/**
* Generates {@code d+1}-dimensional subspace candidates from the specified {@code d}-dimensional
* subspaces.
*
* @param subspaces the {@code d}-dimensional subspaces
* @return the {@code d+1}-dimensional subspace candidates
*/
private List<Subspace> generateSubspaceCandidates(List<Subspace> subspaces) {
List<Subspace> candidates = new ArrayList<>();
if (subspaces.isEmpty()) {
return candidates;
}
// Generate (d+1)-dimensional candidate subspaces
int d = subspaces.get(0).dimensionality();
StringBuilder msgFine = new StringBuilder("\n");
if (LOG.isDebuggingFiner()) {
msgFine.append("subspaces ").append(subspaces).append('\n');
}
for (int i = 0; i < subspaces.size(); i++) {
Subspace s1 = subspaces.get(i);
for (int j = i + 1; j < subspaces.size(); j++) {
Subspace s2 = subspaces.get(j);
Subspace candidate = s1.join(s2);
if (candidate != null) {
if (LOG.isDebuggingFiner()) {
msgFine.append("candidate: ").append(candidate.dimensonsToString()).append('\n');
}
// prune irrelevant candidate subspaces
List<Subspace> lowerSubspaces = lowerSubspaces(candidate);
if (LOG.isDebuggingFiner()) {
msgFine.append("lowerSubspaces: ").append(lowerSubspaces).append('\n');
}
boolean irrelevantCandidate = false;
for (Subspace s : lowerSubspaces) {
if (!subspaces.contains(s)) {
irrelevantCandidate = true;
break;
}
}
if (!irrelevantCandidate) {
candidates.add(candidate);
}
}
}
}
if (LOG.isDebuggingFiner()) {
LOG.debugFiner(msgFine.toString());
}
if (LOG.isDebugging()) {
StringBuilder msg = new StringBuilder();
msg.append(d + 1).append("-dimensional candidate subspaces: ");
for (Subspace candidate : candidates) {
msg.append(candidate.dimensonsToString()).append(' ');
}
LOG.debug(msg.toString());
}
return candidates;
}
/**
* Performs the SUBCLU algorithm on the given database.
*
* @param relation Relation to process
* @return Clustering result
*/
public Clustering<SubspaceModel> run(Relation<V> relation) {
final int dimensionality = RelationUtil.dimensionality(relation);
StepProgress stepprog = LOG.isVerbose() ? new StepProgress(dimensionality) : null;
// Generate all 1-dimensional clusters
LOG.beginStep(stepprog, 1, "Generate all 1-dimensional clusters.");
// mapping of dimensionality to set of subspaces
HashMap<Integer, List<Subspace>> subspaceMap = new HashMap<>();
// list of 1-dimensional subspaces containing clusters
List<Subspace> s_1 = new ArrayList<>();
subspaceMap.put(0, s_1);
// mapping of subspaces to list of clusters
TreeMap<Subspace, List<Cluster<Model>>> clusterMap =
new TreeMap<>(new Subspace.DimensionComparator());
for (int d = 0; d < dimensionality; d++) {
Subspace currentSubspace = new Subspace(d);
List<Cluster<Model>> clusters = runDBSCAN(relation, null, currentSubspace);
if (LOG.isDebuggingFiner()) {
StringBuilder msg = new StringBuilder();
msg.append('\n')
.append(clusters.size())
.append(" clusters in subspace ")
.append(currentSubspace.dimensonsToString())
.append(": \n");
for (Cluster<Model> cluster : clusters) {
msg.append(" " + cluster.getIDs() + "\n");
}
LOG.debugFiner(msg.toString());
}
if (!clusters.isEmpty()) {
s_1.add(currentSubspace);
clusterMap.put(currentSubspace, clusters);
}
}
// Generate (d+1)-dimensional clusters from d-dimensional clusters
for (int d = 0; d < dimensionality - 1; d++) {
if (stepprog != null) {
stepprog.beginStep(
d + 2,
"Generate "
+ (d + 2)
+ "-dimensional clusters from "
+ (d + 1)
+ "-dimensional clusters.",
LOG);
}
List<Subspace> subspaces = subspaceMap.get(d);
if (subspaces == null || subspaces.isEmpty()) {
if (stepprog != null) {
for (int dim = d + 1; dim < dimensionality - 1; dim++) {
stepprog.beginStep(
dim + 2,
"Generation of"
+ (dim + 2)
+ "-dimensional clusters not applicable, because no more "
+ (d + 2)
+ "-dimensional subspaces found.",
LOG);
}
}
break;
}
List<Subspace> candidates = generateSubspaceCandidates(subspaces);
List<Subspace> s_d = new ArrayList<>();
for (Subspace candidate : candidates) {
Subspace bestSubspace = bestSubspace(subspaces, candidate, clusterMap);
if (LOG.isDebuggingFine()) {
LOG.debugFine(
"best subspace of "
+ candidate.dimensonsToString()
+ ": "
+ bestSubspace.dimensonsToString());
}
List<Cluster<Model>> bestSubspaceClusters = clusterMap.get(bestSubspace);
List<Cluster<Model>> clusters = new ArrayList<>();
for (Cluster<Model> cluster : bestSubspaceClusters) {
List<Cluster<Model>> candidateClusters = runDBSCAN(relation, cluster.getIDs(), candidate);
if (!candidateClusters.isEmpty()) {
clusters.addAll(candidateClusters);
}
}
if (LOG.isDebuggingFine()) {
StringBuilder msg = new StringBuilder();
msg.append(clusters.size() + " cluster(s) in subspace " + candidate + ": \n");
for (Cluster<Model> c : clusters) {
msg.append(" " + c.getIDs() + "\n");
}
LOG.debugFine(msg.toString());
}
if (!clusters.isEmpty()) {
s_d.add(candidate);
clusterMap.put(candidate, clusters);
}
}
if (!s_d.isEmpty()) {
subspaceMap.put(d + 1, s_d);
}
}
// build result
int numClusters = 1;
result = new Clustering<>("SUBCLU clustering", "subclu-clustering");
for (Subspace subspace : clusterMap.descendingKeySet()) {
List<Cluster<Model>> clusters = clusterMap.get(subspace);
for (Cluster<Model> cluster : clusters) {
Cluster<SubspaceModel> newCluster = new Cluster<>(cluster.getIDs());
newCluster.setModel(new SubspaceModel(subspace, Centroid.make(relation, cluster.getIDs())));
newCluster.setName("cluster_" + numClusters++);
result.addToplevelCluster(newCluster);
}
}
LOG.setCompleted(stepprog);
return result;
}
/**
* Performs a single run of DOC, finding a single cluster.
*
* @param database Database context
* @param relation used to get actual values for DBIDs.
* @param S The set of points we're working on.
* @param d Dimensionality of the data set we're currently working on.
* @param r Size of random samples.
* @param m Number of inner iterations (per seed point).
* @param n Number of outer iterations (seed points).
* @param minClusterSize Minimum size a cluster must have to be accepted.
* @return a cluster, if one is found, else <code>null</code>.
*/
private Cluster<SubspaceModel> runDOC(
Database database,
Relation<V> relation,
ArrayModifiableDBIDs S,
final int d,
int n,
int m,
int r,
int minClusterSize) {
// Best cluster for the current run.
DBIDs C = null;
// Relevant attributes for the best cluster.
long[] D = null;
// Quality of the best cluster.
double quality = Double.NEGATIVE_INFINITY;
// Bounds for our cluster.
// ModifiableHyperBoundingBox bounds = new ModifiableHyperBoundingBox(new
// double[d], new double[d]);
// Weights for distance (= rectangle query)
SubspaceMaximumDistanceFunction df = new SubspaceMaximumDistanceFunction(BitsUtil.zero(d));
DistanceQuery<V> dq = database.getDistanceQuery(relation, df);
RangeQuery<V> rq = database.getRangeQuery(dq);
// Inform the user about the progress in the current iteration.
FiniteProgress iprogress =
LOG.isVerbose()
? new FiniteProgress("Iteration progress for current cluster", m * n, LOG)
: null;
Random random = rnd.getSingleThreadedRandom();
DBIDArrayIter iter = S.iter();
for (int i = 0; i < n; ++i) {
// Pick a random seed point.
iter.seek(random.nextInt(S.size()));
for (int j = 0; j < m; ++j) {
// Choose a set of random points.
DBIDs randomSet = DBIDUtil.randomSample(S, r, random);
// Initialize cluster info.
long[] nD = BitsUtil.zero(d);
// Test each dimension and build bounding box.
for (int k = 0; k < d; ++k) {
if (dimensionIsRelevant(k, relation, randomSet)) {
BitsUtil.setI(nD, k);
}
}
if (BitsUtil.cardinality(nD) > 0) {
// Get all points in the box.
df.setSelectedDimensions(nD);
// TODO: add filtering capabilities into query API!
DBIDs nC = DBIDUtil.intersection(S, rq.getRangeForDBID(iter, w));
if (LOG.isDebuggingFiner()) {
LOG.finer(
"Testing a cluster candidate, |C| = "
+ nC.size()
+ ", |D| = "
+ BitsUtil.cardinality(nD));
}
// Is the cluster large enough?
if (nC.size() < minClusterSize) {
// Too small.
if (LOG.isDebuggingFiner()) {
LOG.finer("... but it's too small.");
}
} else {
// Better cluster than before?
double nQuality = computeClusterQuality(nC.size(), BitsUtil.cardinality(nD));
if (nQuality > quality) {
if (LOG.isDebuggingFiner()) {
LOG.finer("... and it's the best so far: " + nQuality + " vs. " + quality);
}
C = nC;
D = nD;
quality = nQuality;
} else {
if (LOG.isDebuggingFiner()) {
LOG.finer("... but we already have a better one.");
}
}
}
}
LOG.incrementProcessed(iprogress);
}
}
LOG.ensureCompleted(iprogress);
return (C != null) ? makeCluster(relation, C, D) : null;
}