edge

Classification edge

Syntax

E = edge(obj,X,Y)
E = edge(obj,X,Y,Name,Value)


Description

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

E = edge(obj,X,Y,Name,Value) computes the edge with additional options specified by one or more Name,Value pair arguments.

Note

If the predictor data X contains 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

obj	Discriminant analysis classifier of class ClassificationDiscriminant or CompactClassificationDiscriminant, typically constructed with fitcdiscr.
X	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 obj.
Y	Class labels, with the same data type as exists in obj. The number of elements of Y must equal the number of rows of 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.

weights

Observation weights, a numeric vector of length size(X,1). If you supply weights, edge computes the weighted classification edge. Default: ones(size(X,1),1)

Output Arguments

E	Edge, a scalar representing the weighted average value of the margin.

Examples

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 =
    0.6551
    0.4838
    0.6551
   -0.5127
    0.5659
    0.4611
    0.4949
    0.1024
    0.2787
   -0.1439
   -0.4444

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 =
    0.9983
    1.0000
    0.9991
    0.9978
    1.0000
    1.0000
    0.9999
    0.9882
    0.9937
    1.0000
    0.9649

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.

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

Version History

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 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