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
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
|
package de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.density;
/*
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
Copyright (C) 2012
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.awt.image.BufferedImage;
import java.util.Arrays;
import java.util.Comparator;
import org.apache.batik.util.SVGConstants;
import org.w3c.dom.Element;
import de.lmu.ifi.dbs.elki.database.ids.DBID;
import de.lmu.ifi.dbs.elki.math.MathUtil;
import de.lmu.ifi.dbs.elki.math.MeanVariance;
import de.lmu.ifi.dbs.elki.result.HierarchicalResult;
import de.lmu.ifi.dbs.elki.result.KMLOutputHandler;
import de.lmu.ifi.dbs.elki.result.Result;
import de.lmu.ifi.dbs.elki.result.ResultUtil;
import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
import de.lmu.ifi.dbs.elki.utilities.iterator.IterableIterator;
import de.lmu.ifi.dbs.elki.visualization.VisualizationTask;
import de.lmu.ifi.dbs.elki.visualization.batikutil.ThumbnailRegistryEntry;
import de.lmu.ifi.dbs.elki.visualization.projections.CanvasSize;
import de.lmu.ifi.dbs.elki.visualization.projector.ScatterPlotProjector;
import de.lmu.ifi.dbs.elki.visualization.svg.SVGUtil;
import de.lmu.ifi.dbs.elki.visualization.visualizers.AbstractVisFactory;
import de.lmu.ifi.dbs.elki.visualization.visualizers.Visualization;
import de.lmu.ifi.dbs.elki.visualization.visualizers.scatterplot.AbstractScatterplotVisualization;
/**
* A simple density estimation visualization, based on a simple kernel-density
* <em>in the projection, not the actual data!</em>
*
* @author Erich Schubert
*/
// TODO: make parameterizable, in particular color map, kernel bandwidth and
// kernel function
public class DensityEstimationOverlay extends AbstractScatterplotVisualization {
/**
* A short name characterizing this Visualizer.
*/
private static final String NAME = "Density estimation overlay";
/**
* Density map resolution
*/
private int resolution = 500;
/**
* The actual image
*/
private BufferedImage img = null;
/**
* Constructor.
*
* @param task Task
*/
public DensityEstimationOverlay(VisualizationTask task) {
super(task);
incrementalRedraw();
}
@Override
protected void redraw() {
if(img == null) {
renderImage();
}
CanvasSize canvas = proj.estimateViewport();
String imguri = ThumbnailRegistryEntry.INTERNAL_PREFIX + ThumbnailRegistryEntry.registerImage(img);
Element itag = svgp.svgElement(SVGConstants.SVG_IMAGE_TAG);
SVGUtil.setAtt(itag, SVGConstants.SVG_IMAGE_RENDERING_ATTRIBUTE, SVGConstants.SVG_OPTIMIZE_SPEED_VALUE);
SVGUtil.setAtt(itag, SVGConstants.SVG_X_ATTRIBUTE, canvas.minx);
SVGUtil.setAtt(itag, SVGConstants.SVG_Y_ATTRIBUTE, canvas.miny);
SVGUtil.setAtt(itag, SVGConstants.SVG_WIDTH_ATTRIBUTE, canvas.maxx - canvas.minx);
SVGUtil.setAtt(itag, SVGConstants.SVG_HEIGHT_ATTRIBUTE, canvas.maxy - canvas.miny);
SVGUtil.setAtt(itag, SVGConstants.SVG_STYLE_ATTRIBUTE, SVGConstants.CSS_OPACITY_PROPERTY + ": .5");
itag.setAttributeNS(SVGConstants.XLINK_NAMESPACE_URI, SVGConstants.XLINK_HREF_QNAME, imguri);
layer.appendChild(itag);
}
@Reference(authors = "D. W. Scott", title = "Multivariate density estimation", booktitle = "Multivariate Density Estimation: Theory, Practice, and Visualization", url = "http://dx.doi.org/10.1002/9780470316849.fmatter")
private double[] initializeBandwidth(double[][] data) {
MeanVariance mv0 = new MeanVariance();
MeanVariance mv1 = new MeanVariance();
// For Kernel bandwidth.
for(double[] projected : data) {
mv0.put(projected[0]);
mv1.put(projected[1]);
}
// Set bandwidths according to Scott's rule:
// Note: in projected space, d=2.
double[] bandwidth = new double[2];
bandwidth[0] = MathUtil.SQRT5 * mv0.getSampleStddev() * Math.pow(rel.size(), -1 / 6.);
bandwidth[1] = MathUtil.SQRT5 * mv1.getSampleStddev() * Math.pow(rel.size(), -1 / 6.);
return bandwidth;
}
private void renderImage() {
// TODO: SAMPLE? Do region queries?
// Project the data just once, keep a copy.
double[][] data = new double[rel.size()][];
{
int i = 0;
for(DBID id : rel.iterDBIDs()) {
data[i] = proj.fastProjectDataToRenderSpace(rel.get(id));
i++;
}
}
double[] bandwidth = initializeBandwidth(data);
// Compare by first component
Comparator<double[]> comp0 = new Comparator<double[]>() {
@Override
public int compare(double[] o1, double[] o2) {
return Double.compare(o1[0], o2[0]);
}
};
// Compare by second component
Comparator<double[]> comp1 = new Comparator<double[]>() {
@Override
public int compare(double[] o1, double[] o2) {
return Double.compare(o1[1], o2[1]);
}
};
// TODO: choose comparator order based on smaller bandwidth?
Arrays.sort(data, comp0);
CanvasSize canvas = proj.estimateViewport();
double min0 = canvas.minx, max0 = canvas.maxx, ste0 = (max0 - min0) / resolution;
double min1 = canvas.miny, max1 = canvas.maxy, ste1 = (max1 - min1) / resolution;
double kernf = 9. / (16 * bandwidth[0] * bandwidth[1]);
double maxdens = 0.0;
double[][] dens = new double[resolution][resolution];
{
// TODO: incrementally update the loff/roff values?
for(int x = 0; x < resolution; x++) {
double xlow = min0 + ste0 * x, xhig = xlow + ste0;
int loff = unflip(Arrays.binarySearch(data, new double[] { xlow - bandwidth[0] }, comp0));
int roff = unflip(Arrays.binarySearch(data, new double[] { xhig + bandwidth[0] }, comp0));
// Resort by second component
Arrays.sort(data, loff, roff, comp1);
for(int y = 0; y < resolution; y++) {
double ylow = min1 + ste1 * y, yhig = ylow + ste1;
int boff = unflip(Arrays.binarySearch(data, loff, roff, new double[] { 0, ylow - bandwidth[1] }, comp1));
int toff = unflip(Arrays.binarySearch(data, loff, roff, new double[] { 0, yhig + bandwidth[1] }, comp1));
for(int pos = boff; pos < toff; pos++) {
double[] val = data[pos];
double d0 = (val[0] < xlow) ? (xlow - val[0]) : (val[0] > xhig) ? (val[0] - xhig) : 0;
double d1 = (val[1] < ylow) ? (ylow - val[1]) : (val[1] > yhig) ? (val[1] - yhig) : 0;
d0 = d0 / bandwidth[0];
d1 = d1 / bandwidth[1];
dens[x][y] += kernf * (1 - d0 * d0) * (1 - d1 * d1);
}
maxdens = Math.max(maxdens, dens[x][y]);
}
// Restore original sorting, as the intervals overlap
Arrays.sort(data, loff, roff, comp0);
}
}
img = new BufferedImage(resolution, resolution, BufferedImage.TYPE_INT_ARGB);
{
for(int x = 0; x < resolution; x++) {
for(int y = 0; y < resolution; y++) {
int rgb = KMLOutputHandler.getColorForValue(dens[x][y] / maxdens).getRGB();
img.setRGB(x, y, rgb);
}
}
}
}
private int unflip(int binarySearch) {
if(binarySearch < 0) {
return (-binarySearch) - 1;
}
else {
return binarySearch;
}
}
/**
* The visualization factory
*
* @author Erich Schubert
*
* @apiviz.stereotype factory
* @apiviz.uses DensityEstimation2DVisualization oneway - - «create»
*/
public static class Factory extends AbstractVisFactory {
/**
* Constructor, adhering to
* {@link de.lmu.ifi.dbs.elki.utilities.optionhandling.Parameterizable}
*/
public Factory() {
super();
}
@Override
public Visualization makeVisualization(VisualizationTask task) {
return new DensityEstimationOverlay(task);
}
@Override
public void processNewResult(HierarchicalResult baseResult, Result result) {
IterableIterator<ScatterPlotProjector<?>> ps = ResultUtil.filteredResults(result, ScatterPlotProjector.class);
for(ScatterPlotProjector<?> p : ps) {
final VisualizationTask task = new VisualizationTask(NAME, p.getRelation(), p.getRelation(), this);
task.put(VisualizationTask.META_LEVEL, VisualizationTask.LEVEL_DATA + 1);
task.put(VisualizationTask.META_VISIBLE_DEFAULT, false);
baseResult.getHierarchy().add(p, task);
}
}
}
}
|
