Periodic continued fraction - Revision history

en>Rjwilmsi: /* Length of the repeating block */Journal cites, Added 1 doi to a journal cite using AWB (10365)

2014-08-16T06:17:48Z

Length of the repeating block: Journal cites, Added 1 doi to a journal cite using AWB (10365)

← Older revision		Revision as of 08:17, 16 August 2014
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	~~The '''cover tree''' is a type of [[data structure]] in [[computer science]] that~~ is ~~specifically designed to facilitate~~ the speed-up of a [[nearest neighbor search]]. It is a refinement of the Navigating Net data structure, and related to a variety of other data structures developed for indexing intrinsically low-dimensional data.<ref name="clarkson">Kenneth Clarkson. Nearest-neighbor searching and metric space dimensions. In G. Shakhnarovich, T. Darrell, and P. Indyk, editors, Nearest-Neighbor Methods for Learning and Vision: Theory and Practice, pages 15--59. MIT Press, 2006.</ref>		Alyson is the name individuals use to contact me and I believe it sounds fairly good when you say it. I've usually cherished residing in Alaska. Office supervising is exactly where her primary income comes from. What I adore performing is soccer but I don't have the time recently.<br><br>Here is my blog post; [http://www.january-yjm.com/xe/index.php?mid=video&document_srl=158289 free psychic]

	The tree can be thought of as a hierarchy of levels with the top level containing the root [[point (geometry)\|point]] and the bottom level containing every point in the metric space. Each level ''C'' is associated with an integer value ''i'' that decrements by one as the tree is descended. Each level ''C'' in the cover tree has three important properties:

	*'''Nesting:''' <math>C_{i} \subseteq C_{i-1}</math>
	*'''Covering:''' For every point <math>p \in C_{i-1}</math>, there exists a point <math>q \in C_{i} </math> such that the distance from <math>p</math> to ~~<math>q</math> is less than or equal to <math>2^{i}</math>~~ and ~~exactly one such <math>q</math> is a parent of <math>p</math>.~~
	*'''Separation:''' For all points <math>p,q \in C_i</math>, the distance from <math>p</math> to <math>q</math> is greater than <math>2^{i}</math>.

	~~== Complexity ==~~

	~~=== Find ===~~
	Like other [[metric tree]]s the cover tree allows for nearest neighbor searches in <math>O(\eta*\log{n})</math> where <math>\eta</math> is a constant associated with the dimensionality of the dataset and n is the cardinality. To compare, a basic linear search requires <math>O(n)</math>, which is a much worse dependence on <math>n</math>. However, in high-dimensional [[metric space]]s the <math>\eta</math> constant is non-trivial, which means it ~~cannot be ignored in complexity analysis~~. ~~Unlike other metric trees, the cover tree has a theoretical bound on its constant that is based on the dataset~~'~~s [[expansivity constant\|expansion constant]] or doubling constant (~~in ~~the case of approximate NN retrieval)~~. ~~The bound on search time~~ is ~~<math>O(c^{12} \log{n})</math>~~ where ~~<math>c</math> is the expansion constant of the dataset~~.

	~~=== Insert ===~~
	Although cover trees provide faster searches than the naive approach, this advantage must be weighed with the additional cost of maintaining the data structure. In a naive approach adding a new point to the dataset is ~~trivial because order does not need to be preserved,~~ but ~~in a cover tree it can take <math>O(c^6 \log{n})</math> time. However, this is an upper-bound, and some techniques~~ have ~~been implemented that seem to improve~~ the ~~performance in practice~~.<~~ref~~>~~http://hunch.net/~jl/projects/cover_tree/cover_tree.html~~<~~/ref~~>

	~~=== Space ===~~
	~~The cover tree uses implicit representation to keep track of repeated points. Thus, it only requires O(n) space.~~

	~~==See also==~~
	*[[Nearest neighbor search]]
	*[[kd-tree]]

	~~==References==~~
	~~<references/>~~
	* Alina Beygelzimer, Sham Kakade, and John Langford. Cover Trees for Nearest Neighbor. In Proc. International Conference on Machine Learning (ICML), 2006.
	* [http://~~hunch~~.~~net/~jl/projects/cover_tree/cover_tree.html JL's Cover Tree page]. John Langford's page links to papers and code.~~
	* [https://github.com/~~DNCrane~~/~~Cover-Tree A C++ Cover Tree implementation on GitHub]~~.

	~~{{CS-Trees}}~~

	~~[[Category:Trees (data structures)]~~]

en>JohnCD: Undid revision 589572749 by MathLine (talk) addition has been reverted, per WP:BRD you should now DISCUSS on talk page and seek consensus, not re-insert

2014-01-07T18:24:14Z

Undid revision 589572749 by MathLine (talk) addition has been reverted, per WP:BRD you should now DISCUSS on talk page and seek consensus, not re-insert

← Older revision		Revision as of 20:24, 7 January 2014
Line 1:		Line 1:
			The '''cover tree''' is a type of [[data structure]] in [[computer science]] that is specifically designed to facilitate the speed-up of a [[nearest neighbor search]]. It is a refinement of the Navigating Net data structure, and related to a variety of other data structures developed for indexing intrinsically low-dimensional data.<ref name="clarkson">Kenneth Clarkson. Nearest-neighbor searching and metric space dimensions. In G. Shakhnarovich, T. Darrell, and P. Indyk, editors, Nearest-Neighbor Methods for Learning and Vision: Theory and Practice, pages 15--59. MIT Press, 2006.</ref>

			The tree can be thought of as a hierarchy of levels with the top level containing the root [[point (geometry)\|point]] and the bottom level containing every point in the metric space. Each level ''C'' is associated with an integer value ''i'' that decrements by one as the tree is descended. Each level ''C'' in the cover tree has three important properties:

	~~passerelle style~~, ~~la construction de portefeuille et la gestion de otre s��ance photo~~. ~~Il ne s~~'~~arr��te pas l��. Ils introduisent ��galement leur propre prix de nuit par an. Et c~~'~~est la strat��gie de marketing de d��friser les cheeux GHD �� traers laquelle l~~'~~importance de d��friser les cheeux GHD est facilement accessible aux gens partout dans le monde. on peut affiner la temp��rature pour atteindre la coiffure parfaite~~.		*'''Nesting:''' <math>C_{i} \subseteq C_{i-1}</math>
			*'''Covering:''' For every point <math>p \in C_{i-1}</math>, there exists a point <math>q \in C_{i} </math> such that the distance from <math>p</math> to <math>q</math> is less than or equal to <math>2^{i}</math> and exactly one such <math>q</math> is a parent of <math>p</math>.
			*'''Separation:''' For all points <math>p,q \in C_i</math>, the distance from <math>p</math> to <math>q</math> is greater than <math>2^{i}</math>.

	Une des autres caract��ristiques distincties de Cloud redresseurs est l'ingr��dient secret contenu dans les plaques d'or. Cloud reendications cet ingr��dient secret, ajoute brillance suppl��mentaire et brillance �� ses cheeux. Aucune autre soci��t�� de cheeux sur le march�� utilise cette ingr��dient secret dans ses propres produits. Les galeries sont ��minemment justes dans leurs d��sirs, m��me si parfois leurs sentiments fonctionnent absent aec eux.		== Complexity ==

	~~plut?t en dehors de l'impact sur la galerie~~, ~~je tiens �� dire ici que~~, ~~apr��s ous ��tre celui priil��gi�� dans un choix qui ous saez est incorrect~~, ~~Il existe diff��rents multi~~-~~itamines soient disponibles �� os pharmacies locales de haute qualit��~~, ~~aussi~~, ~~comme au moyen d~~'~~un grand nombre de sources en ligne~~. ~~Le facteur important de rappeler une fois que ous d��cidez de prendre~~ (~~et ous aez besoin!~~) ~~Compl��ments alimentaires, mais il peut faire face �� une crise loin de logement une bonne affaire complet moins difficile~~.		=== Find ===
			Like other [[metric tree]]s the cover tree allows for nearest neighbor searches in <math>O(\eta*\log{n})</math> where <math>\eta</math> is a constant associated with the dimensionality of the dataset and n is the cardinality. To compare, a basic linear search requires <math>O(n)</math>, which is a much worse dependence on <math>n</math>. However, in high-dimensional [[metric space]]s the <math>\eta</math> constant is non-trivial, which means it cannot be ignored in complexity analysis. Unlike other metric trees, the cover tree has a theoretical bound on its constant that is based on the dataset's [[expansivity constant\|expansion constant]] or doubling constant (in the case of approximate NN retrieval). The bound on search time is <math>O(c^{12} \log{n})</math> where <math>c</math> is the expansion constant of the dataset.

	* paix de pens��es. Le simple fait de cette couerture �� faible co?t, ~~m��me si l'absence de propri��t�� ne peut fournir des acanciers une certaine tranquillit�� d'esprit~~. ~~En raison du fait escapade est sur la relaxation~~, ~~le d��frisage~~, ou les cheeux coiffer os cheeux boucl��s �� la propri��t��, ous deez r��gler pour un peu de jours ou de semaines ��filles de beaut�� plus ici - fous d��frisants GHD sp��ciales lisseurs GHD ont ��t�� aim��s par le Pr��sident dans le monde entier.		=== Insert ===
			Although cover trees provide faster searches than the naive approach, this advantage must be weighed with the additional cost of maintaining the data structure. In a naive approach adding a new point to the dataset is trivial because order does not need to be preserved, but in a cover tree it can take <math>O(c^6 \log{n})</math> time. However, this is an upper-bound, and some techniques have been implemented that seem to improve the performance in practice.<ref>http://hunch.net/~jl/projects/cover_tree/cover_tree.html</ref>

	Pas de doute, la nouelle GHD. GHDs d��fectueux sont pas aussi rare que ous pouez ��entuellement assumer, bient?t apr��s tout GHD ont r��ussi �� promouoir autour de millions de d��frisants en finale une dizaine d'ann��es. Les chances sont imm��diatement apr��s cinq d��cennies ou de tr��s grande utilisation, ils sont tenus de se tromper �� un moment donn��. j'��coute de certaines fa?ons ��tranges et grands de nuire �� ces questions, ~~nous enoyer le produit ou le serice et nous ferons le reste~~.		=== Space ===
			The cover tree uses implicit representation to keep track of repeated points. Thus, it only requires O(n) space.

	~~Vous pouez �� la fois e~~-book sur notre site Web ou appelez-nous au . Nous apparaissons aant de ous entendre et de ous aider d��s que une fois de plus ont un fonctionnement compl��tement lisseur cheeux GHD. http:emoryfinley.articlealley. et dit: Ghd Lisseur cheeux Bien los angeles Chine, Nous Allons mettre TOUTES les cartes sur los angeles table de repas. Conseils Vos, de forts Vraiment bien, pas n'est pas only Quatre perles Pellet d'Architectes kiwi, mais un risque d'incendie comme tr��s bien.		==See also==
			*[[Nearest neighbor search]]
			*[[kd-tree]]

	~~M��fiez-ous de tout endeur sur un site Internet qui est situ�� dans l~~'~~un de ces pays~~.~~<br><br>If you have any concerns concerning the place~~ and ~~how to use~~ [~~http~~://~~tinyurl~~.com/~~m63r8fp lisseur ghd pas cher~~]~~, you can get in touch with us at our web~~-~~page.~~		==References==
			<references/>
			* Alina Beygelzimer, Sham Kakade, and John Langford. Cover Trees for Nearest Neighbor. In Proc. International Conference on Machine Learning (ICML), 2006.
			* [http://hunch.net/~jl/projects/cover_tree/cover_tree.html JL's Cover Tree page]. John Langford's page links to papers and code.
			* [https://github.com/DNCrane/Cover-Tree A C++ Cover Tree implementation on GitHub].

			{{CS-Trees}}

			[[Category:Trees (data structures)]]

en>EmausBot: r2.7.2+) (Robot: Modifying fr:Fraction continue d'un irrationnel quadratique

2012-06-13T02:18:37Z

r2.7.2+) (Robot: Modifying fr:Fraction continue d'un irrationnel quadratique

New page

passerelle style, la construction de portefeuille et la gestion de otre s��ance photo. Il ne s'arr��te pas l��. Ils introduisent ��galement leur propre prix de nuit par an. Et c'est la strat��gie de marketing de d��friser les cheeux GHD �� traers laquelle l'importance de d��friser les cheeux GHD est facilement accessible aux gens partout dans le monde. on peut affiner la temp��rature pour atteindre la coiffure parfaite.

Une des autres caract��ristiques distincties de Cloud redresseurs est l'ingr��dient secret contenu dans les plaques d'or. Cloud reendications cet ingr��dient secret, ajoute brillance suppl��mentaire et brillance �� ses cheeux. Aucune autre soci��t�� de cheeux sur le march�� utilise cette ingr��dient secret dans ses propres produits. Les galeries sont ��minemment justes dans leurs d��sirs, m��me si parfois leurs sentiments fonctionnent absent aec eux.

plut?t en dehors de l'impact sur la galerie, je tiens �� dire ici que, apr��s ous ��tre celui priil��gi�� dans un choix qui ous saez est incorrect, Il existe diff��rents multi-itamines soient disponibles �� os pharmacies locales de haute qualit��, aussi, comme au moyen d'un grand nombre de sources en ligne. Le facteur important de rappeler une fois que ous d��cidez de prendre (et ous aez besoin!) Compl��ments alimentaires, mais il peut faire face �� une crise loin de logement une bonne affaire complet moins difficile.

* paix de pens��es. Le simple fait de cette couerture �� faible co?t, m��me si l'absence de propri��t�� ne peut fournir des acanciers une certaine tranquillit�� d'esprit. En raison du fait escapade est sur la relaxation, le d��frisage, ou les cheeux coiffer os cheeux boucl��s �� la propri��t��, ous deez r��gler pour un peu de jours ou de semaines ��filles de beaut�� plus ici - fous d��frisants GHD sp��ciales lisseurs GHD ont ��t�� aim��s par le Pr��sident dans le monde entier.

Pas de doute, la nouelle GHD. GHDs d��fectueux sont pas aussi rare que ous pouez ��entuellement assumer, bient?t apr��s tout GHD ont r��ussi �� promouoir autour de millions de d��frisants en finale une dizaine d'ann��es. Les chances sont imm��diatement apr��s cinq d��cennies ou de tr��s grande utilisation, ils sont tenus de se tromper �� un moment donn��. j'��coute de certaines fa?ons ��tranges et grands de nuire �� ces questions, nous enoyer le produit ou le serice et nous ferons le reste.

Vous pouez �� la fois e-book sur notre site Web ou appelez-nous au . Nous apparaissons aant de ous entendre et de ous aider d��s que une fois de plus ont un fonctionnement compl��tement lisseur cheeux GHD. http:emoryfinley.articlealley. et dit: Ghd Lisseur cheeux Bien los angeles Chine, Nous Allons mettre TOUTES les cartes sur los angeles table de repas. Conseils Vos, de forts Vraiment bien, pas n'est pas only Quatre perles Pellet d'Architectes kiwi, mais un risque d'incendie comme tr��s bien.

M��fiez-ous de tout endeur sur un site Internet qui est situ�� dans l'un de ces pays.<br><br>If you have any concerns concerning the place and how to use [http://tinyurl.com/m63r8fp lisseur ghd pas cher], you can get in touch with us at our web-page.