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package de.lmu.ifi.dbs.elki.distance.similarityfunction.kernel;
/*
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
Copyright (C) 2013
Ludwig-Maximilians-Universität München
Lehr- und Forschungseinheit für Datenbanksysteme
ELKI Development Team
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Affero General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
import java.util.Collection;
import java.util.Iterator;
import java.util.List;
import java.util.logging.Level;
import de.lmu.ifi.dbs.elki.data.FeatureVector;
import de.lmu.ifi.dbs.elki.database.ids.ArrayDBIDs;
import de.lmu.ifi.dbs.elki.database.ids.DBIDUtil;
import de.lmu.ifi.dbs.elki.database.relation.Relation;
import de.lmu.ifi.dbs.elki.distance.distancevalue.DoubleDistance;
import de.lmu.ifi.dbs.elki.distance.similarityfunction.PrimitiveSimilarityFunction;
import de.lmu.ifi.dbs.elki.logging.LoggingUtil;
import de.lmu.ifi.dbs.elki.math.linearalgebra.Matrix;
/**
* Provides a class for storing the kernel matrix and several extraction methods
* for convenience.
*
* @author Simon Paradies
*
* @apiviz.uses de.lmu.ifi.dbs.elki.distance.similarityfunction.PrimitiveSimilarityFunction
*/
public class KernelMatrix {
/**
* The kernel matrix
*/
Matrix kernel;
/**
* Wraps the matrixArray in a KernelMatrix
*
* @param matrixArray two dimensional double array
*/
public KernelMatrix(final double[][] matrixArray) {
kernel = new Matrix(matrixArray);
}
/**
* Provides a new kernel matrix.
*
* @param kernelFunction the kernel function used to compute the kernel matrix
* @param database the database for which the kernel matrix is computed
*
* @deprecated ID mapping is not reliable!
*/
@Deprecated
public <O extends FeatureVector<?>> KernelMatrix(final PrimitiveSimilarityFunction<? super O, DoubleDistance> kernelFunction, final Relation<? extends O> database) {
this(kernelFunction, database, DBIDUtil.ensureArray(database.getDBIDs()));
}
/**
* Provides a new kernel matrix.
*
* @param kernelFunction the kernel function used to compute the kernel matrix
* @param database the database that holds the objects
* @param ids the IDs of those objects for which the kernel matrix is computed
*/
public <O extends FeatureVector<?>> KernelMatrix(final PrimitiveSimilarityFunction<? super O, DoubleDistance> kernelFunction, final Relation<? extends O> database, final ArrayDBIDs ids) {
LoggingUtil.logExpensive(Level.FINER, "Computing kernel matrix");
kernel = new Matrix(ids.size(), ids.size());
double value;
for(int idx = 0; idx < ids.size(); idx++) {
for(int idy = idx; idy < ids.size(); idy++) {
value = kernelFunction.similarity(database.get(ids.get(idx)), database.get(ids.get(idy))).doubleValue();
kernel.set(idx, idy, value);
kernel.set(idy, idx, value);
}
}
}
/**
* Makes a new kernel matrix from matrix (with data copying).
*
* @param matrix a matrix
*/
public KernelMatrix(final Matrix matrix) {
kernel = matrix.copy();
}
/**
* Returns the kernel distance between the two specified objects.
*
* @param o1 first ObjectID
* @param o2 second ObjectID
* @return the distance between the two objects
*/
// FIXME: really use objectids!
public double getDistance(final int o1, final int o2) {
return Math.sqrt(getSquaredDistance(o1, o2));
}
/**
* Get the kernel matrix.
*
* @return kernel
*/
public Matrix getKernel() {
return kernel;
}
/**
* Returns the kernel value of object o1 and object o2
*
* @param o1 ID of first object
* @param o2 ID of second object
* @return the kernel value of object o1 and object o2
*/
public double getSimilarity(final int o1, final int o2) {
return kernel.get(o1 - 1, o2 - 1); // correct index shifts.
}
/**
* Returns the squared kernel distance between the two specified objects.
*
* @param o1 first ObjectID
* @param o2 second ObjectID
* @return the distance between the two objects
*/
public double getSquaredDistance(final int o1, final int o2) {
return getSimilarity(o1, o1) + getSimilarity(o2, o2) - 2 * getSimilarity(o1, o2);
}
/**
* Returns the ith kernel matrix column for all objects in ids
*
* @param i the column which should be returned
* @param ids the objects
* @return the ith kernel matrix column for all objects in ids
*/
public Matrix getSubColumn(final int i, final List<Integer> ids) {
final int[] ID = new int[1];
ID[0] = i - 1; // correct index shift
final int[] IDs = new int[ids.size()];
for(int x = 0; x < IDs.length; x++) {
IDs[x] = ids.get(x) - 1; // correct index shift
}
return kernel.getMatrix(IDs, ID);
}
/**
* Returns a sub kernel matrix for all objects in ids
*
* @param ids the objects
* @return a sub kernel matrix for all objects in ids.
*/
public Matrix getSubMatrix(final Collection<Integer> ids) {
final int[] IDs = new int[ids.size()];
int i = 0;
for(Iterator<Integer> it = ids.iterator(); it.hasNext(); i++) {
IDs[i] = it.next() - 1; // correct index shift
}
return kernel.getMatrix(IDs, IDs);
}
/**
* Centers the matrix in feature space according to Smola et. Schoelkopf,
* Learning with Kernels p. 431 Alters the input matrix. If you still need the
* original matrix, use
* <code>centeredMatrix = centerKernelMatrix(uncenteredMatrix.copy()) {</code>
*
* @param matrix the matrix to be centered
* @return centered matrix (for convenience)
*/
public static Matrix centerMatrix(final Matrix matrix) {
final Matrix normalizingMatrix = new Matrix(matrix.getRowDimensionality(), matrix.getColumnDimensionality(), 1.0 / matrix.getColumnDimensionality());
return matrix.minusEquals(normalizingMatrix.times(matrix)).minusEquals(matrix.times(normalizingMatrix)).plusEquals(normalizingMatrix.times(matrix).times(normalizingMatrix));
}
@Override
public String toString() {
return super.toString();
}
/**
* Centers the Kernel Matrix in Feature Space according to Smola et.
* Schoelkopf, Learning with Kernels p. 431 Alters the input matrix. If you
* still need the original matrix, use
* <code>centeredMatrix = centerKernelMatrix(uncenteredMatrix.copy()) {</code>
*
* @param kernelMatrix the kernel matrix to be centered
* @return centered kernelMatrix (for convenience)
*/
public static Matrix centerKernelMatrix(final KernelMatrix kernelMatrix) {
return centerMatrix(kernelMatrix.getKernel());
}
}
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