A convex set (in pink), a supporting hyperplane of (the dashed line), and the supporting half-space delimited by the hyperplane which contains (in light blue).
In geometry, a supporting hyperplane of a set in Euclidean space is a hyperplane that has both of the following two properties:[1]
is entirely contained in one of the two closed half-spaces bounded by the hyperplane,
has at least one boundary-point on the hyperplane.
Here, a closed half-space is the half-space that includes the points within the hyperplane.
^Luenberger, David G. (1969). Optimization by Vector Space Methods. New York: John Wiley & Sons. p. 133. ISBN 978-0-471-18117-0.
and 24 Related for: Supporting hyperplane information
In geometry, a supportinghyperplane of a set S {\displaystyle S} in Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is a hyperplane that has both...
In geometry, a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension. Like...
is the supportinghyperplane theorem. In the context of support-vector machines, the optimally separating hyperplane or maximum-margin hyperplane is a hyperplane...
measurable space Supportinghyperplane, sometimes referred to as supportSupport of a module, a set of prime ideals in commutative algebra Support, the natural...
points in Q. Supportinghyperplane is a concept in geometry. A hyperplane divides a space into two half-spaces. A hyperplane is said to support a set S {\displaystyle...
stability.[citation needed] More formally, a support vector machine constructs a hyperplane or set of hyperplanes in a high or infinite-dimensional space,...
^{n}} describes the (signed) distances of supporting hyperplanes of A from the origin. The support function is a convex function on R n {\displaystyle...
convex set may be represented as such intersection, one needs the supportinghyperplane theorem in the form that for a given closed convex set C and point...
corresponds with a supportinghyperplane of the polytope, a hyperplane bounding a half-space that contains the polytope. If a supportinghyperplane also intersects...
analysis and mathematical optimization, the supporting functional is a generalization of the supportinghyperplane of a set. Let X be a locally convex topological...
interior. The notion of a supporting line to a planar curve or convex shape can be generalized to n dimension as a supportinghyperplane. If two bounded connected...
not differentiable Supportinghyperplane - a hyperplane meeting certain conditions Supportinghyperplane theorem - that defines a supportinghyperplane...
is a normal at the origin of a hyperplane that supports C. y and C lie on the same side of that supportinghyperplane. C* is closed and convex. C 1 ⊆...
of the closed half-spaces of V containing K and bounded by the supportinghyperplanes of K at x. The boundary TK of the solid tangent cone is the tangent...
terms of its supportinghyperplanes. This can be seen as consequence of the following two observations. On the one hand, the hyperplane tangent to the...
is replaced by a hyperplane. The problem of determining if a pair of sets is linearly separable and finding a separating hyperplane if they are, arises...
consists of a reflection across a hyperplane and a translation ("glide") in a direction parallel to that hyperplane, combined into a single transformation...
is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete...
encoding of the convex hull of the function's epigraph in terms of its supportinghyperplanes. For more examples, see § Table of selected convex conjugates. The...
exhibit the saddle property on nonexistence of locally strictly supportinghyperplanes.[P89] As such, his construction provided further obstruction to...
linear cone. However, it is still called an affine convex cone. A (linear) hyperplane is a set in the form { x ∈ V ∣ f ( x ) = c } {\displaystyle \{x\in V\mid...
output label of a classifier is ambiguous. If the decision surface is a hyperplane, then the classification problem is linear, and the classes are linearly...
( w , b ) {\displaystyle (\mathbf {w} ,b)} are the parameters of the hyperplane and x {\displaystyle \mathbf {x} } is the input variable(s). When t and...
Global Information
