/**
* 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 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();
}
@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!
}
/**
* Refine a range query.
*
* @param neighc Original result
* @param adjustedEps New epsilon
* @return refined list
*/
private DoubleDBIDList refineRange(DoubleDBIDList neighc, double adjustedEps) {
ModifiableDoubleDBIDList n = DBIDUtil.newDistanceDBIDList(neighc.size());
// We don't have a guarantee for this list to be sorted
for (DoubleDBIDListIter neighbor = neighc.iter(); neighbor.valid(); neighbor.advance()) {
DoubleDBIDPair p = neighbor.getPair();
double dist = p.doubleValue();
if (dist <= adjustedEps) {
n.add(dist, p);
}
}
return n;
}
/**
* 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();
}
/**
* Refine neighbors within a subset.
*
* @param neighc Neighbor candidates
* @param dbid Query object
* @param df distance function
* @param adjustedEps Epsilon range
* @param kernel Kernel
* @return Neighbors of neighbor object
*/
private DoubleDBIDList subsetNeighborhoodQuery(
DoubleDBIDList neighc,
DBIDRef dbid,
PrimitiveDistanceFunction<? super V> df,
double adjustedEps,
KernelDensityEstimator kernel) {
ModifiableDoubleDBIDList n = DBIDUtil.newDistanceDBIDList(neighc.size());
V query = kernel.relation.get(dbid);
for (DoubleDBIDListIter neighbor = neighc.iter(); neighbor.valid(); neighbor.advance()) {
DoubleDBIDPair p = neighbor.getPair();
double dist = df.distance(query, kernel.relation.get(p));
if (dist <= adjustedEps) {
n.add(dist, p);
}
}
return n;
}
/**
* Main loop of OUTRES. Run for each object
*
* @param s start dimension
* @param subspace Current subspace
* @param id Current object ID
* @param kernel Kernel
* @return Score
*/
public double outresScore(
final int s, long[] subspace, DBIDRef id, KernelDensityEstimator kernel) {
double score = 1.0; // Initial score is 1.0
final SubspaceEuclideanDistanceFunction df = new SubspaceEuclideanDistanceFunction(subspace);
MeanVariance meanv = new MeanVariance();
for (int i = s; i < kernel.dim; i++) {
if (BitsUtil.get(subspace, i)) { // TODO: needed? Or should we always start
// with i=0?
continue;
}
BitsUtil.setI(subspace, i);
df.setSelectedDimensions(subspace);
final double adjustedEps = kernel.adjustedEps(kernel.dim);
// Query with a larger window, to also get neighbors of neighbors
// Subspace euclidean is metric!
final double range = adjustedEps * 2.;
RangeQuery<V> rq = QueryUtil.getRangeQuery(kernel.relation, df, range);
DoubleDBIDList neighc = rq.getRangeForDBID(id, range);
DoubleDBIDList neigh = refineRange(neighc, adjustedEps);
if (neigh.size() > 2) {
// Relevance test
if (relevantSubspace(subspace, neigh, kernel)) {
final double density = kernel.subspaceDensity(subspace, neigh);
// Compute mean and standard deviation for densities of neighbors.
meanv.reset();
for (DoubleDBIDListIter neighbor = neigh.iter(); neighbor.valid(); neighbor.advance()) {
DoubleDBIDList n2 = subsetNeighborhoodQuery(neighc, neighbor, df, adjustedEps, kernel);
meanv.put(kernel.subspaceDensity(subspace, n2));
}
final double deviation = (meanv.getMean() - density) / (2. * meanv.getSampleStddev());
// High deviation:
if (deviation >= 1) {
score *= (density / deviation);
}
// Recursion
score *= outresScore(i + 1, subspace, id, kernel);
}
}
BitsUtil.clearI(subspace, i);
}
return score;
}
/**
* 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;
}
