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
|
package de.lmu.ifi.dbs.elki.distance.distancefunction;
/*
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 de.lmu.ifi.dbs.elki.data.NumberVector;
import de.lmu.ifi.dbs.elki.data.spatial.SpatialComparable;
import de.lmu.ifi.dbs.elki.database.query.distance.SpatialPrimitiveDistanceQuery;
import de.lmu.ifi.dbs.elki.database.relation.Relation;
import de.lmu.ifi.dbs.elki.distance.distancevalue.DoubleDistance;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.OptionID;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.constraints.GreaterConstraint;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameterization.Parameterization;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameters.DoubleParameter;
/**
* Provides a LP-Norm for FeatureVectors.
*
* @author Arthur Zimek
*
* @apiviz.landmark
*/
public class LPNormDistanceFunction extends AbstractVectorDoubleDistanceNorm implements SpatialPrimitiveDoubleDistanceFunction<NumberVector<?, ?>> {
/**
* OptionID for the "p" parameter
*/
public static final OptionID P_ID = OptionID.getOrCreateOptionID("lpnorm.p", "the degree of the L-P-Norm (positive number)");
/**
* Keeps the currently set p.
*/
private double p;
/**
* Constructor, internal version.
*
* @param p Parameter p
*/
public LPNormDistanceFunction(double p) {
super();
this.p = p;
}
/**
* Returns the distance between the specified FeatureVectors as a LP-Norm for
* the currently set p.
*
* @param v1 first FeatureVector
* @param v2 second FeatureVector
* @return the distance between the specified FeatureVectors as a LP-Norm for
* the currently set p
*/
@Override
public double doubleDistance(NumberVector<?, ?> v1, NumberVector<?, ?> v2) {
final int dim1 = v1.getDimensionality();
if(dim1 != v2.getDimensionality()) {
throw new IllegalArgumentException("Different dimensionality of FeatureVectors\n first argument: " + v1.toString() + "\n second argument: " + v2.toString());
}
double sqrDist = 0;
for(int i = 1; i <= dim1; i++) {
final double delta = Math.abs(v1.doubleValue(i) - v2.doubleValue(i));
sqrDist += Math.pow(delta, p);
}
return Math.pow(sqrDist, 1.0 / p);
}
@Override
public double doubleNorm(NumberVector<?, ?> v) {
final int dim = v.getDimensionality();
double sqrDist = 0;
for(int i = 1; i <= dim; i++) {
final double delta = v.doubleValue(i);
sqrDist += Math.pow(delta, p);
}
return Math.pow(sqrDist, 1.0 / p);
}
/**
* Get the functions p parameter.
*
* @return p
*/
public double getP() {
return p;
}
@Override
public double doubleMinDist(SpatialComparable mbr1, SpatialComparable mbr2) {
// Optimization for the simplest case
if(mbr1 instanceof NumberVector) {
if(mbr2 instanceof NumberVector) {
return doubleDistance((NumberVector<?, ?>) mbr1, (NumberVector<?, ?>) mbr2);
}
}
// TODO: optimize for more simpler cases: obj vs. rect?
final int dim1 = mbr1.getDimensionality();
if(dim1 != mbr2.getDimensionality()) {
throw new IllegalArgumentException("Different dimensionality of objects\n " + "first argument: " + mbr1.toString() + "\n " + "second argument: " + mbr2.toString());
}
double sumDist = 0;
for(int d = 1; d <= dim1; d++) {
final double m1, m2;
if(mbr1.getMax(d) < mbr2.getMin(d)) {
m1 = mbr2.getMin(d);
m2 = mbr1.getMax(d);
}
else if(mbr1.getMin(d) > mbr2.getMax(d)) {
m1 = mbr1.getMin(d);
m2 = mbr2.getMax(d);
}
else { // The mbrs intersect!
continue;
}
final double manhattanI = m1 - m2;
sumDist += Math.pow(manhattanI, p);
}
return Math.pow(sumDist, 1.0 / p);
}
@Override
public DoubleDistance minDist(SpatialComparable mbr1, SpatialComparable mbr2) {
return new DoubleDistance(doubleMinDist(mbr1, mbr2));
}
@Override
public boolean isMetric() {
return (p >= 1);
}
@Override
public String toString() {
return "L_" + p + " Norm";
}
@Override
public boolean equals(Object obj) {
if(obj == null) {
return false;
}
if(obj instanceof LPNormDistanceFunction) {
return this.p == ((LPNormDistanceFunction) obj).p;
}
return false;
}
@Override
public <T extends NumberVector<?, ?>> SpatialPrimitiveDistanceQuery<T, DoubleDistance> instantiate(Relation<T> relation) {
return new SpatialPrimitiveDistanceQuery<T, DoubleDistance>(relation, this);
}
/**
* Parameterization class.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer extends AbstractParameterizer {
/**
* The value of p.
*/
protected double p = 0.0;
@Override
protected void makeOptions(Parameterization config) {
super.makeOptions(config);
final DoubleParameter paramP = new DoubleParameter(P_ID, new GreaterConstraint(0));
if(config.grab(paramP)) {
p = paramP.getValue();
}
}
@Override
protected LPNormDistanceFunction makeInstance() {
if(p == 1.0) {
return ManhattanDistanceFunction.STATIC;
}
if(p == 2.0) {
return EuclideanDistanceFunction.STATIC;
}
if(p == Double.POSITIVE_INFINITY) {
return MaximumDistanceFunction.STATIC;
}
return new LPNormDistanceFunction(p);
}
}
}
|
