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* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
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* See the License for the specific language governing permissions and
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package org.apache.commons.math3.ml.neuralnet.twod.util;
import java.util.Collection;
import org.apache.commons.math3.ml.neuralnet.Neuron;
import org.apache.commons.math3.ml.neuralnet.Network;
import org.apache.commons.math3.ml.neuralnet.twod.NeuronSquareMesh2D;
import org.apache.commons.math3.ml.distance.DistanceMeasure;
U-Matrix
visualization of high-dimensional data projection.
Since: 3.6
/**
* <a href="http://en.wikipedia.org/wiki/U-Matrix">U-Matrix</a>
* visualization of high-dimensional data projection.
* @since 3.6
*/
public class UnifiedDistanceMatrix implements MapVisualization {
Whether to show distance between each pair of neighbouring units. /** Whether to show distance between each pair of neighbouring units. */
private final boolean individualDistances;
Distance. /** Distance. */
private final DistanceMeasure distance;
Simple constructor.
Params: - individualDistances – If
true, the 8 individual inter-units distances will be
computed. They will be stored in additional pixels around each of the original units of the 2D-map. The additional pixels that lie along a "diagonal" are shared by two pairs of units: their
value will be set to the average distance between the units belonging
to each of the pairs. The value zero will be stored in the pixel
corresponding to the location of a unit of the 2D-map.
If false, only the average distance between a unit and all its neighbours will be computed (and stored in the pixel corresponding to that unit of the 2D-map). In that case, the number of neighbours taken into account depends on the network's
neighbourhood type. - distance – Distance.
/**
* Simple constructor.
*
* @param individualDistances If {@code true}, the 8 individual
* inter-units distances will be {@link #computeImage(NeuronSquareMesh2D)
* computed}. They will be stored in additional pixels around each of
* the original units of the 2D-map. The additional pixels that lie
* along a "diagonal" are shared by <em>two</em> pairs of units: their
* value will be set to the average distance between the units belonging
* to each of the pairs. The value zero will be stored in the pixel
* corresponding to the location of a unit of the 2D-map.
* <br>
* If {@code false}, only the average distance between a unit and all its
* neighbours will be computed (and stored in the pixel corresponding to
* that unit of the 2D-map). In that case, the number of neighbours taken
* into account depends on the network's
* {@link org.apache.commons.math3.ml.neuralnet.SquareNeighbourhood
* neighbourhood type}.
* @param distance Distance.
*/
public UnifiedDistanceMatrix(boolean individualDistances,
DistanceMeasure distance) {
this.individualDistances = individualDistances;
this.distance = distance;
}
{@inheritDoc} /** {@inheritDoc} */
public double[][] computeImage(NeuronSquareMesh2D map) {
if (individualDistances) {
return individualDistances(map);
} else {
return averageDistances(map);
}
}
Computes the distances between a unit of the map and its neighbours. The image will contain more pixels than the number of neurons in the given map because each neuron has 8 neighbours. The value zero will be stored in the pixels corresponding to the location of a map unit. Params: - map – Map.
Returns: an image representing the individual distances.
/**
* Computes the distances between a unit of the map and its
* neighbours.
* The image will contain more pixels than the number of neurons
* in the given {@code map} because each neuron has 8 neighbours.
* The value zero will be stored in the pixels corresponding to
* the location of a map unit.
*
* @param map Map.
* @return an image representing the individual distances.
*/
private double[][] individualDistances(NeuronSquareMesh2D map) {
final int numRows = map.getNumberOfRows();
final int numCols = map.getNumberOfColumns();
final double[][] uMatrix = new double[numRows * 2 + 1][numCols * 2 + 1];
// 1.
// Fill right and bottom slots of each unit's location with the
// distance between the current unit and each of the two neighbours,
// respectively.
for (int i = 0; i < numRows; i++) {
// Current unit's row index in result image.
final int iR = 2 * i + 1;
for (int j = 0; j < numCols; j++) {
// Current unit's column index in result image.
final int jR = 2 * j + 1;
final double[] current = map.getNeuron(i, j).getFeatures();
Neuron neighbour;
// Right neighbour.
neighbour = map.getNeuron(i, j,
NeuronSquareMesh2D.HorizontalDirection.RIGHT,
NeuronSquareMesh2D.VerticalDirection.CENTER);
if (neighbour != null) {
uMatrix[iR][jR + 1] = distance.compute(current,
neighbour.getFeatures());
}
// Bottom-center neighbour.
neighbour = map.getNeuron(i, j,
NeuronSquareMesh2D.HorizontalDirection.CENTER,
NeuronSquareMesh2D.VerticalDirection.DOWN);
if (neighbour != null) {
uMatrix[iR + 1][jR] = distance.compute(current,
neighbour.getFeatures());
}
}
}
// 2.
// Fill the bottom-rigth slot of each unit's location with the average
// of the distances between
// * the current unit and its bottom-right neighbour, and
// * the bottom-center neighbour and the right neighbour.
for (int i = 0; i < numRows; i++) {
// Current unit's row index in result image.
final int iR = 2 * i + 1;
for (int j = 0; j < numCols; j++) {
// Current unit's column index in result image.
final int jR = 2 * j + 1;
final Neuron current = map.getNeuron(i, j);
final Neuron right = map.getNeuron(i, j,
NeuronSquareMesh2D.HorizontalDirection.RIGHT,
NeuronSquareMesh2D.VerticalDirection.CENTER);
final Neuron bottom = map.getNeuron(i, j,
NeuronSquareMesh2D.HorizontalDirection.CENTER,
NeuronSquareMesh2D.VerticalDirection.DOWN);
final Neuron bottomRight = map.getNeuron(i, j,
NeuronSquareMesh2D.HorizontalDirection.RIGHT,
NeuronSquareMesh2D.VerticalDirection.DOWN);
final double current2BottomRight = bottomRight == null ?
0 :
distance.compute(current.getFeatures(),
bottomRight.getFeatures());
final double right2Bottom = (right == null ||
bottom == null) ?
0 :
distance.compute(right.getFeatures(),
bottom.getFeatures());
// Bottom-right slot.
uMatrix[iR + 1][jR + 1] = 0.5 * (current2BottomRight + right2Bottom);
}
}
// 3. Copy last row into first row.
final int lastRow = uMatrix.length - 1;
uMatrix[0] = uMatrix[lastRow];
// 4.
// Copy last column into first column.
final int lastCol = uMatrix[0].length - 1;
for (int r = 0; r < lastRow; r++) {
uMatrix[r][0] = uMatrix[r][lastCol];
}
return uMatrix;
}
Computes the distances between a unit of the map and its neighbours.
Params: - map – Map.
Returns: an image representing the average distances.
/**
* Computes the distances between a unit of the map and its neighbours.
*
* @param map Map.
* @return an image representing the average distances.
*/
private double[][] averageDistances(NeuronSquareMesh2D map) {
final int numRows = map.getNumberOfRows();
final int numCols = map.getNumberOfColumns();
final double[][] uMatrix = new double[numRows][numCols];
final Network net = map.getNetwork();
for (int i = 0; i < numRows; i++) {
for (int j = 0; j < numCols; j++) {
final Neuron neuron = map.getNeuron(i, j);
final Collection<Neuron> neighbours = net.getNeighbours(neuron);
final double[] features = neuron.getFeatures();
double d = 0;
int count = 0;
for (Neuron n : neighbours) {
++count;
d += distance.compute(features, n.getFeatures());
}
uMatrix[i][j] = d / count;
}
}
return uMatrix;
}
}