Probabilistic analysis of vantage point trees

Abstract

Probabilistic properties of vantage point trees are studied. A vp-tree built from a sequence of independent identically distributed points in ${[-1,\hspace{0.1667em}1]^{d}}$ with the ${\ell _{\infty }}$-distance function is considered. The length of the leftmost path in the tree, as well as partitions over the space it produces are analyzed. The results include several convergence theorems regarding these characteristics, as the number of nodes in the tree tends to infinity.

Keywords

• Fixed-point equation
• machine learning
• Markov chain
• nearest neighbor search
• probabilistic analysis
• random tree