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The multiclass hinge loss — sklearn.metrics.hinge_loss over one decision per class.

public static double MultiClass(ReadOnlySpan<int> yTrue, ReadOnlySpan<double> predDecision, int classCount, ReadOnlySpan<double> sampleWeight = default)

Parameters — yTrue is the true class index of each sample, in [0, classCount). predDecision is one decision per class, row-major: sample 0's classes, then sample 1's. classCount is how many classes each row scores. sampleWeight is one weight per sample, or empty.

Returns — double, 0 or above. 0 when every sample's own class wins by at least 1.

Exceptions — ArgumentException when predDecision is not yTrue.Length × classCount, or a label is not a class index below classCount. ArgumentOutOfRangeException when classCount is below two.

Example — four samples over three classes.

using Lodestar.Metrics;

int[] truth = [0, 1, 2, 1];
double[] decisions =
[
    1.2, 0.3, -0.5,
    0.1, 0.9, 0.2,
    0.4, 0.2, 0.7,
    0.3, 0.1, 0.6,
];

double loss = HingeLoss.MultiClass(truth, decisions, classCount: 3);  // => 0.65

The last sample's own class scores 0.1 against a best rival of 0.6, a margin of -0.5, so it alone costs 1.5 of the 2.6 the four sum to.

Remarks — the margin is the true class's decision less the best of the others, not less all of them: Crammer and Singer's multiclass hinge, which is what the reference computes. Only that one rival matters, so improving a class the sample was never going to be confused with changes nothing.

Applies to — net10.0, netstandard2.0.

See also — HingeLoss.Score, LogLoss.MultiClass, the Python equivalence table.