mas01mc@516: /*
mas01mc@516:  * MultiProbe C++ class
mas01mc@516:  *
mas01mc@518:  * Given a vector of LSH boundary distances for a query, 
mas01mc@518:  * 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@518: #ifndef __LSH_MULTIPROBE_
mas01mc@518: #define __LSH_MULTIPROBE_
mas01mc@518: 
mas01mc@516: #include <functional>
mas01mc@516: #include <queue>
mas01mc@516: #include <vector>
mas01mc@516: #include <set>
mas01mc@517: #include <algorithm>
mas01mc@517: #include <iostream>
mas01mc@516: 
mas01mc@518: using namespace std;
mas01mc@516: 
mas01mc@516: typedef set<int > perturbation_set ;
mas01mc@518: 
mas01mc@518: typedef class MinHeapElement{
mas01mc@518: public:
mas01mc@518:   perturbation_set perturbs;
mas01mc@519:   float score;
mas01mc@519:   MinHeapElement(perturbation_set a, float s);
mas01mc@518:   virtual ~MinHeapElement();
mas01mc@518: } min_heap_element;
mas01mc@518: 
mas01mc@518: typedef priority_queue<min_heap_element, 
mas01mc@518: 		       vector<min_heap_element>, 
mas01mc@518: 		       greater<min_heap_element> 
mas01mc@518: 		       > min_heap_of_perturbation_set ;
mas01mc@518: 
mas01mc@519: typedef pair<float, pair<int, int> > sorted_distance_functions ;
mas01mc@516: 
mas01mc@516: class MultiProbe{
mas01mc@516: protected:
mas01mc@516:   min_heap_of_perturbation_set* minHeap;
mas01mc@518:   min_heap_of_perturbation_set* outSets;
mas01mc@518:   vector<sorted_distance_functions>* distFuns;
mas01mc@517:   unsigned numHashBoundaries;
mas01mc@516: 
mas01mc@518:   // data structure initialization and cleanup
mas01mc@518:   void initialize();
mas01mc@518:   void cleanup();
mas01mc@518:   
mas01mc@516:   // perturbation set operations
mas01mc@517:   perturbation_set& shift(perturbation_set&);
mas01mc@517:   perturbation_set& expand(perturbation_set&);
mas01mc@519:   float score(perturbation_set&);
mas01mc@516:   bool valid(perturbation_set&);
mas01mc@519:   void makeSortedDistFuns(vector<float> &);
mas01mc@519:   void makeSortedDistFuns(float* x, unsigned N);
mas01mc@519: 
mas01mc@519:   // perturbation set generation algorithm
mas01mc@519:   void algorithm1(unsigned T);
mas01mc@518: 
mas01mc@518: public: 
mas01mc@518:   MultiProbe();
mas01mc@518:   ~MultiProbe();
mas01mc@516: 
mas01mc@516:   // generation of perturbation sets
mas01mc@519:   void generatePerturbationSets(vector<float>& vectorOfBounaryDistances, unsigned numSetsToGenerate);  
mas01mc@519:   void generatePerturbationSets(float* arrayOfBoundaryDistances, unsigned numDistances, unsigned numSetsToGenerate);
mas01mc@518:   perturbation_set getNextPerturbationSet();
mas01mc@518:   void dump(perturbation_set);
mas01mc@518:   size_t size(); // Number of perturbation sets are in the output queue
mas01mc@518:   bool empty(); // predicate for empty MultiProbe set
mas01mc@519:   int getIndex(perturbation_set::iterator it); // return index of hash function for given set entry
mas01mc@519:   int getBoundary(perturbation_set::iterator it); // return boundary {-1,+1} for given set entry
mas01mc@516: };
mas01mc@516: 
mas01mc@518: 
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:  */
mas01mc@518: 
mas01mc@518: #endif // __LSH_MULTIPROBE_