Conic separation of finite sets:The homogeneous case

This work addresses the issue of separating two finite sets in $\mathbb{R}^n$ by means of a suitable revolution cone $$\Gamma (z,y,s)= \{x \in \mathbb{R}^n : s\,\Vert x-z\Vert – y^T(x-z)=0\}.$$ The specific challenge at hand is to determine the aperture coefficient $s$, the axis $y$, and the apex $z$ of the cone. These parameters … Read more

Conic separation of finite sets: The non-homogeneous case

We address the issue of separating two finite sets in $\mathbb{R}^n$ by means of a suitable revolution cone $$\Gamma (z,y,s)= \{x \in \mathbb{R}^n :\, s\,\Vert x-z\Vert – y^T(x-z)=0\}.$$ One has to select the aperture coefficient $s$, the axis $y$, and the apex $z$ in such a way as to meet certain optimal separation … Read more