V-detector algorithm generates candidate detectors randomly, in which the radius of a detector is dynamically resized until the boundary of the region comes in contact with the nearest hypersphere
of a self element.
After the initialization, every parameter [[theta].sub.i] will search within a small hypersphere
to find one parameter with the smallest error as its target [T.sub.i].
As illustrated in Figure 2, a XNN hypersphere
, formed by the K's nearest neighboring (XNN) points of [X.sub.i], is a cloud composed of Km-dimensional neighboring points around [X.sub.i].
Bao, "Radar HRRP statistical recognition based on hypersphere
model," Signal Processing, vol.
Whereas in a bulk universe, the event horizon of a four dimensional black hole would have to be three dimensional, known as a "hypersphere
A lot of discriminators which are suitable for corresponding features have been designed just like the generalized ratio test (GLRT) detector  and the hypersphere
support vector machine (HS-SVM) .
One of the most noteworthy depth-first techniques is the SE algorithm [26, 27], which restricts the search for the perturbation vector to the set of nodes with [D.sub.i][less than or equal to] R that lie within a hypersphere
of radius R centered around a reference signal.
Thus, at each iteration, the search for an optimum new point in the w space is restricted to a small hypersphere
centered at the point defined by the current vector w.
The fuzzy retractions of [[??].sup.4] model are the fuzzy unit hyperboloid, fuzzy hyperbolic, fuzzy hypersphere
, fuzzy circle, and fuzzy minimal manifolds.
In case of k-NN the procedure has a similarity with the previous one excepts for samples of the data system those classifier take [k.sub.n] and choose the furthest distance between around the [k.sub.n] nearest neighbor in a circle or in N-dimension (N characteristics) hypersphere
. If the volume of this hypersphere
estimates in a proper way the probability to belong class i with these samples is lower than a thershold, the data would not be inside this N-dimensional space, the opposite if this probability is higher.
is a map which carries M to the unit hypersphere
[S.sup.n] of [E.sup.n+1.] The Gauss map is a continuous map such that v(p)is a unitnormal vector [zeta](p) of M at p.
Another way to calculate dfactor depends on estimate the volume of the unit; assume the shape to be circle, sphere, or hypersphere
and we estimate the volume of the shape with radius equal max or avg; then divide the volume by the NumCore as indication to the unit density.