Calculator Inputs
Plotly Graph
Single mode plots hinge loss against decision score. Batch mode plots sample losses for each entered observation.
Example Data Table
| Sample | True Label y | Decision Score f(x) | Weight | Functional Margin y·f(x) | Hinge Loss max(0, 1 - y·f(x)) |
|---|---|---|---|---|---|
| 1 | 1 | 0.90 | 1.00 | 0.90 | 0.10 |
| 2 | 1 | 0.40 | 1.00 | 0.40 | 0.60 |
| 3 | -1 | -0.70 | 1.00 | 0.70 | 0.30 |
| 4 | -1 | 0.20 | 1.00 | -0.20 | 1.20 |
| 5 | 1 | -0.10 | 0.50 | -0.10 | 1.10 |
Formula Used
Functional margin: m = y · f(x)
Hinge loss: L = max(0, t - y · f(x))
Weighted hinge loss: Lw = w · max(0, t - y · f(x))
Regularized objective: J = 0.5 · ‖w‖² + C · ΣLw
Here, y is the class label and must be either -1 or 1. The value f(x) is the model score before thresholding. The parameter t is the required margin threshold, usually 1 in support vector machines.
The loss becomes zero only when the signed score clears the margin. A positive but small margin still creates loss because the example is correct yet not confidently separated. Negative margins indicate incorrect sign classification and larger penalties.
The regularized objective combines the total loss with a complexity term based on the squared weight norm. This helps balance fit quality and model simplicity during optimization.
How to Use This Calculator
- Select Single sample to inspect one prediction, or Batch dataset to summarize multiple samples.
- Enter the margin threshold, regularization constant, and squared norm term.
- For single mode, choose label -1 or 1, then enter the decision score and sample weight.
- For batch mode, paste rows in the format y, score, weight.
- Press Calculate Hinge Loss to show the result above the form.
- Review margin size, hinge loss, violation status, weighted summary, and objective value.
- Use the CSV and PDF buttons to export your current results.
- Inspect the Plotly graph to see how score movement changes the penalty.
Frequently Asked Questions
1. What does hinge loss measure?
Hinge loss measures how far a classifier prediction falls below a desired margin. It penalizes incorrect predictions and also weak correct predictions that are not confidently separated.
2. Why must labels be -1 and 1?
The standard hinge loss formula uses signed labels because the product y·f(x) directly gives the functional margin. That margin determines whether loss is zero or positive.
3. What happens when the score is correct but small?
The sample can still receive positive loss. Hinge loss demands not only correct sign classification, but also a sufficient distance from the decision boundary.
4. What does the margin threshold control?
The threshold sets the minimum desired signed score. A larger threshold makes the rule stricter, so more predictions count as margin violations and produce higher loss.
5. Why include sample weights?
Weights let you make some observations count more than others. This is useful for class imbalance, cost-sensitive learning, or emphasizing especially important examples.
6. What is the regularized objective value?
It combines model complexity with classification penalty. Lower values usually indicate a better tradeoff between fitting training data and keeping the model from becoming too complex.
7. Is hinge loss a probability error measure?
No. Hinge loss works on decision scores and margins rather than calibrated probabilities. It is common in large-margin classification methods such as support vector machines.
8. When is hinge loss equal to zero?
It becomes zero when the signed prediction score meets or exceeds the chosen margin threshold. That means the observation is correctly classified with enough separation.