# Optimal Separating Hyperplane

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An Optimal Separating Hyperplane is a Hyperplane that cleanly separates the points in a dataset **X** into sets that contain only members of their own type, such that the Margin between the Hyperplane and any point is maximal.

**Context:**- The hyperplane is in canonical form w.r.t. the data if the minimum distance between any data point in X and the hyperplane is 1.
- Is an Optimal Canonical Separating Hyperplane when the distance from a closest vector (or Support Vector) to the hyperplane (i.e. ((
**w**·**x**)+*b*)/ ||w**||) is equal to 1.**

**See:**Support Vector Machine, Primal Optimization Task.