Calculation Results
Observation Results
Calculation Report
Formula Used
How to Use
Select a calculator mode. Enter vectors with commas or spaces. Keep vector dimensions equal.
Use dataset mode for many observations. Configure optional IDs, weights, and alpha values. Review every classification result.
Use kernel mode for nonlinear boundaries. Enter support vectors and kernel parameters. Export the final report.
Example Data
| ID | x₁ | x₂ | Label | Weight | Alpha |
|---|---|---|---|---|---|
| A | 2 | 1 | +1 | 1 | 0.5 |
| B | 1 | 3 | -1 | 1 | 0.8 |
| C | 3 | 0 | +1 | 1 | 1 |
Frequently Asked Questions
What is an SVM margin?
It measures separation from the decision boundary. Larger margins usually improve robustness. Support vectors define this separation.
What is a functional margin?
It is the signed class score. Its value changes with weight scaling. It is not normalized.
What is a geometric margin?
It divides the functional margin by weight norm. This gives a true geometric distance. Units follow the feature space.
When is a point a support vector?
Canonical support vectors satisfy a margin near one. Soft-margin models can include bound vectors. Numerical tolerance prevents false mismatches.
What does hinge loss mean?
Zero loss means sufficient correct separation. Positive loss indicates margin intrusion. Large loss can indicate misclassification.
How does C affect the model?
Larger C penalizes violations more strongly. Smaller C permits a softer boundary. The best value needs validation.
Can kernel margin be computed?
Yes, feature-space norm uses kernel values. The score uses support vectors. Results depend on correct coefficients.
Why does scaling matter?
Features with large ranges can dominate distances. Scaling creates more balanced geometry. Weights must match that space.
What are KKT conditions?
They describe optimal support-vector relationships. Alpha bounds determine expected margins. Tolerance handles floating-point error.