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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 .. statistical-classification. statistical classification. hypersurface. hypersurface. vector space. vector space. 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 .. classifier. Pattern recognition#Probabilistic classifiers. A decision boundary is the region of a problem space in which the output label of a classifier is ambiguous .. classifier. Pattern recognition#Probabilistic classifiers. If the decision surface is a hyperplane , then the classification problem is linear , and the classes are linearly separable .. hyperplane. hyperplane. linearly separable. 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 .