We generalize the Tukey depth to use cones instead of halfspaces. We prove a generalization of the center point theorem that for S ⊂ R2, there is a point s ∈S, with depth at least n/d+1 for cones of half-angle 45◦. This gives a notion of data depth for which an approximate median can always be found among the original set
The concept of location depth was introduced as a way to extend the univariate notion of ranking to ...
We show that, for any set of n points in d dimensions, there exists a hyperplane with regression dep...
AbstractUsing a technique that Tverberg and Vrecica (1993) [16] discovered to give a surprisingly si...
We generalize the Tukey depth to use cones instead of halfspaces. We prove a generalization of the c...
GeneralThe Centerpoint Theorem states that, for any set S of n points in R(d), there exists a point ...
The centerpoint theorem is a well-known and widely used result in discrete geometry. It states that ...
In 2008, Bukh, Matoušek, and Nivasch conjectured that for every n-point set S in ℝd and every k, 0 ≤...
Determining the representativeness of a point within a data cloud has recently become a desirable ta...
At the core of successful manipulation and computation over large geometric data is the notion of ap...
We prove an optimal generalization of the centerpoint theorem: given a set P of n points in the pla...
Oja depth (Oja 1983) is a generalization of the median to multivariate data that measures the centra...
In this thesis we introduce the halfspace median, which is one of the possibilities how to extend th...
Given a set P = {p1,..., pn} of points and a point q in the plane, we define a function ψ(q) that pr...
In this note we investigate a problem formulated by Pleijel in 1955. It asks for the cone over a con...
The concept of location depth was introduced as a way to extend the univariate notion of ranking to ...
The concept of location depth was introduced as a way to extend the univariate notion of ranking to ...
We show that, for any set of n points in d dimensions, there exists a hyperplane with regression dep...
AbstractUsing a technique that Tverberg and Vrecica (1993) [16] discovered to give a surprisingly si...
We generalize the Tukey depth to use cones instead of halfspaces. We prove a generalization of the c...
GeneralThe Centerpoint Theorem states that, for any set S of n points in R(d), there exists a point ...
The centerpoint theorem is a well-known and widely used result in discrete geometry. It states that ...
In 2008, Bukh, Matoušek, and Nivasch conjectured that for every n-point set S in ℝd and every k, 0 ≤...
Determining the representativeness of a point within a data cloud has recently become a desirable ta...
At the core of successful manipulation and computation over large geometric data is the notion of ap...
We prove an optimal generalization of the centerpoint theorem: given a set P of n points in the pla...
Oja depth (Oja 1983) is a generalization of the median to multivariate data that measures the centra...
In this thesis we introduce the halfspace median, which is one of the possibilities how to extend th...
Given a set P = {p1,..., pn} of points and a point q in the plane, we define a function ψ(q) that pr...
In this note we investigate a problem formulated by Pleijel in 1955. It asks for the cone over a con...
The concept of location depth was introduced as a way to extend the univariate notion of ranking to ...
The concept of location depth was introduced as a way to extend the univariate notion of ranking to ...
We show that, for any set of n points in d dimensions, there exists a hyperplane with regression dep...
AbstractUsing a technique that Tverberg and Vrecica (1993) [16] discovered to give a surprisingly si...
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