in previous releases, adjust the prior probabilities and observation weights for the nondefault cost matrix, as described in Adjust Prior Probabilities and Observation Weights for Misclassification Cost Matrix. Then, when you train a classification model, specify the adjusted prior probabilities and observation weights by using the Prior and Weights name-value arguments, respectively, and use the default cost matrix.

R2022a: edge can return NaN for predictor data with missing values

The edge function no longer omits an observation with a NaN score when computing the weighted mean of the classification margins. Therefore, edge can now return NaN when the predictor data X or the predictor variables in tbl contain any missing values. In most cases, if the test set observations do not contain missing predictors, the edge function does not return NaN.

This change improves the automatic selection of a classification model when you use fitcauto. Before this change, the software might select a model (expected to best classify new data) with few non-NaN predictors.

If edge in your code returns NaN, you can update your code to avoid this result. Remove or replace the missing values by using rmmissing or fillmissing, respectively.

The following table shows the classification models for which the edge object function might return NaN. For more details, see the Compatibility Considerations for each edge function.

Model Type	Full or Compact Model Object	edge Object Function
Discriminant analysis classification model	ClassificationDiscriminant, CompactClassificationDiscriminant	edge
Ensemble of learners for classification	ClassificationEnsemble, CompactClassificationEnsemble	edge
Gaussian kernel classification model	ClassificationKernel	edge
k-nearest neighbor classification model	ClassificationKNN	edge
Linear classification model	ClassificationLinear	edge
Neural network classification model	ClassificationNeuralNetwork, CompactClassificationNeuralNetwork	edge
Support vector machine (SVM) classification model	ClassificationSVM, CompactClassificationSVM	edge