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.
Decision boundaries can be approximations of optimal stopping boundaries. [2] The decision boundary is the set of points of that hyperplane that pass through zero. [3] For example, the angle between a vector and points in a set must be zero for points that are on or close to the decision boundary. [4]
Decision boundary instability can be incorporated with generalization error as a standard for selecting the most accurate and stable classifier. [5]
^Corso, Jason J. (Spring 2013). "Quiz 1 of 14 - Solutions" (PDF). Department of Computer Science and Engineering - University at Buffalo School of Engineering and Applied Sciences. Johnson, David.
^Whittle, P. (1973). "An Approximate Characterisation of Optimal Stopping Boundaries". Journal of Applied Probability. 10 (1): 158–165. doi:10.2307/3212503. ISSN 0021-9002. JSTOR 3212503. Retrieved 2022-11-28.
^Laber, Eric B.; Murphy, Susan A. (2011). "Rejoinder". Journal of the American Statistical Association. 106 (495): 940–945. ISSN 0162-1459. JSTOR 23427564. Retrieved 2022-11-28.
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to get linear learning algorithms to learn a nonlinear function or decisionboundary. For all x {\displaystyle \mathbf {x} } and x ′ {\displaystyle \mathbf...
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pre-processing Data stream clustering Dataiku Davies–Bouldin index DecisionboundaryDecision list Decision tree model Deductive classifier DeepArt DeepDream Deep...
are fundamentally algorithmic that cannot be learned by finding a decisionboundary. So far, DNCs have been demonstrated to handle only relatively simple...
mental shortcuts), called heuristics, that the brain uses to produce decisions or judgments. Biases have a variety of forms and appear as cognitive ("cold")...
classifier which is able to give an associated distance from the decisionboundary for each example. For instance, if a linear classifier (e.g. perceptron...
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