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.

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 Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

'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))

Output Arguments

E

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

Definitions

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.

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
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