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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;
import info.debatty.java.utils.SparseDoubleVector;
import info.debatty.java.utils.SparseIntegerVector;
import java.io.Serializable;
import java.util.Random;
/**
* Implementation of Super-Bit Locality-Sensitive Hashing.
* Super-Bit is an improvement of Random Projection LSH.
* It computes an estimation of cosine similarity.
*
* Super-Bit Locality-Sensitive Hashing
* Jianqiu Ji, Jianmin Li, Shuicheng Yan, Bo Zhang, Qi Tian
* http://papers.nips.cc/paper/4847-super-bit-locality-sensitive-hashing.pdf
* Advances in Neural Information Processing Systems 25, 2012
*
* Supported input types:
* - SparseIntegerVector
* - double[]
* - others to come...
*
* @author Thibault Debatty
*/
public class SuperBit implements Serializable {
private double[][] hyperplanes;
private static final int DEFAULT_CODE_LENGTH = 10000;
/**
* Initialize SuperBit algorithm.
* Super-Bit depth n must be [1 .. d] and number of Super-Bit l in [1 ..
* The resulting code length k = n * l
* The K vectors are orthogonalized in L batches of N vectors
*
* @param d data space dimension
* @param n Super-Bit depth [1 .. d]
* @param l number of Super-Bit [1 ..
*/
public SuperBit(final int d, final int n, final int l) {
this(d, n, l, new Random());
}
/**
* Initialize SuperBit algorithm.
* Super-Bit depth n must be [1 .. d] and number of Super-Bit l in [1 ..
* The resulting code length k = n * l
* The K vectors are orthogonalized in L batches of N vectors
*
* @param d data space dimension
* @param n Super-Bit depth [1 .. d]
* @param l number of Super-Bit [1 ..
* @param seed to use for the random number generator
*/
public SuperBit(final int d, final int n, final int l, final long seed) {
this(d, n, l, new Random(seed));
}
private SuperBit(final int d, final int n, final int l, final Random rand) {
if (d <= 0) {
throw new IllegalArgumentException("Dimension d must be >= 1");
}
if (n < 1 || n > d) {
throw new IllegalArgumentException(
"Super-Bit depth N must be 1 <= N <= d");
}
if (l < 1) {
throw new IllegalArgumentException(
"Number of Super-Bit L must be >= 1");
}
// Input: Data space dimension d, Super-Bit depth 1 <= N <= d,
// number of Super-Bit L >= 1,
// resulting code length K = N * L
// Generate a random matrix H with each element sampled independently
// from the normal distribution
// N (0, 1), with each column normalized to unit length.
// Denote H = [v1, v2, ..., vK].
int code_length = n * l;
double[][] v = new double[code_length][d];
for (int i = 0; i < code_length; i++) {
double[] vector = new double[d];
for (int j = 0; j < d; j++) {
vector[j] = rand.nextGaussian();
}
normalize(vector);
v[i] = vector;
}
// for i = 0 to L - 1 do
// for j = 1 to N do
// w_{iN+j} = v_{iN+j}
// for k = 1 to j - 1 do
// w_{iN+j} = w_{iN+j} - w_{iN+k} w^T_{iN+k} v_{iN+j}
// end for
// wiN+j = wiN+j / | wiN+j |
// end for
// end for
// Output: H˜ = [w1, w2, ..., wK]
double[][] w = new double[code_length][d];
for (int i = 0; i <= l - 1; i++) {
for (int j = 1; j <= n; j++) {
java.lang.System.arraycopy(
v[i * n + j - 1],
0,
w[i * n + j - 1],
0,
d);
for (int k = 1; k <= (j - 1); k++) {
w[i * n + j - 1] = sub(
w[i * n + j - 1],
product(
dotProduct(
w[i * n + k - 1],
v[ i * n + j - 1]),
w[i * n + k - 1]));
}
normalize(w[i * n + j - 1]);
}
}
this.hyperplanes = w;
}
/**
* Initialize SuperBit algorithm.
* With code length K = 10000
* The K vectors are orthogonalized in d batches of 10000/d vectors
* The resulting mean error is 0.01
* @param d
*/
public SuperBit(final int d) {
this(d, d, DEFAULT_CODE_LENGTH / d);
}
/**
* Initialize SuperBit algorithm without parameters
* (used only for serialization).
*/
public SuperBit() {
}
/**
* Compute the signature of this vector.
* @param vector
* @return
*/
public final boolean[] signature(final SparseIntegerVector vector) {
boolean[] sig = new boolean[this.hyperplanes.length];
for (int i = 0; i < this.hyperplanes.length; i++) {
sig[i] = (vector.dotProduct(this.hyperplanes[i]) >= 0);
}
return sig;
}
/**
* Compute the signature of this vector.
* @param vector
* @return
*/
public final boolean[] signature(final SparseDoubleVector vector) {
boolean[] sig = new boolean[this.hyperplanes.length];
for (int i = 0; i < this.hyperplanes.length; i++) {
sig[i] = (vector.dotProduct(this.hyperplanes[i]) >= 0);
}
return sig;
}
/**
* Compute the signature of this vector.
* @param vector
* @return
*/
public final boolean[] signature(final double[] vector) {
boolean[] sig = new boolean[this.hyperplanes.length];
for (int i = 0; i < this.hyperplanes.length; i++) {
sig[i] = (dotProduct(this.hyperplanes[i], vector) >= 0);
}
return sig;
}
/**
* Compute the similarity between two signature, which is also an
* estimation of the cosine similarity between the two vectors.
*
* @param sig1
* @param sig2
* @return estimated cosine similarity
*/
public final double similarity(final boolean[] sig1, final boolean[] sig2) {
double agg = 0;
for (int i = 0; i < sig1.length; i++) {
if (sig1[i] == sig2[i]) {
agg++;
}
}
agg = agg / sig1.length;
return Math.cos((1 - agg) * Math.PI);
}
/**
* Get the hyperplanes coefficients used to compute signatures.
* @return
*/
public final double[][] getHyperplanes() {
return this.hyperplanes;
}
/* ---------------------- STATIC ---------------------- */
/**
* Computes the cosine similarity, computed as v1 dot v2 / (|v1| * |v2|).
* Cosine similarity of two vectors is the cosine of the angle between them.
* It ranges between -1 and +1
*
* @param v1
* @param v2
* @return
*/
public static double cosineSimilarity(final double[]v1, final double[] v2) {
return dotProduct(v1, v2) / (norm(v1) * norm(v2));
}
private static double[] product(final double x, final double[] v) {
double[] r = new double[v.length];
for (int i = 0; i < v.length; i++) {
r[i] = x * v[i];
}
return r;
}
private static double[] sub(final double[] a, final double[] b) {
double[] r = new double[a.length];
for (int i = 0; i < a.length; i++) {
r[i] = a[i] - b[i];
}
return r;
}
private static void normalize(final double[] vector) {
double norm = norm(vector);
for (int i = 0; i < vector.length; i++) {
vector[i] = vector[i] / norm;
}
}
/**
* Returns the norm L2. sqrt(sum_i(v_i^2))
* @param v
* @return
*/
private static double norm(final double[] v) {
double agg = 0;
for (int i = 0; i < v.length; i++) {
agg += (v[i] * v[i]);
}
return Math.sqrt(agg);
}
private static double dotProduct(final double[] v1, final double[] v2) {
double agg = 0;
for (int i = 0; i < v1.length; i++) {
agg += (v1[i] * v2[i]);
}
return agg;
}
}
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