/**
* Runs the DBSCAN algorithm on the specified partition of the database in the given subspace. If
* parameter {@code ids} is null DBSCAN will be applied to the whole database.
*
* @param relation the database holding the objects to run DBSCAN on
* @param ids the IDs of the database defining the partition to run DBSCAN on - if this parameter
* is null DBSCAN will be applied to the whole database
* @param subspace the subspace to run DBSCAN on
* @return the clustering result of the DBSCAN run
*/
private List<Cluster<Model>> runDBSCAN(Relation<V> relation, DBIDs ids, Subspace subspace) {
// distance function
distanceFunction.setSelectedDimensions(subspace.getDimensions());
ProxyDatabase proxy;
if (ids == null) {
// TODO: in this case, we might want to use an index - the proxy below
// will prevent this!
ids = relation.getDBIDs();
}
proxy = new ProxyDatabase(ids, relation);
DBSCAN<V> dbscan = new DBSCAN<>(distanceFunction, epsilon, minpts);
// run DBSCAN
if (LOG.isVerbose()) {
LOG.verbose("\nRun DBSCAN on subspace " + subspace.dimensonsToString());
}
Clustering<Model> dbsres = dbscan.run(proxy);
// separate cluster and noise
List<Cluster<Model>> clusterAndNoise = dbsres.getAllClusters();
List<Cluster<Model>> clusters = new ArrayList<>();
for (Cluster<Model> c : clusterAndNoise) {
if (!c.isNoise()) {
clusters.add(c);
}
}
return clusters;
}
/**
* Returns the list of all {@code (d-1)}-dimensional subspaces of the specified {@code
* d}-dimensional subspace.
*
* @param subspace the {@code d}-dimensional subspace
* @return a list of all {@code (d-1)}-dimensional subspaces
*/
private List<Subspace> lowerSubspaces(Subspace subspace) {
int dimensionality = subspace.dimensionality();
if (dimensionality <= 1) {
return null;
}
// order result according to the dimensions
List<Subspace> result = new ArrayList<>();
long[] dimensions = subspace.getDimensions();
for (int dim = BitsUtil.nextSetBit(dimensions, 0);
dim >= 0;
dim = BitsUtil.nextSetBit(dimensions, dim + 1)) {
long[] newDimensions = dimensions.clone();
BitsUtil.clearI(newDimensions, dim);
result.add(new Subspace(newDimensions));
}
return result;
}
/**
* 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;
}
/**
* Determines the {@code d}-dimensional subspace of the {@code (d+1)} -dimensional candidate with
* minimal number of objects in the cluster.
*
* @param subspaces the list of {@code d}-dimensional subspaces containing clusters
* @param candidate the {@code (d+1)}-dimensional candidate subspace
* @param clusterMap the mapping of subspaces to clusters
* @return the {@code d}-dimensional subspace of the {@code (d+1)} -dimensional candidate with
* minimal number of objects in the cluster
*/
private Subspace bestSubspace(
List<Subspace> subspaces,
Subspace candidate,
TreeMap<Subspace, List<Cluster<Model>>> clusterMap) {
Subspace bestSubspace = null;
for (Subspace subspace : subspaces) {
int min = Integer.MAX_VALUE;
if (subspace.isSubspace(candidate)) {
List<Cluster<Model>> clusters = clusterMap.get(subspace);
for (Cluster<Model> cluster : clusters) {
int clusterSize = cluster.size();
if (clusterSize < min) {
min = clusterSize;
bestSubspace = subspace;
}
}
}
}
return bestSubspace;
}
/**
* 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;
}