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・ Ballad opera
・ Ballad stanza
・ Ballad Zulu
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・ Ballada o Januszku
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・ Ballade in the Form of Variations on a Norwegian Folk Song
・ Ballade No. 1 (Liszt)
・ Ballade No. 2 (Liszt)
・ Ball Trap on the Cote Sauvage
Ball tree
・ Ball turret
・ Ball v. United States
・ Ball valve
・ Ball washer
・ BALL Watch Company
・ Ball's Bluff Battlefield and National Cemetery
・ Ball's Bluff Confederate order of battle
・ Ball's Bluff order of battle
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・ Ball's Falls, Ontario
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Ball tree : ウィキペディア英語版
Ball tree

In computer science, a ball tree, balltree or metric tree, is a space partitioning data structure for organizing points in a multi-dimensional space. The ball tree gets its name from the fact that it partitions data points into a nested set of hyperspheres known as "balls". The resulting data structure has characteristics that make it useful for a number of applications, most notably nearest neighbor search.
== Informal description ==
A ball tree is a binary tree in which every node defines a D-dimensional hypersphere, or ball, containing a subset of the points to be searched. Each internal node of the tree partitions the data points into two disjoint sets which are associated with different balls. While the balls themselves may intersect, each point is assigned to one or the other ball in the partition according to its distance from the ball's center. Each leaf node in the tree defines a ball and enumerates all data points inside that ball.
Each node in the tree defines the smallest ball that contains all data points in its subtree. This gives rise to the useful property that, for a given test point ''t'', the distance to any point in a ball ''B'' in the tree is greater than or equal to the distance from t to the ball. Formally:


D^(t) =
\begin
max(|t - B.pivot| - B.radius, D^),
& \textNode \neq Root \\
max(|t - B.pivot| - B.radius, 0),
& \textB = Root \\
\end

Where D^(t) is the minimum possible distance from any point in the ball ''B'' to some point ''t''.
Ball-trees are related to the M-tree, but only support binary splits, whereas in the M-tree each level splits m to 2m fold, thus leading to a less deep tree structure. The M-tree also keeps the distances from the parent node precomputed to speed up queries.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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