edge

Classification edge for discriminant analysis classifier

Syntax

e = edge(Mdl,Tbl,ResponseVarName)

e = edge(Mdl,Tbl,Y)

e = edge(Mdl,X,Y)

e = edge(___,Weights=weights)

Description

e = edge(Mdl,Tbl,ResponseVarName) returns the classification Edge e for the trained discriminant analysis classifier model Mdl using the predictor data in table Tbl and the class labels in Tbl.ResponseVarName.

The classification edge is the weighted mean value of the classification Margin.

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

e = edge(Mdl,X,Y) returns the classification edge e for the trained discriminant analysis classifier model Mdl using the predictor data in matrix X and the class labels in Y.

e = edge(___,Weights=weights) returns the classification edge e using the weights in weights.

Note

If the predictor data X contains any missing values, the edge function might return NaN. For more details, see edge might return NaN for predictor data with missing values.

Examples

Classification Edge and Margin for Fisher Iris Data

Compute the classification edge and margin for the Fisher iris data, trained on its first two columns of data, and view the last 10 entries.

load fisheriris
X = meas(:,1:2);
obj = fitcdiscr(X,species);
E = edge(obj,X,species)

E = 
0.4980

M = margin(obj,X,species);
M(end-10:end)

ans = 11×1

    0.6551
    0.4838
    0.6551
   -0.5127
    0.5659
    0.4611
    0.4949
    0.1024
    0.2787
   -0.1439
      ⋮

The classifier trained on all the data is better.

obj = fitcdiscr(meas,species);
E = edge(obj,meas,species)

E = 
0.9454

M = margin(obj,meas,species);
M(end-10:end)

ans = 11×1

    0.9983
    1.0000
    0.9991
    0.9978
    1.0000
    1.0000
    0.9999
    0.9882
    0.9937
    1.0000
      ⋮

Input Arguments

Mdl — Trained discriminant analysis classifier

ClassificationDiscriminant model object | CompactClassificationDiscriminant model object

Trained discriminant analysis classifier, specified as a ClassificationDiscriminant model object trained with fitcdiscr, or a CompactClassificationDiscriminant model object created with compact.

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. Categorical predictor variables are not supported. The variables in the columns of X must be the same as the variables used to train Mdl. The number of rows in X must equal the number of rows in Y.

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

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. Categorical predictor variables are not supported. Optionally, Tbl can contain an additional columns for the response variable, which can be categorical. 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 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 the name of a variable in Tbl. If Tbl contains the response variable used to train Mdl, then you do not need to specify ResponseVarName.

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.

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 the response data used to train Mdl. (The software treats string arrays as cell arrays of character vectors.)

The length of Y must equal the number of rows in Tbl or X.

Data Types: categorical | char | string | logical | single | double | cell

weights — Observation weights

ones(size(X,1),1) (default) | numeric vector

Observation weights, specified as a numeric vector. The size of weights must be equal to the number of observations in X or Tbl.

Example: weights=[0.5 0.9 0.2 0.5]

Data Types: single | double

More About

Edge

The edge is the weighted mean value of the classification margin. The weights are class prior probabilities. If you supply additional weights, those weights are normalized to sum to the prior probabilities in the respective classes, and are then used to compute the weighted average.

Margin

The classification margin is the difference between the classification score for the true class and maximal classification score for the false classes.

The classification margin is a column vector with the same number of rows as in the matrix X. A high value of margin indicates a more reliable prediction than a low value.

Score (discriminant analysis)

For discriminant analysis, the score of a classification is the posterior probability of the classification. For the definition of posterior probability in discriminant analysis, see Posterior Probability.

Extended Capabilities

Tall Arrays

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

The edge function fully supports tall arrays. For more information, see Tall Arrays.

Version History

Introduced in R2011b

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 contains 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