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package de.lmu.ifi.dbs.elki.algorithm.clustering.kmeans.initialization;
/*
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 java.util.ArrayList;
import java.util.List;
import java.util.Random;
import de.lmu.ifi.dbs.elki.data.NumberVector;
import de.lmu.ifi.dbs.elki.database.Database;
import de.lmu.ifi.dbs.elki.database.datastore.DataStoreFactory;
import de.lmu.ifi.dbs.elki.database.datastore.DataStoreUtil;
import de.lmu.ifi.dbs.elki.database.datastore.WritableDoubleDataStore;
import de.lmu.ifi.dbs.elki.database.ids.ArrayModifiableDBIDs;
import de.lmu.ifi.dbs.elki.database.ids.DBIDIter;
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.DBIDs;
import de.lmu.ifi.dbs.elki.database.query.distance.DistanceQuery;
import de.lmu.ifi.dbs.elki.database.relation.Relation;
import de.lmu.ifi.dbs.elki.distance.distancefunction.NumberVectorDistanceFunction;
import de.lmu.ifi.dbs.elki.logging.LoggingUtil;
import de.lmu.ifi.dbs.elki.math.random.RandomFactory;
import de.lmu.ifi.dbs.elki.utilities.Alias;
import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
import de.lmu.ifi.dbs.elki.utilities.exceptions.AbortException;
/**
* K-Means++ initialization for k-means.
*
* Reference:
* <p>
* D. Arthur, S. Vassilvitskii<br />
* k-means++: the advantages of careful seeding<br />
* In: Proc. of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms,
* SODA 2007
* </p>
*
* @author Erich Schubert
* @since 0.5.0
*
* @param <O> Vector type
*/
@Reference(authors = "D. Arthur, S. Vassilvitskii", //
title = "k-means++: the advantages of careful seeding", //
booktitle = "Proc. of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007", //
url = "http://dx.doi.org/10.1145/1283383.1283494")
@Alias("de.lmu.ifi.dbs.elki.algorithm.clustering.kmeans.KMeansPlusPlusInitialMeans")
public class KMeansPlusPlusInitialMeans<O> extends AbstractKMeansInitialization<NumberVector> implements KMedoidsInitialization<O> {
/**
* Constructor.
*
* @param rnd Random generator.
*/
public KMeansPlusPlusInitialMeans(RandomFactory rnd) {
super(rnd);
}
@Override
public <T extends NumberVector, V extends NumberVector> List<V> chooseInitialMeans(Database database, Relation<T> relation, int k, NumberVectorDistanceFunction<? super T> distanceFunction, NumberVector.Factory<V> factory) {
DistanceQuery<T> distQ = database.getDistanceQuery(relation, distanceFunction);
DBIDs ids = relation.getDBIDs();
WritableDoubleDataStore weights = DataStoreUtil.makeDoubleStorage(ids, DataStoreFactory.HINT_HOT | DataStoreFactory.HINT_TEMP, 0.);
// Chose first mean
List<V> means = new ArrayList<>(k);
if(ids.size() <= k) {
throw new AbortException("Don't use k-means with k >= data set size.");
}
Random random = rnd.getSingleThreadedRandom();
DBIDRef first = DBIDUtil.randomSample(ids, random);
T firstvec = relation.get(first);
means.add(factory.newNumberVector(firstvec));
// Initialize weights
double weightsum = initialWeights(weights, ids, firstvec, distQ);
while(true) {
if(weightsum > Double.MAX_VALUE) {
LoggingUtil.warning("Could not choose a reasonable mean for k-means++ - too many data points, too large squared distances?");
}
if(weightsum < Double.MIN_NORMAL) {
LoggingUtil.warning("Could not choose a reasonable mean for k-means++ - to few data points?");
}
double r = random.nextDouble() * weightsum, s = 0.;
DBIDIter it = ids.iter();
for(; s < r && it.valid(); it.advance()) {
s += weights.doubleValue(it);
}
if(!it.valid()) { // Rare case, but happens due to floating math
weightsum -= (r - s); // Decrease
continue; // Retry
}
// Add new mean:
final T newmean = relation.get(it);
means.add(factory.newNumberVector(newmean));
if(means.size() >= k) {
break;
}
// Update weights:
weights.putDouble(it, 0.);
// Choose optimized version for double distances, if applicable.
weightsum = updateWeights(weights, ids, newmean, distQ);
}
// Explicitly destroy temporary data.
weights.destroy();
return means;
}
@Override
public DBIDs chooseInitialMedoids(int k, DBIDs ids, DistanceQuery<? super O> distQ) {
@SuppressWarnings("unchecked")
final Relation<O> rel = (Relation<O>) distQ.getRelation();
ArrayModifiableDBIDs means = DBIDUtil.newArray(k);
WritableDoubleDataStore weights = DataStoreUtil.makeDoubleStorage(ids, DataStoreFactory.HINT_HOT | DataStoreFactory.HINT_TEMP, 0.);
Random random = rnd.getSingleThreadedRandom();
DBIDRef first = DBIDUtil.randomSample(ids, random);
means.add(first);
// Initialize weights
double weightsum = initialWeights(weights, ids, rel.get(first), distQ);
while(true) {
if(weightsum > Double.MAX_VALUE) {
LoggingUtil.warning("Could not choose a reasonable mean for k-means++ - too many data points, too large squared distances?");
}
if(weightsum < Double.MIN_NORMAL) {
LoggingUtil.warning("Could not choose a reasonable mean for k-means++ - to few unique data points?");
}
double r = random.nextDouble() * weightsum;
while(r <= 0 && weightsum > Double.MIN_NORMAL) {
r = random.nextDouble() * weightsum; // Try harder to not choose 0.
}
DBIDIter it = ids.iter();
for(; r > 0. && it.valid(); it.advance()) {
r -= weights.doubleValue(it);
}
// Add new mean:
means.add(it);
if(means.size() >= k) {
break;
}
// Update weights:
weights.putDouble(it, 0.);
weightsum = updateWeights(weights, ids, rel.get(it), distQ);
}
return means;
}
/**
* Initialize the weight list.
*
* @param weights Weight list
* @param ids IDs
* @param latest Added ID
* @param distQ Distance query
* @return Weight sum
* @param <T> Object type
*/
protected <T> double initialWeights(WritableDoubleDataStore weights, DBIDs ids, T latest, DistanceQuery<? super T> distQ) {
double weightsum = 0.;
for(DBIDIter it = ids.iter(); it.valid(); it.advance()) {
// Distance will usually already be squared
double weight = distQ.distance(latest, it);
weights.putDouble(it, weight);
weightsum += weight;
}
return weightsum;
}
/**
* Update the weight list.
*
* @param weights Weight list
* @param ids IDs
* @param latest Added ID
* @param distQ Distance query
* @return Weight sum
* @param <T> Object type
*/
protected <T> double updateWeights(WritableDoubleDataStore weights, DBIDs ids, T latest, DistanceQuery<? super T> distQ) {
double weightsum = 0.;
for(DBIDIter it = ids.iter(); it.valid(); it.advance()) {
double weight = weights.doubleValue(it);
if(weight <= 0.) {
continue; // Duplicate, or already chosen.
}
double newweight = distQ.distance(latest, it);
if(newweight < weight) {
weights.putDouble(it, newweight);
weight = newweight;
}
weightsum += weight;
}
return weightsum;
}
/**
* Parameterization class.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer<V> extends AbstractKMeansInitialization.Parameterizer {
@Override
protected KMeansPlusPlusInitialMeans<V> makeInstance() {
return new KMeansPlusPlusInitialMeans<>(rnd);
}
}
}
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