package org.apache.mahout.math.random;
import java.util.List;
import com.google.common.collect.Lists;
import org.apache.commons.lang.math.RandomUtils;
import org.apache.mahout.math.DenseMatrix;
import org.apache.mahout.math.DenseVector;
import org.apache.mahout.math.Matrix;
import org.apache.mahout.math.MatrixSlice;
import org.apache.mahout.math.Vector;
import org.apache.mahout.math.function.DoubleFunction;
public final class RandomProjector {
private RandomProjector() {
}
/**
* Generates a basis matrix of size projectedVectorSize x vectorSize. Multiplying a a vector by
* this matrix results in the projected vector.
*
* The rows of the matrix are sampled from a multi normal distribution.
*
* @param projectedVectorSize final projected size of a vector (number of projection vectors)
* @param vectorSize initial vector size
* @return a projection matrix
*/
public static Matrix generateBasisNormal(int projectedVectorSize, int vectorSize) {
Matrix basisMatrix = new DenseMatrix(projectedVectorSize, vectorSize);
basisMatrix.assign(new Normal());
for (MatrixSlice row : basisMatrix) {
row.vector().assign(row.normalize());
}
return basisMatrix;
}
/**
* Generates a basis matrix of size projectedVectorSize x vectorSize. Multiplying a a vector by
* this matrix results in the projected vector.
*
* The rows of a matrix are sample from a distribution where:
* - +1 has probability 1/2,
* - -1 has probability 1/2
*
* See Achlioptas, D. (2003). Database-friendly random projections: Johnson-Lindenstrauss with binary coins.
* Journal of Computer and System Sciences, 66(4), 671–687. doi:10.1016/S0022-0000(03)00025-4
*
* @param projectedVectorSize final projected size of a vector (number of projection vectors)
* @param vectorSize initial vector size
* @return a projection matrix
*/
public static Matrix generateBasisPlusMinusOne(int projectedVectorSize, int vectorSize) {
Matrix basisMatrix = new DenseMatrix(projectedVectorSize, vectorSize);
for (int i = 0; i < projectedVectorSize; ++i) {
for (int j = 0; j < vectorSize; ++j) {
basisMatrix.set(i, j, RandomUtils.nextInt(2) == 0 ? 1 : -1);
}
}
for (MatrixSlice row : basisMatrix) {
row.vector().assign(row.normalize());
}
return basisMatrix;
}
/**
* Generates a basis matrix of size projectedVectorSize x vectorSize. Multiplying a a vector by
* this matrix results in the projected vector.
*
* The rows of a matrix are sample from a distribution where:
* - 0 has probability 2/3,
* - +1 has probability 1/6,
* - -1 has probability 1/6
*
* See Achlioptas, D. (2003). Database-friendly random projections: Johnson-Lindenstrauss with binary coins.
* Journal of Computer and System Sciences, 66(4), 671–687. doi:10.1016/S0022-0000(03)00025-4
*
* @param projectedVectorSize final projected size of a vector (number of projection vectors)
* @param vectorSize initial vector size
* @return a projection matrix
*/
public static Matrix generateBasisZeroPlusMinusOne(int projectedVectorSize, int vectorSize) {
Matrix basisMatrix = new DenseMatrix(projectedVectorSize, vectorSize);
Multinomial<Double> choice = new Multinomial<Double>();
choice.add(0.0, 2 / 3.0);
choice.add(Math.sqrt(3.0), 1 / 6.0);
choice.add(-Math.sqrt(3.0), 1 / 6.0);
for (int i = 0; i < projectedVectorSize; ++i) {
for (int j = 0; j < vectorSize; ++j) {
basisMatrix.set(i, j, choice.sample());
}
}
for (MatrixSlice row : basisMatrix) {
row.vector().assign(row.normalize());
}
return basisMatrix;
}
/**
* Generates a list of projectedVectorSize vectors, each of size vectorSize. This looks like a
* matrix of size (projectedVectorSize, vectorSize).
* @param projectedVectorSize final projected size of a vector (number of projection vectors)
* @param vectorSize initial vector size
* @return a list of projection vectors
*/
public static List<Vector> generateVectorBasis(int projectedVectorSize, int vectorSize) {
DoubleFunction random = new Normal();
List<Vector> basisVectors = Lists.newArrayList();
for (int i = 0; i < projectedVectorSize; ++i) {
Vector basisVector = new DenseVector(vectorSize);
basisVector.assign(random);
basisVector.normalize();
basisVectors.add(basisVector);
}
return basisVectors;
}
}