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package de.lmu.ifi.dbs.elki.algorithm.clustering.hierarchical;
/*
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
Copyright (C) 2015
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.algorithm.AbstractDistanceBasedAlgorithm;
import de.lmu.ifi.dbs.elki.database.datastore.WritableDBIDDataStore;
import de.lmu.ifi.dbs.elki.database.datastore.WritableDoubleDataStore;
import de.lmu.ifi.dbs.elki.database.ids.ArrayDBIDs;
import de.lmu.ifi.dbs.elki.database.ids.DBIDArrayIter;
import de.lmu.ifi.dbs.elki.database.ids.DBIDRef;
import de.lmu.ifi.dbs.elki.database.ids.DBIDUtil;
import de.lmu.ifi.dbs.elki.database.ids.DBIDVar;
import de.lmu.ifi.dbs.elki.distance.distancefunction.DistanceFunction;
import de.lmu.ifi.dbs.elki.logging.Logging;
import de.lmu.ifi.dbs.elki.utilities.Alias;
import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
/**
* CLINK algorithm for complete linkage.
*
* This algorithm runs in O(n^2) time, and needs only O(n) memory. The results
* can differ from the standard algorithm in unfavorable ways, and are
* order-dependent (Defays: "Modifications of the labeling permit us to obtain
* different minimal superior ultrametric dissimilarities"). Unfortunately, the
* results are usually perceived to be substantially worse than the more
* expensive algorithms for complete linkage clustering. This arises from the
* fact that this algorithm has to add the new object to the existing tree in
* every step, instead of being able to always do the globally best merge.
*
* Reference:
* <p>
* D. Defays<br />
* An Efficient Algorithm for the Complete Link Cluster Method<br />
* In: The Computer Journal 20.4
* </p>
*
* @author Erich Schubert
*
* @apiviz.has CompleteLinkageMethod
*
* @param <O> the type of DatabaseObject the algorithm is applied on
*/
@Reference(authors = "D. Defays", //
title = "An Efficient Algorithm for the Complete Link Cluster Method", //
booktitle = "The Computer Journal 20.4", //
url = "http://dx.doi.org/10.1093/comjnl/20.4.364")
@Alias({ "CLINK", "Defays" })
public class CLINK<O> extends SLINK<O> {
/**
* The logger for this class.
*/
private static final Logging LOG = Logging.getLogger(CLINK.class);
/**
* Constructor.
*
* @param distanceFunction Distance function
*/
public CLINK(DistanceFunction<? super O> distanceFunction) {
super(distanceFunction);
}
/**
* CLINK main loop, based on the SLINK main loop.
*
* @param id Current object
* @param ids All objects
* @param it Array iterator
* @param n Last object to process at this run
* @param pi Parent
* @param lambda Height
* @param m Distance
*/
@Override
protected void process(DBIDRef id, ArrayDBIDs ids, DBIDArrayIter it, int n, WritableDBIDDataStore pi, WritableDoubleDataStore lambda, WritableDoubleDataStore m) {
clinkstep3(id, it, n, pi, lambda, m);
clinkstep4567(id, ids, it, n, pi, lambda, m);
clinkstep8(id, it, n, pi, lambda, m);
}
/**
* Third step: Determine the values for P and L
*
* @param id the id of the object to be inserted into the pointer
* representation
* @param i Iterator
* @param n Stopping position
* @param pi Pi data store
* @param lambda Lambda data store
* @param m Distance data store
*/
private void clinkstep3(DBIDRef id, DBIDArrayIter i, int n, WritableDBIDDataStore pi, WritableDoubleDataStore lambda, WritableDoubleDataStore m) {
DBIDVar p_i = DBIDUtil.newVar();
// for i = 1..n
for(i.seek(0); i.getOffset() < n; i.advance()) {
double l_i = lambda.doubleValue(i);
double m_i = m.doubleValue(i);
// if L(i) < M(i)
if(l_i < m_i) {
p_i.from(pi, i); // p_i = pi(it)
double mp_i = m.doubleValue(p_i);
// M(P(i)) = max { M(P(i)), M(i) }
if(mp_i < m_i) {
m.putDouble(p_i, m_i);
}
// M(i) = inf
m.putDouble(i, Double.POSITIVE_INFINITY);
}
}
}
/**
* Fourth to seventh step of CLINK: find best insertion
*
* @param id Current objct
* @param ids All objects
* @param it Iterator
* @param n Index threshold
* @param pi Parent data store
* @param lambda Height data store
* @param m Distance data store
*/
private void clinkstep4567(DBIDRef id, ArrayDBIDs ids, DBIDArrayIter it, int n, WritableDBIDDataStore pi, WritableDoubleDataStore lambda, WritableDoubleDataStore m) {
// step 4: a = n
DBIDArrayIter a = ids.iter().seek(n - 1);
// step 5:
{
DBIDVar p_i = DBIDUtil.newVar();
for(it.seek(n - 1); it.valid(); it.retract()) {
double l_i = lambda.doubleValue(it);
double mp_i = m.doubleValue(p_i.from(pi, it));
if(l_i >= mp_i) {
if(m.doubleValue(it) < m.doubleValue(a)) {
a.seek(it.getOffset());
}
}
else {
m.putDouble(it, Double.POSITIVE_INFINITY);
}
}
}
// step 6
DBIDVar b = DBIDUtil.newVar().from(pi, a); // b = pi[a]
double c = lambda.doubleValue(a);
pi.putDBID(a, id);
lambda.putDouble(a, m.doubleValue(a));
// step 7
if(a.getOffset() < n - 1) {
DBIDRef last = DBIDUtil.newVar(it.seek(n - 1)); // Used below
DBIDVar d = DBIDUtil.newVar();
// if b < n: (then goto 7)
while(!DBIDUtil.equal(b, id)) {
if(DBIDUtil.equal(b, last)) {
pi.putDBID(b, id);
lambda.putDouble(b, c);
break;
}
d.from(pi, b); // d = pi[b]
pi.putDBID(b, id); // pi[b] = n + 1
c = lambda.putDouble(b, c); // c = old l[b], l[b] = c
b.set(d); // b = d = old pi[b]
}
}
}
/**
* Update hierarchy.
*
* @param id Current object
* @param it Iterator
* @param n Last object to process
* @param pi Parent data store
* @param lambda Height data store
* @param m Distance data store
*/
private void clinkstep8(DBIDRef id, DBIDArrayIter it, int n, WritableDBIDDataStore pi, WritableDoubleDataStore lambda, WritableDoubleDataStore m) {
DBIDVar p_i = DBIDUtil.newVar(), pp_i = DBIDUtil.newVar();
for(it.seek(0); it.getOffset() < n; it.advance()) {
p_i.from(pi, it); // p_i = pi[i]
pp_i.from(pi, p_i); // pp_i = pi[pi[i]]
if(DBIDUtil.equal(pp_i, id) && lambda.doubleValue(it) >= lambda.doubleValue(p_i)) {
pi.putDBID(it, id);
}
}
}
@Override
protected Logging getLogger() {
return LOG;
}
/**
* Parameterization class.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer<O> extends AbstractDistanceBasedAlgorithm.Parameterizer<O> {
@Override
protected CLINK<O> makeInstance() {
return new CLINK<>(distanceFunction);
}
}
}
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