Module 3: Hashing
  Lecture 11: Locality Sensitive Hashing and Grid File
 

                                            

 

 

kNN query
  • 1-NN query of has true answer
  • Applying 1-NN on l projections gives l collision sets:
 
  • 2,9,13:
 
  • 7,10,14:
 
  • 1,5,11:
 
  • 8,12,14:
  • Now majority counting gives
  • No guarantee of correct answer
  • Accuracy increases with more runs
  • It can be proved that is approximately distance preserving provided is so ( already is so!)
  • Therefore, this is a Monte Carlo algorithm
  • Time: where is the dimensionality (here, 3)
  • Extensions for Euclidean space: E2LSH