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 ?
The linear classifier is the hyperplane H (wx+b=0) with the maximum width (distance between hyperplanes H1 and H2).
5] defined by the Plucker coordinates of the lines in L, and the hyperplanes defined by the Plucker coefficients of the lines in [[?
i] | i [less than or equal to] n> bijectively onto the hyperplanes of V that contain [[intersection].
Under some mild conditions, it is shown in Shao and Wu [21] that the proposed Criterion LS-C selects the true number of regression hyperplanes with probability one among all class-growing sequences of classifications, when the number of observations n from the population increases to infinity.
7] have used the supporting hyperplanes and efficient surfaces to calculate marginal rates of substitution in DEA.
If [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are adjacent facets of P incident to [upsilon], then the Euclidean dihedral angle between [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is equal to the hyperbolic dihedral angle between the supporting hyperplanes [B.
e] be the random variable that counts how many of the N hyperplanes separate the end-vertices of e.
The support vectors are training samples that define the optimal separating hyperplane and are the most difficult patterns to classify.
Thus, a way to reduce this task to SVM learning is to construct new instances for each pair of ranked instance in the training data, and to learn a hyperplane on this new training data.
The proposed approach consists in the dissection of extended disease region set with a pair of hyperplanes perpendicular to the direction vector of one dissecting class among other ones.
We want to choose the parameters w and b to maximize the margin, or distance between the parallel hyperplanes that are as far apart as possible while still separating the data.