mas01mc@516: /*
mas01mc@516:  * MultiProbe C++ class
mas01mc@516:  *
mas01mc@516:  * Given a LSH structure, perform lookup by probing nearby hash-function locations
mas01mc@516:  *
mas01mc@516:  * Implementation using C++ STL
mas01mc@516:  *
mas01mc@516:  * Reference:
mas01mc@516:  * Qin Lv, William Josephson, Zhe Wang, Moses Charikar and Kai Li,
mas01mc@516:  * "Multi-Probe LSH: Efficient Indexing for High-Dimensional Similarity
mas01mc@516:  * Search", Proc. Intl. Conf. VLDB, 2007
mas01mc@516:  *
mas01mc@516:  *
mas01mc@516:  * Copyright (C) 2009 Michael Casey, Dartmouth College, All Rights Reserved
mas01mc@516:  * License: GNU Public License 2.0
mas01mc@516:  *
mas01mc@516:  */
mas01mc@516: 
mas01mc@516: #include <functional>
mas01mc@516: #include <queue>
mas01mc@516: #include <vector>
mas01mc@516: #include <set>
mas01mc@516: 
mas01mc@516: using namespace std ;
mas01mc@516: 
mas01mc@516: typedef set<int > perturbation_set ;
mas01mc@516: typedef vector<perturbation_set > vector_of_perturbation_set ;
mas01mc@516: typedef pair<perturbation_set, float > min_heap_element ;
mas01mc@516: typedef vector<min_heap_element > vector_of_min_heap_element ;
mas01mc@516: typedef priority_queue<
mas01mc@516:   min_heap_element, 
mas01mc@516:   vector_of_min_heap_element, 
mas01mc@516:   greater<min_heap_element> 
mas01mc@516:   > min_heap_of_perturbation_set ;
mas01mc@516: typedef pair<double, pair<int, int> > sorted_distance_functions ;
mas01mc@516: 
mas01mc@516: bool operator>(const min_heap_element& a, const min_heap_element& b){
mas01mc@516:   return a.second > b.second;
mas01mc@516: }
mas01mc@516: 
mas01mc@516: bool operator<(const min_heap_element& a, const min_heap_element& b){
mas01mc@516:   return a.second < b.second;
mas01mc@516: }
mas01mc@516: 
mas01mc@516: bool operator>(const sorted_distance_functions& a, const sorted_distance_functions& b){
mas01mc@516:   return a.second > b.second;
mas01mc@516: }
mas01mc@516: 
mas01mc@516: bool operator<(const sorted_distance_functions& a, const sorted_distance_functions& b){
mas01mc@516:   return a.second < b.second;
mas01mc@516: }
mas01mc@516: 
mas01mc@516: class MultiProbe{
mas01mc@516: protected:
mas01mc@516:   min_heap_of_perturbation_set* minHeap;
mas01mc@516:   vector_of_perturbation_set* outSets;
mas01mc@516:   sorted_distance_functions distFuns;
mas01mc@516: public: 
mas01mc@516:   MultiProbe();
mas01mc@516:   ~MultiProbe();
mas01mc@516: 
mas01mc@516:   // perturbation set operations
mas01mc@516:   perturbation_set& shift(perturbation_set);
mas01mc@516:   perturbation_set& expand(perturbation_set);
mas01mc@516:   double score(perturbation_set&);
mas01mc@516:   bool valid(perturbation_set&);
mas01mc@516: 
mas01mc@516:   // generation of perturbation sets
mas01mc@516:   void generatePerturbationSets(int, vector<int>&);
mas01mc@516:   sorted_distance_functions& makeSortedDistFuns(vector<int> &);
mas01mc@516: };
mas01mc@516: 
mas01mc@516: /* NOTES:
mas01mc@516: 
mas01mc@516: Reference:
mas01mc@516: Qin Lv, William Josephson, Zhe Wang, Moses Charikar and Kai Li,
mas01mc@516: "Multi-Probe LSH: Efficient Indexing for High-Dimensional Similarity
mas01mc@516: Search", Proc. Intl. Conf. VLDB, 2007
mas01mc@516: 
mas01mc@516:   i = 1..M (number of hash functions used)
mas01mc@516:   f_i(q) = a_i * q + b_i // projection to real line
mas01mc@516:   h_i(q) = floor( ( a_i * q + b_i ) / w ) // hash slot  
mas01mc@516:   delta \in {-1, +1}
mas01mc@516:   x_i( delta ) = distance of query to left or right boundary
mas01mc@516:   Delta = [delta_1 delta_2 ... delta_M]
mas01mc@516:   score(Delta) = sum_{i=1}_M x_i(delta_i).^2
mas01mc@516:   
mas01mc@516:   z = sort(x(delta_i), increasing) // i = 1..2M delta={+1,-1}
mas01mc@516:   p_j = (i, delta) if z_j == x_i(delta) 
mas01mc@516:   
mas01mc@516:   A_k is index into p_j
mas01mc@516: 
mas01mc@516:   Multi-probe algorithm (after Lv et al. 2007)
mas01mc@516:   ---------------------------------------------
mas01mc@516: 
mas01mc@516:   A0 = {1}
mas01mc@516:   minHeap.insert(A0, score(A0))
mas01mc@516:   
mas01mc@516:   for i = 1 to T do   // T = number of perturbation sets
mas01mc@516:      repeat
mas01mc@516:         Ai = minHeap.extractMin()
mas01mc@516: 	As = shift(Ai)
mas01mc@516: 	minHeap.insert(As, score(As))
mas01mc@516: 	Ae = expand(Ai)
mas01mc@516: 	minHeap.insert(Ae, score(Ae))
mas01mc@516:      until valid(Ai)
mas01mc@516:      output Ai
mas01mc@516:   end for
mas01mc@516: 
mas01mc@516:  */