/**
* Preprocessing step: determine the radii of interest for each point.
*
* @param ids IDs to process
* @param rangeQuery Range query
* @param interestingDistances Distances of interest
*/
protected void precomputeInterestingRadii(
DBIDs ids,
RangeQuery<O> rangeQuery,
WritableDataStore<DoubleIntArrayList> interestingDistances) {
FiniteProgress progressPreproc =
LOG.isVerbose() ? new FiniteProgress("LOCI preprocessing", ids.size(), LOG) : null;
for (DBIDIter iditer = ids.iter(); iditer.valid(); iditer.advance()) {
DoubleDBIDList neighbors = rangeQuery.getRangeForDBID(iditer, rmax);
// build list of critical distances
DoubleIntArrayList cdist = new DoubleIntArrayList(neighbors.size() << 1);
{
int i = 0;
DoubleDBIDListIter ni = neighbors.iter();
while (ni.valid()) {
final double curdist = ni.doubleValue();
++i;
ni.advance();
// Skip, if tied to the next object:
if (ni.valid() && curdist == ni.doubleValue()) {
continue;
}
cdist.append(curdist, i);
// Scale radius, and reinsert
if (alpha != 1.) {
final double ri = curdist / alpha;
if (ri <= rmax) {
cdist.append(ri, Integer.MIN_VALUE);
}
}
}
}
cdist.sort();
// fill the gaps to have fast lookups of number of neighbors at a given
// distance.
int lastk = 0;
for (int i = 0, size = cdist.size(); i < size; i++) {
final int k = cdist.getInt(i);
if (k == Integer.MIN_VALUE) {
cdist.setValue(i, lastk);
} else {
lastk = k;
}
}
// TODO: shrink the list, removing duplicate radii?
interestingDistances.put(iditer, cdist);
LOG.incrementProcessed(progressPreproc);
}
LOG.ensureCompleted(progressPreproc);
}
@Override
public void run() {
Database database = input.getDatabase();
Relation<O> relation = database.getRelation(distance.getInputTypeRestriction());
DistanceQuery<O> distanceQuery = database.getDistanceQuery(relation, distance);
KNNQuery<O> knnQ = database.getKNNQuery(distanceQuery, DatabaseQuery.HINT_HEAVY_USE);
// open file.
try (RandomAccessFile file = new RandomAccessFile(out, "rw");
FileChannel channel = file.getChannel();
// and acquire a file write lock
FileLock lock = channel.lock()) {
// write magic header
file.writeInt(KNN_CACHE_MAGIC);
int bufsize = k * 12 * 2 + 10; // Initial size, enough for 2 kNN.
ByteBuffer buffer = ByteBuffer.allocateDirect(bufsize);
FiniteProgress prog =
LOG.isVerbose() ? new FiniteProgress("Computing kNN", relation.size(), LOG) : null;
for (DBIDIter it = relation.iterDBIDs(); it.valid(); it.advance()) {
final KNNList nn = knnQ.getKNNForDBID(it, k);
final int nnsize = nn.size();
// Grow the buffer when needed:
if (nnsize * 12 + 10 > bufsize) {
while (nnsize * 12 + 10 > bufsize) {
bufsize <<= 1;
}
buffer = ByteBuffer.allocateDirect(bufsize);
}
buffer.clear();
ByteArrayUtil.writeUnsignedVarint(buffer, it.internalGetIndex());
ByteArrayUtil.writeUnsignedVarint(buffer, nnsize);
int c = 0;
for (DoubleDBIDListIter ni = nn.iter(); ni.valid(); ni.advance(), c++) {
ByteArrayUtil.writeUnsignedVarint(buffer, ni.internalGetIndex());
buffer.putDouble(ni.doubleValue());
}
if (c != nn.size()) {
throw new AbortException("Sizes did not agree. Cache is invalid.");
}
buffer.flip();
channel.write(buffer);
LOG.incrementProcessed(prog);
}
LOG.ensureCompleted(prog);
lock.release();
} catch (IOException e) {
LOG.exception(e);
}
// FIXME: close!
}
/**
* Compute density in the given subspace.
*
* @param subspace Subspace
* @param neighbors Neighbor distance list
* @return Density
*/
protected double subspaceDensity(long[] subspace, DoubleDBIDList neighbors) {
final double bandwidth = optimalBandwidth(BitsUtil.cardinality(subspace));
double density = 0;
for (DoubleDBIDListIter neighbor = neighbors.iter(); neighbor.valid(); neighbor.advance()) {
double v = neighbor.doubleValue() / bandwidth;
if (v < 1) {
density += 1 - (v * v);
}
}
return density / relation.size();
}
@Override
public String toString() {
StringBuilder buf = new StringBuilder();
buf.append("kNNList[");
for (DoubleDBIDListIter iter = this.iter(); iter.valid(); ) {
buf.append(iter.doubleValue()).append(':').append(DBIDUtil.toString(iter));
iter.advance();
if (iter.valid()) {
buf.append(',');
}
}
buf.append(']');
return buf.toString();
}
/**
* Run the algorithm
*
* @param database Database to process
* @param relation Relation to process
* @return Outlier result
*/
public OutlierResult run(Database database, Relation<O> relation) {
DistanceQuery<O> distFunc = database.getDistanceQuery(relation, getDistanceFunction());
RangeQuery<O> rangeQuery = database.getRangeQuery(distFunc);
DBIDs ids = relation.getDBIDs();
// LOCI preprocessing step
WritableDataStore<DoubleIntArrayList> interestingDistances =
DataStoreUtil.makeStorage(
relation.getDBIDs(),
DataStoreFactory.HINT_TEMP | DataStoreFactory.HINT_SORTED,
DoubleIntArrayList.class);
precomputeInterestingRadii(ids, rangeQuery, interestingDistances);
// LOCI main step
FiniteProgress progressLOCI =
LOG.isVerbose() ? new FiniteProgress("LOCI scores", relation.size(), LOG) : null;
WritableDoubleDataStore mdef_norm =
DataStoreUtil.makeDoubleStorage(relation.getDBIDs(), DataStoreFactory.HINT_STATIC);
WritableDoubleDataStore mdef_radius =
DataStoreUtil.makeDoubleStorage(relation.getDBIDs(), DataStoreFactory.HINT_STATIC);
DoubleMinMax minmax = new DoubleMinMax();
// Shared instance, to save allocations.
MeanVariance mv_n_r_alpha = new MeanVariance();
for (DBIDIter iditer = ids.iter(); iditer.valid(); iditer.advance()) {
final DoubleIntArrayList cdist = interestingDistances.get(iditer);
final double maxdist = cdist.getDouble(cdist.size() - 1);
final int maxneig = cdist.getInt(cdist.size() - 1);
double maxmdefnorm = 0.0;
double maxnormr = 0;
if (maxneig >= nmin) {
// Compute the largest neighborhood we will need.
DoubleDBIDList maxneighbors = rangeQuery.getRangeForDBID(iditer, maxdist);
// TODO: Ensure the result is sorted. This is currently implied.
// For any critical distance, compute the normalized MDEF score.
for (int i = 0, size = cdist.size(); i < size; i++) {
// Only start when minimum size is fulfilled
if (cdist.getInt(i) < nmin) {
continue;
}
final double r = cdist.getDouble(i);
final double alpha_r = alpha * r;
// compute n(p_i, \alpha * r) from list (note: alpha_r is not cdist!)
final int n_alphar = cdist.getInt(cdist.find(alpha_r));
// compute \hat{n}(p_i, r, \alpha) and the corresponding \simga_{MDEF}
mv_n_r_alpha.reset();
for (DoubleDBIDListIter neighbor = maxneighbors.iter();
neighbor.valid();
neighbor.advance()) {
// Stop at radius r
if (neighbor.doubleValue() > r) {
break;
}
DoubleIntArrayList cdist2 = interestingDistances.get(neighbor);
int rn_alphar = cdist2.getInt(cdist2.find(alpha_r));
mv_n_r_alpha.put(rn_alphar);
}
// We only use the average and standard deviation
final double nhat_r_alpha = mv_n_r_alpha.getMean();
final double sigma_nhat_r_alpha = mv_n_r_alpha.getNaiveStddev();
// Redundant divisions by nhat_r_alpha removed.
final double mdef = nhat_r_alpha - n_alphar;
final double sigmamdef = sigma_nhat_r_alpha;
final double mdefnorm = mdef / sigmamdef;
if (mdefnorm > maxmdefnorm) {
maxmdefnorm = mdefnorm;
maxnormr = r;
}
}
} else {
// FIXME: when nmin was not fulfilled - what is the proper value then?
maxmdefnorm = Double.POSITIVE_INFINITY;
maxnormr = maxdist;
}
mdef_norm.putDouble(iditer, maxmdefnorm);
mdef_radius.putDouble(iditer, maxnormr);
minmax.put(maxmdefnorm);
LOG.incrementProcessed(progressLOCI);
}
LOG.ensureCompleted(progressLOCI);
DoubleRelation scoreResult =
new MaterializedDoubleRelation(
"LOCI normalized MDEF", "loci-mdef-outlier", mdef_norm, relation.getDBIDs());
OutlierScoreMeta scoreMeta =
new QuotientOutlierScoreMeta(
minmax.getMin(), minmax.getMax(), 0.0, Double.POSITIVE_INFINITY, 0.0);
OutlierResult result = new OutlierResult(scoreMeta, scoreResult);
result.addChildResult(
new MaterializedDoubleRelation(
"LOCI MDEF Radius", "loci-critical-radius", mdef_radius, relation.getDBIDs()));
return result;
}