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Halfspace depth and $\beta$-skeleton depth are two types of depth functions in nonparametric data analysis. The halfspace depth of a query point $q\in \mathbb{R}^d$ with respect to $S\subset\mathbb{R}^d$ is the minimum portion of the elements of $S$ which are contained in a halfspace which passes through $q$. For $\beta \geq 1$, the $\beta$-skeleto...
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Context 1
... 2/n is the normalization factor 1 , H is the class of all closed halfspaces in R d that pass through q, and |S ∩ H| denotes the number of points within the intersection of S and H. As illustrated in Figure 1, HD(q 1 ; S) = 6/13 and HD(q 1 ; S) = 0, where S a given set of points in the plane and q 1 , q 2 are two query points not in S. 3 β-skeleton Depth Definition: For 1 ≤ β ≤ ∞, the β-skeleton influence region of x i and x j (S β (x i , x j )) is defined as follows: ...
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