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/*
* The MIT License
*
* Copyright 2015 Thibault Debatty.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
package info.debatty.java.lsh;
/**
*
* @author Thibault Debatty
*/
public class LSHMinHash extends LSH {
private final MinHash mh;
private static final double THRESHOLD = 0.5;
/**
* Instantiates a LSH instance that internally uses MinHash,
* with s stages (or bands) and b buckets (per stage), for sets out of a
* dictionary of n elements.
*
* Attention: the number of buckets should be chosen such that we have at
* least 100 items per bucket.
*
* @param s stages
* @param b buckets (per stage)
* @param n dictionary size
*/
public LSHMinHash(final int s, final int b, final int n) {
super(s, b);
int signature_size = computeSignatureSize(s, n);
this.mh = new MinHash(signature_size, n);
}
/**
* Instantiates a LSH instance that internally uses MinHash,
* with s stages (or bands) and b buckets (per stage), for sets out of a
* dictionary of n elements.
*
* Attention: the number of buckets should be chosen such that we have at
* least 100 items per bucket.
*
* @param s stages
* @param b buckets (per stage)
* @param n dictionary size
* @param seed random number generator seed. using the same value will
* guarantee identical hashes across object instantiations
*/
public LSHMinHash(final int s, final int b, final int n, final long seed) {
super(s, b);
int signature_size = computeSignatureSize(s, n);
this.mh = new MinHash(signature_size, n, seed);
}
/**
* Compute the size of the signature according to "Mining of Massive
* Datasets" p88.
* It can be shown that, using MinHash, the probability that the
* signatures of 2 sets with Jaccard similarity s agree in all the
* rows of at least one stage (band), and therefore become a candidate
* pair, is 1−(1−s^R)^b
* where R = signature_size / b (number of rows in a stage/band)
* Thus, the curve that shows the probability that 2 items fall in the
* same bucket for at least one of the stages, as a function of their
* Jaccard index similarity, has a S shape.
* The threshold (the value of similarity at which the probability of
* becoming a candidate is 1/2) is a function of the number of stages
* (s, or bands b in the book) and the signature size:
* threshold ≃ (1/s)^(1/R)
* Hence the signature size can be computed as:
* R = ln(1/s) / ln(threshold)
* signature_size = R * b
*/
private int computeSignatureSize(final int s, final int n) {
int r = (int) Math.ceil(Math.log(1.0 / s) / Math.log(THRESHOLD)) + 1;
return r * s;
}
/**
* Bin this vector to corresponding buckets.
* @param vector
* @return
*/
public final int[] hash(final boolean[] vector) {
return hashSignature(this.mh.signature(vector));
}
/**
* Get the coefficients used by internal hashing functions.
* @return
*/
public final long[][] getCoefficients() {
return mh.getCoefficients();
}
}
