Questions tagged [kd-tree]
8 questions
2
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1 answer
Kd-trees excluding some splitting dimensions
I have a 12-dimensional state-space and would like to use a kd-tree to partition my data, so that nearest neighbour operations can be performed quickly. Unfortunately I have the issue that three of the states are angular values which wrap-around…
Lord Cat
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Visualizing How of KD-tree Data Structure Splits Space
I am trying to understand how KD-tree works when we insert a node and how it splits the xy plane, please. Below $[5, 4]$ splits the xy-plane into left and right parts while $[2,6]$ splits it into top and bottom. Why don't we say that $[2,6]$ again…
Avv
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Adaptive kD-trees
In classical kD-trees, the splitting dimension is chosen using a simple and systematic rule: dimensions are taken in a round-robin fashion.
But extra freedom is available because you could very well choose the splitting dimension at will on every…
user16034
2
votes
1 answer
Lower bound for querying KD tree
In the book Computational Geometry, Algorithms and Applications there is an exercise asking:
In the proof of the query time of the kd-tree we found the following recurrence:
$$
Q(n)= \begin{cases}O(1), & \text { if } n=1, \\ 2+2 Q(n / 4), & \text {…
sn3jd3r
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How can a ball tree improve the efficiency of finding nearest neighbors when it involves finding least-near neighbors?
The motivation for k-d trees and ball trees is that k-nearest neighbors involves eliciting the distances between a particular data point and every other data point, which becomes inefficient as the number of data points grows large.
However, a step…
user10478
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1 answer
Fast construction of a static KD-tree without duplicates
From what I know, the classic way of constructing a KD-tree is with alternating dimensions and finding median at each level. In my dataset, I have a lot of duplicated points, and I want to incorporate the duplicates' filtering inside the creating of…
Valeria
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Rank of random binary string with Bernoulli distribution
For $1\ge p_1 \ge \dots \ge p_n \ge 0$, and for $i\in[n]$ draw $k$ iid binary strings with $m$ length:
$$X_{i,1},\dots,X_{i,k}\stackrel{iid}{\sim} \text{Bernoulli}(p_i)^m.$$
Viewing these binary strings as integers, define their ranks…
Ameer Jewdaki
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Find a bipartition of points using blackbox
Suppose given $n$ pair of points $P=\{(p_1,q_1),\dots,(p_n,q_n)\}$ in the plane that each pair $(p_i,q_i)\in \mathbb{R}^2$ can't belong to the same group. We want to partition points into $K$ groups such that we minimize function $f:x\rightarrow…
user146750