Decision boundary


Decision boundary

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.

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 ANNs and SVMs

In the case of backpropagation based artificial neural networks or perceptrons, the type of decision boundary that the network can learn is determined by the number of hidden layers the network has. If it has no hidden layers, then it can only learn linear problems. If it has one hidden layer, then it can learn problems with convex decision boundaries (and some concave decision boundaries). The network can learn more complex problems if it has two or more hidden layers.

In particular, support vector machines find a hyperplane that separates the feature space into two classes with the maximum margin. If the problem is not originally linearly separable, the kernel trick is used to turn it into a linearly separable one, by increasing the number of dimensions. Thus a general hypersurface in a small dimension space is turned into a hyperplane in a space with much larger dimensions.

Neural networks try to learn the decision boundary which minimizes the empirical error, while support vector machines try to learn the decision boundary which gives the best generalization.



Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Boundary critique — is the concept in critical systems thinking, that states that both the meaning and the validity of professional propositions always depend on boundary judgments as to what are facts or observation and norms or valuation standards. [Werner Ulrich… …   Wikipedia

  • Decision Coverage — Die kontrollflussorientierten Testverfahren, auch Überdeckungstests genannt, gehören zu der Gruppe der strukturorientierten Testmethoden. Die kontrollflussorientierten Testverfahren orientieren sich am Kontrollflussgraphen des Programms. Es… …   Deutsch Wikipedia

  • Local Government Boundary Commission (1945 - 1949) — The Local Government Boundary Commission was established in 1945 to review the boundaries of local authority areas in England and Wales outside the Counties of London and Middlesex. The Commission produced its report in 1948 which proposed large… …   Wikipedia

  • Alaska boundary dispute — The Alaska Boundary Dispute was a territorial dispute between the United States and Canada (then a British Dominion with its foreign affairs controlled from London), and at a subnational level between Alaska on the U.S. side and British Columbia… …   Wikipedia

  • Oregon boundary dispute — The Oregon Country/Columbia District stretched from 42N to 54 40 N.The most heavily disputed portion is highlighted The Oregon boundary dispute, or the Oregon Question, arose as a result of competing British and American claims to the Pacific… …   Wikipedia

  • Multi-criteria decision analysis — Multiple criteria decision making or multiple criteria decision analysis is a sub discipline of operations research that explicitly considers multiple criteria in decision making environments. Whether in our daily lives or in professional… …   Wikipedia

  • Inter-Entity Boundary Line — The Inter Entity Boundary Line (IEBL) divides Bosnia and Herzegovina into two entities, the Republika Srpska and the Federation of Bosnia and Herzegovina. The total length of the Inter Entity Boundary Line is 1,080 km. The IEBL essentially runs… …   Wikipedia

  • Umpire Decision Review System — The Umpire Decision Review System (abbreviated as UDRS or DRS) is a new technology based system currently being used on an experimental basis in the sport of cricket. The system was first introduced in Test Cricket for the sole purpose of… …   Wikipedia

  • Alaska Boundary Question —    Arose out of differences of opinion as to the interpretation of the 1828 Convention between Russia and Great Britain, and particularly as to the boundary of the coast strip. The United States contention was that the boundary should follow a… …   The makers of Canada

  • San Juan Boundary —    Dispute arose between the United States and Great Britain out of a difference of opinion as to the meaning of the phrase middle of the channel which separates the continent from Vancouver Island in the treaty of 1846, and by which the rightful …   The makers of Canada