Locality-sensitive hashing: Difference between revisions

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===Random Projection===
 
The random projection method of LSH is designed to approximate the [[cosine]] distance]] between vectors. The basic idea of this technique is to choose a random [[hyperplane]] (defined by a normal unit vector <math>r</math>) at the outset and use the hyperplane to hash input vectors.
 
Given an input vector <math>v</math> and a hyperplane defined by <math>r</math>, we let <math>h(v) = sgn(v \cdot r)</math>. That is, <math>h(v) = \pm 1</math> depending on which side of the hyperplane <math>v</math> lies.