In this research paper, the concept of hyper-spherical/hyperellipsoidal separability is introduced. Method of arriving at the optimal hypersphere (maximizing margin) separating two classes is discussed. By projecting the quantized patterns into higher dimensional space (as in encoders of error correcting code), the patterns are made hyper-spherically separable. Single/multiple layers of spheric...

We introduce a novel representation for visibility in three dimensions and describe an efficient algorithm to construct it. The data structure is a spherical map that consists of a doubly–connected edge list embedded on the surface of a sphere. Each face of the spherical map is labeled with the polygon visible in the corresponding cone. We demonstrate that the algorithm is efficient and robust ...

In a previous paper we constructed some Haar wavelets on spherical triangulations, which are orthogonal with respect to a weighted inner product on L2(S2). We obtained two classes of wavelets which included certain wavelets obtained by Bonneau and Nielson et al. Each of these classes depended on two parameters which satisfied a relation. In this paper we study which of these wavelets are optima...

One of the main problems in pattern classification and neural network training theory is the generalization performance of learning. This paper extends the results on randomized linear zero empirical error (RLZEE) classifier obtained by Raudys, Dičiūnas and Basalykas for the case of centered multivariate spherical normal classes. We derive an exact formula for an expected probability of misclas...

The main concerned target of this article is to define and study some classes meromorphic function spaces using the general spherical derivatives. Besov-type functions as well normal are considered intensively both compared deeply with each other. Specifically, multiple results concerning meromorphic-type non-normal obtained by help proved constructing specific mild conditions on sequences poin...

Let X be a finite CW-complex. Denote by Sph(X) the abelian group of stable fibre-homotopy classes of spherical fibrations on X. Let F (n) be the monoid of self-homotopy-equivalences of S and let F := colimn→∞ F (n). The classifying space BF represents Sph(X), i.e. Sph(X) ∼= [X;BF ]. For any vector bundle ξ on X, let J(ξ) ∈ Sph(X) be the stable fibre homotopy class of the spherical fibration ξ \...

We construct classes of nonstationary wavelets generated by what we call spherical basis functions (SBFs), which comprise a subclass of Schoen-berg's positive deenite functions on the m-sphere. The wavelets are intrinsically deened on the m-sphere, and are independent of the choice of coordinate system. In addition, they may be orthogonalized easily, if desired. We will discuss decomposition, r...

Motivated by potential applications in architecture, we study Darboux cyclides. These algebraic surfaces of order ≤ 4 are a superset of Dupin cyclides and quadrics, and they carry up to six real families of circles. Revisiting the classical approach to these surfaces based on the spherical model of 3D Möbius geometry, we provide computational tools for the identificiation of circle families on ...