tutorial.clustering.NaiveAgglomerativeHierarchicalClustering3 Maven / Gradle / Ivy
/*
* This file is part of ELKI:
* Environment for Developing KDD-Applications Supported by Index-Structures
*
* Copyright (C) 2019
* 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
* This is the third step, where we add support for different linkage
* strategies.
*
* This is the naive O(n³) algorithm. See {@link SLINK} for a much faster
* algorithm (however, only for single-linkage).
*
* Reference (for the update formulas):
*
* R. M. Cormack
* A Review of Classification
* Journal of the Royal Statistical Society. Series A, Vol. 134, No. 3
*
* @author Erich Schubert
* @since 0.6.0
*
* @param Object type
*/
@Reference(authors = "R. M. Cormack", //
title = "A Review of Classification", //
booktitle = "Journal of the Royal Statistical Society. Series A, Vol. 134, No. 3", //
url = "https://doi.org/10.2307/2344237", //
bibkey = "doi:10.2307/2344237")
public class NaiveAgglomerativeHierarchicalClustering3 extends AbstractDistanceBasedAlgorithm {
/**
* Class logger
*/
private static final Logging LOG = Logging.getLogger(NaiveAgglomerativeHierarchicalClustering3.class);
/**
* Different linkage strategies.
*
* The update formulas here come from:
* R. M. Cormack, A Review of Classification
*
* @author Erich Schubert
*/
public enum Linkage {//
SINGLE {
@Override
public double combine(int sizex, double dx, int sizey, double dy, int sizej, double dxy) {
return Math.min(dx, dy);
}
}, // single-linkage hierarchical clustering
COMPLETE {
@Override
public double combine(int sizex, double dx, int sizey, double dy, int sizej, double dxy) {
return Math.max(dx, dy);
}
}, // complete-linkage hierarchical clustering
GROUP_AVERAGE {
@Override
public double combine(int sizex, double dx, int sizey, double dy, int sizej, double dxy) {
final double wx = sizex / (double) (sizex + sizey);
final double wy = sizey / (double) (sizex + sizey);
return wx * dx + wy * dy;
}
}, // average-linkage hierarchical clustering
WEIGHTED_AVERAGE {
@Override
public double combine(int sizex, double dx, int sizey, double dy, int sizej, double dxy) {
return .5 * (dx + dy);
}
}, // a more naive variant, McQuitty (1966)
CENTROID {
@Override
public double combine(int sizex, double dx, int sizey, double dy, int sizej, double dxy) {
final double wx = sizex / (double) (sizex + sizey);
final double wy = sizey / (double) (sizex + sizey);
final double beta = (sizex * sizey) / (double) ((sizex + sizey) * (sizex + sizey));
return wx * dx + wy * dy - beta * dxy;
}
}, // Sokal and Michener (1958), Gower (1967)
MEDIAN {
@Override
public double combine(int sizex, double dx, int sizey, double dy, int sizej, double dxy) {
return .5 * (dx + dy) - .25 * dxy;
}
}, // Gower (1967)
WARD {
@Override
public double combine(int sizex, double dx, int sizey, double dy, int sizej, double dxy) {
final double wx = (sizex + sizej) / (double) (sizex + sizey + sizej);
final double wy = (sizey + sizej) / (double) (sizex + sizey + sizej);
final double beta = sizej / (double) (sizex + sizey + sizej);
return wx * dx + wy * dy - beta * dxy;
}
}, // Minimum Variance, Wishart (1969), Anderson (1971)
;
abstract public double combine(int sizex, double dx, int sizey, double dy, int sizej, double dxy);
}
/**
* Threshold, how many clusters to extract.
*/
int numclusters;
/**
* Current linkage in use.
*/
Linkage linkage = Linkage.WARD;
/**
* Constructor.
*
* @param distanceFunction Distance function to use
* @param numclusters Number of clusters
* @param linkage Linkage strategy
*/
public NaiveAgglomerativeHierarchicalClustering3(DistanceFunction distanceFunction, int numclusters, Linkage linkage) {
super(distanceFunction);
this.numclusters = numclusters;
this.linkage = linkage;
}
/**
* Run the algorithm
*
* @param db Database
* @param relation Relation
* @return Clustering hierarchy
*/
public Result run(Database db, Relation relation) {
DistanceQuery dq = db.getDistanceQuery(relation, getDistanceFunction());
ArrayDBIDs ids = DBIDUtil.ensureArray(relation.getDBIDs());
final int size = ids.size();
if(size > 0x10000) {
throw new AbortException("This implementation does not scale to data sets larger than " + 0x10000 + " instances (~17 GB RAM), which results in an integer overflow.");
}
if(Linkage.SINGLE.equals(linkage)) {
LOG.verbose("Notice: SLINK is a much faster algorithm for single-linkage clustering!");
}
// Compute the initial (lower triangular) distance matrix.
double[] scratch = new double[triangleSize(size)];
DBIDArrayIter ix = ids.iter(), iy = ids.iter();
// Position counter - must agree with computeOffset!
int pos = 0;
boolean square = Linkage.WARD.equals(linkage) && !getDistanceFunction().isSquared();
for(int x = 0; ix.valid(); x++, ix.advance()) {
iy.seek(0);
for(int y = 0; y < x; y++, iy.advance()) {
scratch[pos] = dq.distance(ix, iy);
// Ward uses variances -- i.e. squared values
if(square) {
scratch[pos] *= scratch[pos];
}
pos++;
}
}
// Initialize space for result:
double[] height = new double[size];
Arrays.fill(height, Double.POSITIVE_INFINITY);
// Parent node, to track merges
// have every object point to itself initially
ArrayModifiableDBIDs parent = DBIDUtil.newArray(ids);
// Active clusters, when not trivial.
Int2ReferenceMap clusters = new Int2ReferenceOpenHashMap<>();
// Repeat until everything merged, except the desired number of clusters:
final int stop = size - numclusters;
FiniteProgress prog = LOG.isVerbose() ? new FiniteProgress("Agglomerative clustering", stop, LOG) : null;
for(int i = 0; i < stop; i++) {
double min = Double.POSITIVE_INFINITY;
int minx = -1, miny = -1;
for(int x = 0; x < size; x++) {
if(height[x] < Double.POSITIVE_INFINITY) {
continue;
}
final int xbase = triangleSize(x);
for(int y = 0; y < x; y++) {
if(height[y] < Double.POSITIVE_INFINITY) {
continue;
}
final int idx = xbase + y;
if(scratch[idx] < min) {
min = scratch[idx];
minx = x;
miny = y;
}
}
}
assert (minx >= 0 && miny >= 0);
// Avoid allocating memory, by reusing existing iterators:
ix.seek(minx);
iy.seek(miny);
// Perform merge in data structure: x -> y
// Since y < x, prefer keeping y, dropping x.
height[minx] = min;
parent.set(minx, iy);
// Merge into cluster
ModifiableDBIDs cx = clusters.get(minx);
ModifiableDBIDs cy = clusters.get(miny);
int sizex = 1, sizey = 1; // cluster sizes, for averaging
if(cy == null) {
cy = DBIDUtil.newHashSet();
cy.add(iy);
}
else {
sizey = cy.size();
}
if(cx == null) {
cy.add(ix);
}
else {
sizex = cx.size();
cy.addDBIDs(cx);
clusters.remove(minx);
}
clusters.put(miny, cy);
// Update distance matrix. Note: miny < minx
// Implementation note: most will not need sizej, and could save the
// hashmap lookup.
final int xbase = triangleSize(minx), ybase = triangleSize(miny);
// Write to (y, j), with j < y
for(int j = 0; j < miny; j++) {
if(height[j] < Double.POSITIVE_INFINITY) {
continue;
}
final DBIDs idsj = clusters.get(j);
final int sizej = (idsj == null) ? 1 : idsj.size();
scratch[ybase + j] = linkage.combine(sizex, scratch[xbase + j], sizey, scratch[ybase + j], sizej, min);
}
// Write to (j, y), with y < j < x
for(int j = miny + 1; j < minx; j++) {
if(height[j] < Double.POSITIVE_INFINITY) {
continue;
}
final int jbase = triangleSize(j);
final DBIDs idsj = clusters.get(j);
final int sizej = (idsj == null) ? 1 : idsj.size();
scratch[jbase + miny] = linkage.combine(sizex, scratch[xbase + j], sizey, scratch[jbase + miny], sizej, min);
}
// Write to (j, y), with y < x < j
for(int j = minx + 1; j < size; j++) {
if(height[j] < Double.POSITIVE_INFINITY) {
continue;
}
final DBIDs idsj = clusters.get(j);
final int sizej = (idsj == null) ? 1 : idsj.size();
final int jbase = triangleSize(j);
scratch[jbase + miny] = linkage.combine(sizex, scratch[jbase + minx], sizey, scratch[jbase + miny], sizej, min);
}
LOG.incrementProcessed(prog);
}
LOG.ensureCompleted(prog);
// Build the clustering result
final Clustering dendrogram = new Clustering<>("Hierarchical-Clustering", "hierarchical-clustering");
for(int x = 0; x < size; x++) {
if(height[x] < Double.POSITIVE_INFINITY) {
DBIDs cids = clusters.get(x);
if(cids == null) {
ix.seek(x);
cids = DBIDUtil.deref(ix);
}
Cluster cluster = new Cluster<>("Cluster", cids);
dendrogram.addToplevelCluster(cluster);
}
}
return dendrogram;
}
/**
* Compute the size of a complete x by x triangle (minus diagonal)
*
* @param x Offset
* @return Size of complete triangle
*/
protected static int triangleSize(int x) {
return (x * (x - 1)) >>> 1;
}
@Override
public TypeInformation[] getInputTypeRestriction() {
// The input relation must match our distance function:
return TypeUtil.array(getDistanceFunction().getInputTypeRestriction());
}
@Override
protected Logging getLogger() {
return LOG;
}
/**
* Parameterization class
*
* @author Erich Schubert
*
* @hidden
*
* @param Object type
*/
public static class Parameterizer extends AbstractDistanceBasedAlgorithm.Parameterizer {
/**
* Option ID for linkage parameter.
*/
private static final OptionID LINKAGE_ID = new OptionID("hierarchical.linkage", "Parameter to choose the linkage strategy.");
/**
* Desired number of clusters.
*/
int numclusters = 0;
/**
* Current linkage in use.
*/
protected Linkage linkage = Linkage.SINGLE;
@Override
protected void makeOptions(Parameterization config) {
super.makeOptions(config);
IntParameter numclustersP = new IntParameter(CutDendrogramByNumberOfClusters.Parameterizer.MINCLUSTERS_ID) //
.addConstraint(CommonConstraints.GREATER_EQUAL_ONE_INT);
if(config.grab(numclustersP)) {
numclusters = numclustersP.intValue();
}
EnumParameter linkageP = new EnumParameter<>(LINKAGE_ID, Linkage.class) //
.setDefaultValue(Linkage.WARD);
if(config.grab(linkageP)) {
linkage = linkageP.getValue();
}
}
@Override
protected NaiveAgglomerativeHierarchicalClustering3 makeInstance() {
return new NaiveAgglomerativeHierarchicalClustering3<>(distanceFunction, numclusters, linkage);
}
}
}