1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
|
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* 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,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
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;
/**
* <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. */
private final boolean individualDistances;
/** Distance. */
private final DistanceMeasure 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} */
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 {@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.
*
* @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;
}
}
|
