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A vantage-point tree (or VP tree) is a metric tree that segregates data in a metric space by choosing a position in the space (the "vantage point") and partitioning the data points into two parts: those points that are nearer to the vantage point than a threshold, and those points that are not.
VP-Tree (Vantage Point Tree) is a data structure that enables efficient nearest neighbor search in metric spaces, with applications in machine learning, computer vision, and information retrieval.
1 de jul. de 2022 · Vantage Point Trees are constructed by iteratively separating the data points based on their absolute distances from randomly picked centres (VPTs). These "Vantage Points" (VPs) divide the data into halves for each iteration, with half of the data falling inside a certain threshold and the other half falling outside of it.
Vantage-Point-trees (VPT) have been used in fewer applications than K-d trees and R-Trees, which have been in the areas such as image segmentation [14]. VPT are most advantageous for high dimensional data [26], where K-d trees and R-trees are known to degrade [22]. Recently, VPT have proven themselves useful in area of computer security [18, 2].
Vantage Point Tree: Construction 1. Select a vantage point v in X (eg. following a uniform distribution); 2. Compute the distances d(v, xi) between v and each point xi in X; V 3 Euclidean in this example but works with any metric respecting the triangle inequality!
A vp-tree is a binary tree in which each node T stores two values: an element ${x_{T}}\in \mathcal{X}$ called a vantage point and a threshold ${\tau _{T}}>0$. One of the most common ways to construct a vp-tree is to do this in a recursive manner from a sequence of elements ${x_{1}},{x_{2}},\dots \hspace{0.1667em}$ .
We prove that a sequence of sets, associated with the left boundary of a vantage-point tree, forms a recurrent Harris chain on the space of convex bodies in (ℝ d, ∥ ⋅ ∥) (\mathbb{R}^{d},\|\cdot\|) ( blackboard_R start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT , ∥ ⋅ ∥ ).
