Hyperplane Distance Calculator for Machine Learning

Calculator Inputs

Number of dimensions

Hyperplane bias, b

Second parallel bias

Used for parallel-plane distance.

Weight vector

Enter one weight per dimension.

Point row format

Positive class label

Negative class label

Points or dataset rows

Import CSV

Separate coordinates with commas. Separate row sections using vertical bars.

Classification threshold

Boundary tolerance

Support-vector tolerance

Decimal precision

Zero-score handling

Multiple hyperplane biases

Uses the same weight vector.

Calculate projected points

Show detailed steps

Include SVM margin analysis

Formula Used

Point distance: d = |w · x + b| / ||w|| Signed distance: dₛ = (w · x + b) / ||w|| SVM geometric margin: γ = y(w · x + b) / ||w|| Parallel hyperplanes: d = |b₂ - b₁| / ||w|| Margin width: 2 / ||w|| Projection: xₚ = x - ((w · x + b) / ||w||²)w

The weight vector is perpendicular to the hyperplane. The sign identifies the point’s side. The absolute value gives perpendicular distance.

How to Use

Choose the number of dimensions.
Enter matching hyperplane weights and one bias.
Select a point row format.
Paste one or many point rows.
Add labels for SVM accuracy analysis.
Set tolerances, precision, and threshold.
Submit the form and review ranked results.
Copy, print, or download the report.

Example Data

Item	Example	Meaning
Weights	2, -1	Normal vector for a two-dimensional line.
Bias	-3	Hyperplane equation becomes 2x₁ - x₂ - 3 = 0.
Point	A \| 3, 2 \| 1	Named point with positive class label.
Second bias	2	Creates a parallel comparison hyperplane.

Frequently Asked Questions

What is a hyperplane?

A hyperplane is a flat decision boundary. It has one fewer dimension than its space. Linear classifiers often use hyperplanes.

What does signed distance show?

Signed distance includes direction. Positive and negative signs identify opposite sides. Zero indicates the boundary.

Why divide by the weight norm?

The raw score depends on weight scale. Dividing removes that scaling effect. The result becomes geometric distance.

Can this evaluate multiple points?

Yes, enter one point per line. Results are ranked by distance. Batch statistics summarize the dataset.

How are support vectors identified?

Canonical SVM support vectors satisfy scores near positive or negative one. The tolerance controls acceptable deviation. Scaling must match canonical form.

What is functional margin?

Functional margin multiplies the score by the class sign. Its size changes with weight scaling. Geometric margin removes that scaling.

What is the projected point?

It is the nearest point on the hyperplane. The connecting segment is perpendicular. Its length equals the absolute distance.

Can nonparallel hyperplanes be compared?

A single constant distance exists only for parallel hyperplanes. This calculator reuses one weight vector. Different weights require another analysis.

Why might the chart not appear?

Charts are limited to two or three dimensions. Higher-dimensional results remain numerically valid. Use projections for detailed inspection.