Postnikov and Stanley  introduced the idea of a deformation of the Coxeter arrangement--this is an affine arrangement each of whose hyperplanes
is parallel to some hyperplane
of the Coxeter arrangement.
The support vectors are training samples that define the optimal separating hyperplane
and are the most difficult patterns to classify.
Detection of extended-distributed images of the patient cardiovascular system by a pair of parallel hyperplanes
where w is a normal vector, x is a data point, "*" is the dot product between two vectors, and b / [absolute value of w] is the offset of the hyperplane
a vector whose Euclidian length is very small that is not contained in a hyperplane
generated by a sublist of X.
They consider such topics as vanishing products of one-forms and critical points of master functions, middle convolution for completely integrable systems with logarithmic singularities along hyperplane
arrangements, resonance webs of hyperplane
arrangements, the homology of configuration spaces associated to centers of mass, and varieties of lines on Fermat hypersurfaces.
The primal problems for finding these two hyperplanes
are two convex quadratic programming problems (Shao et al.
In order to compute the parameters of these hyperplanes
, a set of functions from [R.
A support vector machine in a high dimensional space, is used to construct a hyperplane
or a set of hyperplanes
which can be used for classification, regression or other tasks.
To obtain this dual cell complex, one has to "cut up" the manifold using (N-1)-dimensionai hyperplanes
normal to [M.
4] (y), whose metric tensor [eta] is Minkowskian, such that an ensemble of Minkowskian tangent hyperplanes
, that is,
For example, space-like hyperplanes
, Lorentzian hyperplanes
, hyperbolic spaces [H.