Hinge Loss Calculator (SVM / Squared Hinge Loss)

Hinge loss is the loss function behind the support vector machine (SVM). For each sample it measures how badly a linear classifier violates the margin — the band of width 2 around the separating hyperplane. This calculator follows the definition published in scikit-learn's sklearn.metrics.hinge_loss reference and the soft-margin formulation introduced by Cortes and Vapnik (1995).

1. Map the labels. Each true label must be ±1. If your data uses {0, 1}, the tool maps 0 → −1 and 1 → +1 so the margin gets the correct sign (scikit-learn requires y_true ∈ {−1, +1}).
2. Compute the margin. For every sample, m = y · f(x), where f(x) is the decision-function score (a signed distance), not a probability. A large positive margin means confidently correct; a negative margin means misclassified.
3. Apply the hinge. Standard hinge: ℓ = max(0, 1 − m). Squared hinge: ℓ = max(0, 1 − m)². Any sample with m ≥ 1 contributes exactly 0 — it is correct and safely outside the margin.
4. Reduce. The mean (1/N)·Σ ℓᵢ is scikit-learn's default; the sum Σ ℓᵢ is also offered. If you supply per-sample weights, the mean becomes the weighted average Σ wᵢ·ℓᵢ / Σ wᵢ, matching the metric's sample_weight argument.

Every result is verified two ways. The per-sample loss is computed both with Math.max(0, 1 − m) and with the algebraic identity max(0, x) = (x + |x|) / 2; the two agree to floating-point tolerance, which the “Cross-check” tile reports. Because hinge loss consumes decision scores rather than calibrated probabilities, it is the wrong tool for a model that outputs probabilities — reach for log loss (cross-entropy) there instead.

• scikit-learn — sklearn.metrics.hinge_loss (API reference)
• scikit-learn User Guide §3.3 — Hinge loss definition and averaging
• Cortes & Vapnik (1995) — Support-Vector Networks, Machine Learning 20(3)

Definitions and worked examples were last cross-checked against the scikit-learn documentation on 2026-07-12. The binary hinge and squared-hinge formulas here reproduce sklearn.metrics.hinge_loss to the digits shown.