edge

Classification edge for classification ensemble model

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 e for the trained classification ensemble model ens using the predictor data in table tbl and the class labels in tbl.ResponseVarName.

The classification edge e is a vector or scalar depending on the setting of the Mode name-value argument.

e = edge(ens,tbl,Y) returns the classification edge using the predictor data in table tbl and the class labels in Y.

e = edge(ens,X,Y) returns the classification edge using the predictor data in matrix X and the class labels in Y.

e = edge(___,Name=Value) specifies options using one or more name-value arguments in addition to any of the input argument combinations in the previous syntaxes. For example, you can specify the indices of weak learners in the ensemble to use for calculating margins, specify observation weights, and perform computations in parallel.

Note

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

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

Input Arguments

ens — Classification ensemble model

ClassificationEnsemble model object | ClassificationBaggedEnsemble model object | CompactClassificationEnsemble model object

Classification ensemble model, specified as a ClassificationEnsemble or ClassificationBaggedEnsemble model object trained with fitcensemble, or a CompactClassificationEnsemble model object created with compact.

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. 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 edge must also be in a table.

Data Types: table

ResponseVarName — Response variable name

name of variable in tbl

Response variable name, specified as the name of a variable in tbl. If tbl contains the response variable used to train ens, then you do not need to specify ResponseVarName.

If you specify ResponseVarName, you must specify it 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.

The response variable must be a categorical, character, or string array, a logical or numeric vector, or a cell array of character vectors. If the response variable is a character array, then each element must correspond to one row of the array.

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. Y must have the same data type as tbl or X. (The software treats string arrays as cell arrays of character vectors.)

Y must be of the same type as the classification used to train ens, and its number of elements must equal the number of rows of tbl or X.

Data Types: categorical | char | string | logical | single | double | 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 variable. The variables in the columns of X must be the same as the variables used to train ens.

The number of rows in X must equal the number of rows in Y.

If you trained ens using sample data contained in a matrix, then the input data for edge must also be in a matrix.

Data Types: double | single

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: edge(Mdl,X,Mode="individual",UseParallel=true) specifies to output a vector with one element per trained learner, and to run in parallel.

Learners — Indices of weak learners

[1:ens.NumTrained] (default) | vector of positive integers

Indices of the weak learners in the ensemble to use with edge, specified as a vector of positive integers in the range [1:ens.NumTrained]. By default, the function uses all learners.

Example: Learners=[1 2 4]

Data Types: single | double

Mode — Aggregation level for output

"ensemble" (default) | "individual" | "cumulative"

Aggregation level for the output, specified as "ensemble", "individual", or "cumulative".

Value	Description
"ensemble"	The output is a scalar value, the loss for the entire ensemble.
"individual"	The output is a vector with one element per trained learner.
"cumulative"	The output is a vector in which element J is obtained by using learners 1:J from the input list of learners.

Example: Mode="individual"

Data Types: char | string

UseObsForLearner — Option to use observations for learners

true(N,T) (default) | logical matrix

Option to use observations for learners, specified as 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 (default), learner j is used in predicting the class of row i of X.

Example: UseObsForLearner=logical([1 1; 0 1; 1 0])

Data Types: logical matrix

UseParallel — Flag to run in parallel

false or 0 (default) | true or 1

Flag to run in parallel, specified as a numeric or logical 1 (true) or 0 (false). If you specify UseParallel=true, the edge function executes for-loop iterations by using parfor. The loop runs in parallel when you have Parallel Computing Toolbox™.

Example: UseParallel=true

Data Types: logical

Weights — Observation weights

ones(size(X,1),1) (default) | numeric vector | name of variable in tbl

Observation weights, specified as a numeric vector or the name of a variable in tbl. If you supply weights, edge computes the weighted classification edge.

If you specify Weights as a numeric vector, then the size of Weights must be equal to the number of observations in X or tbl. The software normalizes Weights to sum up to the value of the prior probability in the respective class.

If you specify Weights as the name of a variable in tbl, you must specify it as a character vector or string scalar. For example, if the weights are stored as tbl.w, then specify Weights as "w". Otherwise, the software treats all columns of tbl, including tbl.w, as predictors.

Data Types: single | double | char | string

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.

Classification 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 argument, 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 the UseParallel name-value argument 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 the UseParallel name-value argument with tall arrays, GPU arrays, or code generation.

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

Introduced in R2011a

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 changes, see Cost property stores the user-specified cost matrix.

If you want the software to handle the cost matrix, prior probabilities, and observation weights in the same way 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 might 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 might 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