# Decision Boundary

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A Decision Boundary is a hypersurface in a classification model that partitions the underlying vector space into two sets, one for each class.

**AKA:**Decision Surface.**Context:**- It can range from being a Linear Decision Boundary to being a Non-Linear Decision Boundary.
- It can range from being a Continuous Decision Boundary to being a Discontinuous Decision Boundary (such as a piece-wise decision boundary).

**See:**Support Vector, Hyperplane, Margin, Predictive Function, Statistical Classification, Hypersurface, Vector Space.

## References

### 2015

- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/decision_boundary Retrieved:2015-1-14.
- In a statistical-classification problem with two classes, a
**decision boundary**or decision surface is a hypersurface that partitions the underlying vector space into two sets, one for each class. The classifier will classify all the points on one side of the decision boundary as belonging to one class and all those on the other side as belonging to the other class.A decision boundary is the region of a problem space in which the output label of a classifier is ambiguous.

^{[1]}If the decision surface is a hyperplane, then the classification problem is linear, and the classes are linearly separable.

Decision boundaries are not always clear cut. That is, the transition from one class in the feature space to another is not discontinuous, but gradual. This effect is common in fuzzy logic based classification algorithms, where membership in one class or another is ambiguous.

- In a statistical-classification problem with two classes, a