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
|
package de.lmu.ifi.dbs.elki.index.tree.spatial.rstarvariants.strategies.split;
/*
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.util.Arrays;
import java.util.BitSet;
import de.lmu.ifi.dbs.elki.data.ModifiableHyperBoundingBox;
import de.lmu.ifi.dbs.elki.data.spatial.SpatialComparable;
import de.lmu.ifi.dbs.elki.data.spatial.SpatialUtil;
import de.lmu.ifi.dbs.elki.utilities.datastructures.arraylike.ArrayAdapter;
import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
import de.lmu.ifi.dbs.elki.utilities.pairs.DoubleIntPair;
/**
* Quadratic-time complexity split as used by Diane Greene for the R-Tree.
*
* Seed selection is quadratic, distribution is O(n log n).
*
* This contains a slight modification to improve performance with point data:
* with points as seeds, the normalized separation is always 1, so we choose the
* raw separation then.
*
* <p>
* Diane Greene:<br />
* An implementation and performance analysis of spatial data access methods<br />
* In: Proceedings of the Fifth International Conference on Data Engineering
* </p>
*
* @author Erich Schubert
*/
@Reference(authors = "Diane Greene", title = "An implementation and performance analysis of spatial data access methods", booktitle = "Proceedings of the Fifth International Conference on Data Engineering", url = "http://dx.doi.org/10.1109/ICDE.1989.47268")
public class GreeneSplit implements SplitStrategy {
/**
* Static instance.
*/
public static final GreeneSplit STATIC = new GreeneSplit();
@Override
public <E extends SpatialComparable, A> BitSet split(A entries, ArrayAdapter<E, A> getter, int minEntries) {
final int num = getter.size(entries);
// Choose axis by best normalized separation
int axis = -1;
{
// PickSeeds - find the two most distant rectangles
double worst = Double.NEGATIVE_INFINITY;
int w1 = 0, w2 = 0;
// Compute individual areas
double[] areas = new double[num];
for (int e1 = 0; e1 < num - 1; e1++) {
final E e1i = getter.get(entries, e1);
areas[e1] = SpatialUtil.volume(e1i);
}
// Compute area increase
for (int e1 = 0; e1 < num - 1; e1++) {
final E e1i = getter.get(entries, e1);
for (int e2 = e1 + 1; e2 < num; e2++) {
final E e2i = getter.get(entries, e2);
final double areaJ = SpatialUtil.volumeUnion(e1i, e2i);
final double d = areaJ - areas[e1] - areas[e2];
if (d > worst) {
worst = d;
w1 = e1;
w2 = e2;
}
}
}
if (worst > 0) {
// Data to keep
// Initial mbrs and areas
E m1 = getter.get(entries, w1);
E m2 = getter.get(entries, w2);
double bestsep = Double.NEGATIVE_INFINITY;
double bestsep2 = Double.NEGATIVE_INFINITY;
for (int d = 0; d < m1.getDimensionality(); d++) {
final double s1 = m1.getMin(d) - m2.getMax(d);
final double s2 = m2.getMin(d) - m1.getMax(d);
final double sm = Math.max(s1, s2);
final double no = Math.max(m1.getMax(d), m2.getMax(d)) - Math.min(m1.getMin(d), m2.getMin(d));
final double sep = sm / no;
if (sep > bestsep || (sep == bestsep && sm > bestsep2)) {
bestsep = sep;
bestsep2 = sm;
axis = d;
}
}
} else {
// All objects are identical!
final BitSet assignment = new BitSet(num);
final int half = (num + 1) >> 1;
// Put the first half into second node
for (int i = 0; i < half; i++) {
assignment.set(i);
}
return assignment;
}
}
// Sort by minimum value
DoubleIntPair[] data = new DoubleIntPair[num];
for (int i = 0; i < num; i++) {
data[i] = new DoubleIntPair(getter.get(entries, i).getMin(axis), i);
}
Arrays.sort(data);
// Object assignment
final BitSet assignment = new BitSet(num);
final int half = (num + 1) >> 1;
// Put the first half into second node
for (int i = 0; i < half; i++) {
assignment.set(data[i].second);
}
// Tie handling
if (num % 2 == 0) {
// We need to compute the bounding boxes
ModifiableHyperBoundingBox mbr1 = new ModifiableHyperBoundingBox(getter.get(entries, data[0].second));
for (int i = 1; i < half; i++) {
mbr1.extend(getter.get(entries, data[i].second));
}
ModifiableHyperBoundingBox mbr2 = new ModifiableHyperBoundingBox(getter.get(entries, data[num - 1].second));
for (int i = half + 1; i < num - 1; i++) {
mbr2.extend(getter.get(entries, data[i].second));
}
E e = getter.get(entries, data[half].second);
double inc1 = SpatialUtil.volumeUnion(mbr1, e) - SpatialUtil.volume(mbr1);
double inc2 = SpatialUtil.volumeUnion(mbr2, e) - SpatialUtil.volume(mbr2);
if (inc1 < inc2) {
assignment.set(data[half].second);
}
}
return assignment;
}
/**
* Parameterization class.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer extends AbstractParameterizer {
@Override
protected GreeneSplit makeInstance() {
return GreeneSplit.STATIC;
}
}
}
|
