# hyperplane

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## hyperplane

[¦hī·pər‚plān]
(mathematics)
A hyperplane is an (n- 1)-dimensional subspace of an n-dimensional vector space.
References in periodicals archive ?
Consider the four hyperplanes shown in the same plot, and suppose we had access only to the binary data Q = sign(AX), where A contains the normals to each hyperplane as its rows.
Contrary to the bi-criteria optimization problems, in the case of more than two objective functions, one cannot generalize such a hyperplane to problems with more than two CFs in the same way as the H-hyperplane on bi-objective problems.
As shown in Figure 4, only the darkest samples have enough support vectors to define the separation hyperplane of the two classes with maximum distance.
The residue of the multiple Fibonacci zeta function [[zeta].sub.F]([s.sub.1],[s.sub.2]) at [a.sub.l,n] := -2l + i[pi](l + 2n)/log [alpha] is equivalent to take the restriction to the hyperplane [s.sub.2] = [a.sub.l,n].
The calibration flight is used to obtain a compensation hyperplane, and the test flight is used to assess the performance of the compensation hyperplane.
If the sample can be correctly divided into two classes using a classification hyperplane, then the sample is linearly separable and satisfies (8).
The hyperplane related to the model created by the OneClassSVM classifier is shown in Figure 8.
Linear partitioning (or regression) can be realized on a linear hyperplane. The SVM method can solve this problem skillfully by applying the expansion theorem of the kernel function.
In order to improve on the detection possibilities we assume this constrained to a hyperplane quantum dynamics to concern a superconducting condensate.
proposed a method aiming at determining hyperrectangles whose upper and lower corners are defined by determining the intersection of each of the support vectors with the separating hyperplane [41].
The method proposed by [16] is principled on Structural Risk Minimization (SRM) with the aim of finding the best hyperplane to separate two classes in a space.
HyperPlane dataset is represented by the set of points x that satisfy [[summation].sup.d.sub.i=1][w.sub.i][x.sub.i] = [w.sub.0], where [x.sub.i] is the ith coordinate of x.

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