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近似近傍点探索手法 Locality Sensitive Hashing

( 最 ) 近傍点探索 ( Nearest Neighbor Search) とは ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

近傍点探索問題 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

近傍点探索アルゴリズム ,[object Object],[object Object],[object Object],[object Object],[object Object]

近傍点探索アルゴリズムの高速化 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Voronoi diagram From wikipedia http://ja.wikipedia.org/wiki/%E7%94%BB%E5%83%8F:Coloured_Voronoi_2D.png

近傍点探索アルゴリズムの高速化 ,[object Object],[object Object],[object Object],[object Object]

近似近傍点探索問題 ,[object Object],[object Object],[object Object],[object Object],[object Object]

近似近傍点探索問題の定義 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],本当は r 以内のものだけが欲しい！ crの中に含まれているものを列挙できれば最近傍も含む ||p-q||<rの点は得られる q r cr

Locality-Sensitive Hashing ,[object Object],[object Object],[object Object],[object Object],p q p∈P G = {g i : ℜd -> U} …… g1 …… g2 …… g3 …… g4 ….

LS-Hash 関数の定義 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

LSH アルゴリズム ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

LSH Hash Family ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

LSH Hash Family ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],ベクトル u は、正規乱数により生成された d 次元のベクトル

LSH Hash Family for l p norm ,[object Object],[object Object],[object Object],[object Object],[object Object]

LSH Hash Family for l p norm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

参考 ,[object Object],[object Object],[object Object]

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