/**
* 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;
}
/**
* Evaluate a single clustering.
*
* @param db Database
* @param rel Data relation
* @param c Clustering
* @return Gamma index
*/
public double evaluateClustering(
Database db, Relation<? extends NumberVector> rel, Clustering<?> c) {
List<? extends Cluster<?>> clusters = c.getAllClusters();
int ignorednoise = 0, withinPairs = 0;
for (Cluster<?> cluster : clusters) {
if ((cluster.size() <= 1 || cluster.isNoise())) {
switch (noiseHandling) {
case IGNORE_NOISE:
ignorednoise += cluster.size();
continue;
case TREAT_NOISE_AS_SINGLETONS:
continue; // No concordant distances.
case MERGE_NOISE:
break; // Treat like a cluster below.
}
}
withinPairs += (cluster.size() * (cluster.size() - 1)) >>> 1;
if (withinPairs < 0) {
throw new AbortException(
"Integer overflow - clusters too large to compute pairwise distances.");
}
}
// Materialize within-cluster distances (sorted):
double[] withinDistances = computeWithinDistances(rel, clusters, withinPairs);
int[] withinTies = new int[withinDistances.length];
// Count ties within
countTies(withinDistances, withinTies);
long concordantPairs = 0, discordantPairs = 0, betweenPairs = 0;
// Step two, compute discordant distances:
for (int i = 0; i < clusters.size(); i++) {
Cluster<?> ocluster1 = clusters.get(i);
if ((ocluster1.size() <= 1 || ocluster1.isNoise()) //
&& noiseHandling.equals(NoiseHandling.IGNORE_NOISE)) {
continue;
}
for (int j = i + 1; j < clusters.size(); j++) {
Cluster<?> ocluster2 = clusters.get(j);
if ((ocluster2.size() <= 1 || ocluster2.isNoise()) //
&& noiseHandling.equals(NoiseHandling.IGNORE_NOISE)) {
continue;
}
betweenPairs += ocluster1.size() * ocluster2.size();
for (DBIDIter oit1 = ocluster1.getIDs().iter(); oit1.valid(); oit1.advance()) {
NumberVector obj = rel.get(oit1);
for (DBIDIter oit2 = ocluster2.getIDs().iter(); oit2.valid(); oit2.advance()) {
double dist = distanceFunction.distance(obj, rel.get(oit2));
int p = Arrays.binarySearch(withinDistances, dist);
if (p >= 0) { // Tied distances:
while (p > 0 && withinDistances[p - 1] >= dist) {
--p;
}
concordantPairs += p;
discordantPairs += withinDistances.length - p - withinTies[p];
continue;
}
p = -p - 1;
concordantPairs += p;
discordantPairs += withinDistances.length - p;
}
}
}
}
// Total number of pairs possible:
final long t = ((rel.size() - ignorednoise) * (long) (rel.size() - ignorednoise - 1)) >>> 1;
final long tt = (t * (t - 1)) >>> 1;
final double gamma =
(concordantPairs - discordantPairs) / (double) (concordantPairs + discordantPairs);
final double tau =
computeTau(concordantPairs, discordantPairs, tt, withinDistances.length, betweenPairs);
if (LOG.isStatistics()) {
LOG.statistics(new StringStatistic(key + ".pbm.noise-handling", noiseHandling.toString()));
if (ignorednoise > 0) {
LOG.statistics(new LongStatistic(key + ".pbm.ignored", ignorednoise));
}
LOG.statistics(new DoubleStatistic(key + ".gamma", gamma));
LOG.statistics(new DoubleStatistic(key + ".tau", tau));
}
EvaluationResult ev =
EvaluationResult.findOrCreate(
db.getHierarchy(), c, "Internal Clustering Evaluation", "internal evaluation");
MeasurementGroup g = ev.findOrCreateGroup("Concordance-based Evaluation");
g.addMeasure("Gamma", gamma, -1., 1., 0., false);
g.addMeasure("Tau", tau, -1., +1., 0., false);
db.getHierarchy().resultChanged(ev);
return gamma;
}
/**
* Performs the DOC or FastDOC (as configured) algorithm on the given Database.
*
* <p>This will run exhaustively, i.e. run DOC until no clusters are found anymore / the database
* size has shrunk below the threshold for minimum cluster size.
*
* @param database Database
* @param relation Data relation
*/
public Clustering<SubspaceModel> run(Database database, Relation<V> relation) {
// Dimensionality of our set.
final int d = RelationUtil.dimensionality(relation);
// Get available DBIDs as a set we can remove items from.
ArrayModifiableDBIDs S = DBIDUtil.newArray(relation.getDBIDs());
// Precompute values as described in Figure 2.
double r = Math.abs(Math.log(d + d) / Math.log(beta * .5));
// Outer loop count.
int n = (int) (2. / alpha);
// Inner loop count.
int m = (int) (Math.pow(2. / alpha, r) * Math.log(4));
if (heuristics) {
m = Math.min(m, Math.min(1000000, d * d));
}
// Minimum size for a cluster for it to be accepted.
int minClusterSize = (int) (alpha * S.size());
// List of all clusters we found.
Clustering<SubspaceModel> result = new Clustering<>("DOC Clusters", "DOC");
// Inform the user about the number of actual clusters found so far.
IndefiniteProgress cprogress =
LOG.isVerbose() ? new IndefiniteProgress("Number of clusters", LOG) : null;
// To not only find a single cluster, we continue running until our set
// of points is empty.
while (S.size() > minClusterSize) {
Cluster<SubspaceModel> C;
if (heuristics) {
C = runFastDOC(database, relation, S, d, n, m, (int) r);
} else {
C = runDOC(database, relation, S, d, n, m, (int) r, minClusterSize);
}
if (C == null) {
// Stop trying if we couldn't find a cluster.
break;
}
// Found a cluster, remember it, remove its points from the set.
result.addToplevelCluster(C);
// Remove all points of the cluster from the set and continue.
S.removeDBIDs(C.getIDs());
if (cprogress != null) {
cprogress.setProcessed(result.getAllClusters().size(), LOG);
}
}
// Add the remainder as noise.
if (S.size() > 0) {
long[] alldims = BitsUtil.ones(d);
result.addToplevelCluster(
new Cluster<>(
S,
true,
new SubspaceModel(new Subspace(alldims), Centroid.make(relation, S).getArrayRef())));
}
LOG.setCompleted(cprogress);
return result;
}
/**
* Evaluate a single clustering.
*
* @param db Database
* @param rel Data relation
* @param c Clustering
* @return Mean simplified silhouette
*/
public double evaluateClustering(
Database db, Relation<? extends NumberVector> rel, Clustering<?> c) {
List<? extends Cluster<?>> clusters = c.getAllClusters();
NumberVector[] centroids = new NumberVector[clusters.size()];
int ignorednoise = centroids(rel, clusters, centroids, noiseOption);
MeanVariance mssil = new MeanVariance();
Iterator<? extends Cluster<?>> ci = clusters.iterator();
for (int i = 0; ci.hasNext(); i++) {
Cluster<?> cluster = ci.next();
if (cluster.size() <= 1) {
// As suggested in Rousseeuw, we use 0 for singletons.
mssil.put(0., cluster.size());
continue;
}
if (cluster.isNoise()) {
switch (noiseOption) {
case IGNORE_NOISE:
continue; // Ignore elements
case TREAT_NOISE_AS_SINGLETONS:
// As suggested in Rousseeuw, we use 0 for singletons.
mssil.put(0., cluster.size());
continue;
case MERGE_NOISE:
break; // Treat as cluster below
}
}
// Cluster center:
final NumberVector center = centroids[i];
assert (center != null);
for (DBIDIter it = cluster.getIDs().iter(); it.valid(); it.advance()) {
NumberVector obj = rel.get(it);
// a: Distance to own centroid
double a = distance.distance(center, obj);
// b: Distance to other clusters centroids:
double min = Double.POSITIVE_INFINITY;
Iterator<? extends Cluster<?>> cj = clusters.iterator();
for (int j = 0; cj.hasNext(); j++) {
Cluster<?> ocluster = cj.next();
if (i == j) {
continue;
}
NumberVector other = centroids[j];
if (other == null) { // Noise!
switch (noiseOption) {
case IGNORE_NOISE:
continue;
case TREAT_NOISE_AS_SINGLETONS:
// Treat each object like a centroid!
for (DBIDIter it2 = ocluster.getIDs().iter(); it2.valid(); it2.advance()) {
double dist = distance.distance(rel.get(it2), obj);
min = dist < min ? dist : min;
}
continue;
case MERGE_NOISE:
break; // Treat as cluster below, but should not be reachable.
}
}
// Clusters: use centroid.
double dist = distance.distance(other, obj);
min = dist < min ? dist : min;
}
// One 'real' cluster only?
min = min < Double.POSITIVE_INFINITY ? min : a;
mssil.put((min - a) / (min > a ? min : a));
}
}
double penalty = 1.;
// Only if {@link NoiseHandling#IGNORE_NOISE}:
if (penalize && ignorednoise > 0) {
penalty = (rel.size() - ignorednoise) / (double) rel.size();
}
final double meanssil = penalty * mssil.getMean();
final double stdssil = penalty * mssil.getSampleStddev();
if (LOG.isStatistics()) {
LOG.statistics(
new StringStatistic(
key + ".simplified-silhouette.noise-handling", noiseOption.toString()));
if (ignorednoise > 0) {
LOG.statistics(new LongStatistic(key + ".simplified-silhouette.ignored", ignorednoise));
}
LOG.statistics(new DoubleStatistic(key + ".simplified-silhouette.mean", meanssil));
LOG.statistics(new DoubleStatistic(key + ".simplified-silhouette.stddev", stdssil));
}
EvaluationResult ev =
EvaluationResult.findOrCreate(
db.getHierarchy(), c, "Internal Clustering Evaluation", "internal evaluation");
MeasurementGroup g = ev.findOrCreateGroup("Distance-based Evaluation");
g.addMeasure(
"Simp. Silhouette +-" + FormatUtil.NF2.format(stdssil), meanssil, -1., 1., 0., false);
db.getHierarchy().resultChanged(ev);
return meanssil;
}
protected void autoEvaluateOutliers(ResultHierarchy hier, Result newResult) {
Collection<OutlierResult> outliers =
ResultUtil.filterResults(hier, newResult, OutlierResult.class);
if (LOG.isDebugging()) {
LOG.debug("Number of new outlier results: " + outliers.size());
}
if (outliers.size() > 0) {
Database db = ResultUtil.findDatabase(hier);
ResultUtil.ensureClusteringResult(db, db);
Collection<Clustering<?>> clusterings = ResultUtil.filterResults(hier, db, Clustering.class);
if (clusterings.size() == 0) {
LOG.warning(
"Could not find a clustering result, even after running 'ensureClusteringResult'?!?");
return;
}
Clustering<?> basec = clusterings.iterator().next();
// Find minority class label
int min = Integer.MAX_VALUE;
int total = 0;
String label = null;
if (basec.getAllClusters().size() > 1) {
for (Cluster<?> c : basec.getAllClusters()) {
final int csize = c.getIDs().size();
total += csize;
if (csize < min) {
min = csize;
label = c.getName();
}
}
}
if (label == null) {
LOG.warning("Could not evaluate outlier results, as I could not find a minority label.");
return;
}
if (min == 1) {
LOG.warning(
"The minority class label had a single object. Try using 'ClassLabelFilter' to identify the class label column.");
}
if (min > 0.05 * total) {
LOG.warning(
"The minority class I discovered (labeled '"
+ label
+ "') has "
+ (min * 100. / total)
+ "% of objects. Outlier classes should be more rare!");
}
LOG.verbose("Evaluating using minority class: " + label);
Pattern pat = Pattern.compile("^" + Pattern.quote(label) + "$");
// Evaluate rankings.
new OutlierRankingEvaluation(pat).processNewResult(hier, newResult);
// Compute ROC curve
new OutlierROCCurve(pat).processNewResult(hier, newResult);
// Compute Precision at k
new OutlierPrecisionAtKCurve(pat, min << 1).processNewResult(hier, newResult);
// Compute ROC curve
new OutlierPrecisionRecallCurve(pat).processNewResult(hier, newResult);
// Compute outlier histogram
new ComputeOutlierHistogram(pat, 50, new LinearScaling(), false)
.processNewResult(hier, newResult);
}
}
/**
* Evaluate a single clustering.
*
* @param db Database
* @param rel Data relation
* @param c Clustering
* @return C-Index
*/
public double evaluateClustering(
Database db, Relation<? extends O> rel, DistanceQuery<O> dq, Clustering<?> c) {
List<? extends Cluster<?>> clusters = c.getAllClusters();
// theta is the sum, w the number of within group distances
double theta = 0;
int w = 0;
int ignorednoise = 0;
int isize = clusters.size() <= 1 ? rel.size() : rel.size() / (clusters.size() - 1);
DoubleArray pairDists = new DoubleArray(isize);
for (int i = 0; i < clusters.size(); i++) {
Cluster<?> cluster = clusters.get(i);
if (cluster.size() <= 1 || cluster.isNoise()) {
switch (noiseOption) {
case IGNORE_NOISE:
ignorednoise += cluster.size();
continue; // Ignore
case TREAT_NOISE_AS_SINGLETONS:
continue; // No within-cluster distances!
case MERGE_NOISE:
break; // Treat like a cluster
}
}
for (DBIDIter it1 = cluster.getIDs().iter(); it1.valid(); it1.advance()) {
O obj = rel.get(it1);
// Compare object to every cluster, but only once
for (int j = i; j < clusters.size(); j++) {
Cluster<?> ocluster = clusters.get(j);
if (ocluster.size() <= 1 || ocluster.isNoise()) {
switch (noiseOption) {
case IGNORE_NOISE:
continue; // Ignore this cluster.
case TREAT_NOISE_AS_SINGLETONS:
case MERGE_NOISE:
break; // Treat like a cluster
}
}
for (DBIDIter it2 = ocluster.getIDs().iter(); it2.valid(); it2.advance()) {
if (DBIDUtil.compare(it1, it2) <= 0) { // Only once.
continue;
}
double dist = dq.distance(obj, rel.get(it2));
pairDists.add(dist);
if (ocluster == cluster) { // Within-cluster distances.
theta += dist;
w++;
}
}
}
}
}
// Simulate best and worst cases:
pairDists.sort();
double min = 0, max = 0;
for (int i = 0, j = pairDists.size() - 1; i < w; i++, j--) {
min += pairDists.get(i);
max += pairDists.get(j);
}
double cIndex = (max > min) ? (theta - min) / (max - min) : 0.;
if (LOG.isStatistics()) {
LOG.statistics(new StringStatistic(key + ".c-index.noise-handling", noiseOption.toString()));
if (ignorednoise > 0) {
LOG.statistics(new LongStatistic(key + ".c-index.ignored", ignorednoise));
}
LOG.statistics(new DoubleStatistic(key + ".c-index", cIndex));
}
EvaluationResult ev =
EvaluationResult.findOrCreate(
db.getHierarchy(), c, "Internal Clustering Evaluation", "internal evaluation");
MeasurementGroup g = ev.findOrCreateGroup("Distance-based Evaluation");
g.addMeasure("C-Index", cIndex, 0., 1., 0., true);
db.getHierarchy().resultChanged(ev);
return cIndex;
}
