summaryrefslogtreecommitdiff
path: root/src/de/lmu/ifi/dbs/elki/algorithm/outlier/lof/ALOCI.java
diff options
context:
space:
mode:
authorErich Schubert <erich@debian.org>2013-10-29 20:02:37 +0100
committerAndrej Shadura <andrewsh@debian.org>2019-03-09 22:30:37 +0000
commitec7f409f6e795bbcc6f3c005687954e9475c600c (patch)
treefbf36c0ab791c556198b487ca40ae56ae5ab1ee5 /src/de/lmu/ifi/dbs/elki/algorithm/outlier/lof/ALOCI.java
parent974d4cf6d54cadc06258039f2cd0515cc34aeac6 (diff)
parent8300861dc4c62c5567a4e654976072f854217544 (diff)
Import Debian changes 0.6.0~beta2-1
elki (0.6.0~beta2-1) unstable; urgency=low * New upstream beta release. * 3DPC extension is not yet included.
Diffstat (limited to 'src/de/lmu/ifi/dbs/elki/algorithm/outlier/lof/ALOCI.java')
-rw-r--r--src/de/lmu/ifi/dbs/elki/algorithm/outlier/lof/ALOCI.java737
1 files changed, 737 insertions, 0 deletions
diff --git a/src/de/lmu/ifi/dbs/elki/algorithm/outlier/lof/ALOCI.java b/src/de/lmu/ifi/dbs/elki/algorithm/outlier/lof/ALOCI.java
new file mode 100644
index 00000000..d48679a9
--- /dev/null
+++ b/src/de/lmu/ifi/dbs/elki/algorithm/outlier/lof/ALOCI.java
@@ -0,0 +1,737 @@
+package de.lmu.ifi.dbs.elki.algorithm.outlier.lof;
+
+/*
+ This file is part of ELKI:
+ Environment for Developing KDD-Applications Supported by Index-Structures
+
+ Copyright (C) 2012
+ Ludwig-Maximilians-Universität München
+ Lehr- und Forschungseinheit für Datenbanksysteme
+ ELKI Development Team
+
+ This program is free software: you can redistribute it and/or modify
+ it under the terms of the GNU Affero General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU Affero General Public License for more details.
+
+ You should have received a copy of the GNU Affero General Public License
+ along with this program. If not, see <http://www.gnu.org/licenses/>.
+ */
+
+import java.util.ArrayList;
+import java.util.List;
+import java.util.Random;
+
+import de.lmu.ifi.dbs.elki.algorithm.AbstractAlgorithm;
+import de.lmu.ifi.dbs.elki.algorithm.outlier.OutlierAlgorithm;
+import de.lmu.ifi.dbs.elki.data.NumberVector;
+import de.lmu.ifi.dbs.elki.data.type.TypeInformation;
+import de.lmu.ifi.dbs.elki.data.type.TypeUtil;
+import de.lmu.ifi.dbs.elki.database.Database;
+import de.lmu.ifi.dbs.elki.database.datastore.DataStoreFactory;
+import de.lmu.ifi.dbs.elki.database.datastore.DataStoreUtil;
+import de.lmu.ifi.dbs.elki.database.datastore.WritableDoubleDataStore;
+import de.lmu.ifi.dbs.elki.database.ids.ArrayModifiableDBIDs;
+import de.lmu.ifi.dbs.elki.database.ids.DBIDArrayIter;
+import de.lmu.ifi.dbs.elki.database.ids.DBIDIter;
+import de.lmu.ifi.dbs.elki.database.ids.DBIDUtil;
+import de.lmu.ifi.dbs.elki.database.relation.MaterializedRelation;
+import de.lmu.ifi.dbs.elki.database.relation.Relation;
+import de.lmu.ifi.dbs.elki.database.relation.RelationUtil;
+import de.lmu.ifi.dbs.elki.distance.distancefunction.NumberVectorDistanceFunction;
+import de.lmu.ifi.dbs.elki.distance.distancefunction.minkowski.EuclideanDistanceFunction;
+import de.lmu.ifi.dbs.elki.distance.distancevalue.NumberDistance;
+import de.lmu.ifi.dbs.elki.logging.Logging;
+import de.lmu.ifi.dbs.elki.logging.progress.FiniteProgress;
+import de.lmu.ifi.dbs.elki.math.DoubleMinMax;
+import de.lmu.ifi.dbs.elki.math.linearalgebra.Vector;
+import de.lmu.ifi.dbs.elki.result.outlier.OutlierResult;
+import de.lmu.ifi.dbs.elki.result.outlier.OutlierScoreMeta;
+import de.lmu.ifi.dbs.elki.result.outlier.QuotientOutlierScoreMeta;
+import de.lmu.ifi.dbs.elki.utilities.DatabaseUtil;
+import de.lmu.ifi.dbs.elki.utilities.RandomFactory;
+import de.lmu.ifi.dbs.elki.utilities.documentation.Description;
+import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
+import de.lmu.ifi.dbs.elki.utilities.documentation.Title;
+import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
+import de.lmu.ifi.dbs.elki.utilities.optionhandling.OptionID;
+import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameterization.Parameterization;
+import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameters.IntParameter;
+import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameters.ObjectParameter;
+import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameters.RandomParameter;
+import de.lmu.ifi.dbs.elki.utilities.pairs.Pair;
+
+/**
+ * Fast Outlier Detection Using the "approximate Local Correlation Integral".
+ *
+ * Outlier detection using multiple epsilon neighborhoods.
+ *
+ * Reference:
+ * <p>
+ * S. Papadimitriou, H. Kitagawa, P. B. Gibbons and C. Faloutsos:<br />
+ * LOCI: Fast Outlier Detection Using the Local Correlation Integral.<br />
+ * In: Proc. 19th IEEE Int. Conf. on Data Engineering (ICDE '03), Bangalore,
+ * India, 2003.
+ * </p>
+ *
+ * @author Jonathan von Brünken
+ * @author Erich Schubert
+ *
+ * @apiviz.composedOf ALOCIQuadTree
+ *
+ * @param <O> Object type
+ * @param <D> Distance type
+ */
+@Title("LOCI: Fast Outlier Detection Using the Local Correlation Integral")
+@Description("Algorithm to compute outliers based on the Local Correlation Integral")
+@Reference(authors = "S. Papadimitriou, H. Kitagawa, P. B. Gibbons, C. Faloutsos", title = "LOCI: Fast Outlier Detection Using the Local Correlation Integral", booktitle = "Proc. 19th IEEE Int. Conf. on Data Engineering (ICDE '03), Bangalore, India, 2003", url = "http://dx.doi.org/10.1109/ICDE.2003.1260802")
+public class ALOCI<O extends NumberVector<?>, D extends NumberDistance<D, ?>> extends AbstractAlgorithm<OutlierResult> implements OutlierAlgorithm {
+ /**
+ * The logger for this class.
+ */
+ private static final Logging LOG = Logging.getLogger(ALOCI.class);
+
+ /**
+ * Minimum size for a leaf.
+ */
+ private int nmin;
+
+ /**
+ * Alpha (level difference of sampling and counting neighborhoods)
+ */
+ private int alpha;
+
+ /**
+ * Number of trees to generate (forest size)
+ */
+ private int g;
+
+ /**
+ * Random generator
+ */
+ private RandomFactory rnd;
+
+ /**
+ * Distance function
+ */
+ private NumberVectorDistanceFunction<D> distFunc;
+
+ /**
+ * Constructor.
+ *
+ * @param distanceFunction Distance function
+ * @param nmin Minimum neighborhood size
+ * @param alpha Alpha value
+ * @param g Number of grids to use
+ * @param rnd Random generator.
+ */
+ public ALOCI(NumberVectorDistanceFunction<D> distanceFunction, int nmin, int alpha, int g, RandomFactory rnd) {
+ super();
+ this.distFunc = distanceFunction;
+ this.nmin = nmin;
+ this.alpha = alpha;
+ this.g = g;
+ this.rnd = rnd;
+ }
+
+ public OutlierResult run(Database database, Relation<O> relation) {
+ final int dim = RelationUtil.dimensionality(relation);
+ final Random random = rnd.getRandom();
+ FiniteProgress progressPreproc = LOG.isVerbose() ? new FiniteProgress("Build aLOCI quadtress", g, LOG) : null;
+
+ // Compute extend of dataset.
+ double[] min, max;
+ {
+ Pair<O, O> hbbs = DatabaseUtil.computeMinMax(relation);
+ double maxd = 0;
+ min = new double[dim];
+ max = new double[dim];
+ for(int i = 0; i < dim; i++) {
+ min[i] = hbbs.first.doubleValue(i);
+ max[i] = hbbs.second.doubleValue(i);
+ maxd = Math.max(maxd, max[i] - min[i]);
+ }
+ // Enlarge bounding box to have equal lengths.
+ for(int i = 0; i < dim; i++) {
+ double diff = (maxd - (max[i] - min[i])) * .5;
+ min[i] -= diff;
+ max[i] += diff;
+ }
+ }
+
+ List<ALOCIQuadTree> qts = new ArrayList<>(g);
+
+ double[] nshift = new double[dim];
+ ALOCIQuadTree qt = new ALOCIQuadTree(min, max, nshift, nmin, relation);
+ qts.add(qt);
+ if(progressPreproc != null) {
+ progressPreproc.incrementProcessed(LOG);
+ }
+ /*
+ * create the remaining g-1 shifted QuadTrees. This not clearly described in
+ * the paper and therefore implemented in a way that achieves good results
+ * with the test data.
+ */
+ for(int shift = 1; shift < g; shift++) {
+ double[] svec = new double[dim];
+ for(int i = 0; i < dim; i++) {
+ svec[i] = random.nextDouble() * (max[i] - min[i]);
+ }
+ qt = new ALOCIQuadTree(min, max, svec, nmin, relation);
+ qts.add(qt);
+ if(progressPreproc != null) {
+ progressPreproc.incrementProcessed(LOG);
+ }
+ }
+ if(progressPreproc != null) {
+ progressPreproc.ensureCompleted(LOG);
+ }
+
+ // aLOCI main loop: evaluate
+ FiniteProgress progressLOCI = LOG.isVerbose() ? new FiniteProgress("Compute aLOCI scores", relation.size(), LOG) : null;
+ WritableDoubleDataStore mdef_norm = DataStoreUtil.makeDoubleStorage(relation.getDBIDs(), DataStoreFactory.HINT_STATIC);
+ DoubleMinMax minmax = new DoubleMinMax();
+
+ for(DBIDIter iditer = relation.iterDBIDs(); iditer.valid(); iditer.advance()) {
+ final O obj = relation.get(iditer);
+
+ double maxmdefnorm = 0;
+ // For each level
+ for(int l = 0;; l++) {
+ // Find the closest C_i
+ Node ci = null;
+ for(int i = 0; i < g; i++) {
+ Node ci2 = qts.get(i).findClosestNode(obj, l);
+ if(ci2.getLevel() != l) {
+ continue;
+ }
+ // TODO: always use manhattan?
+ if(ci == null || distFunc.distance(ci.getCenter(), obj).compareTo(distFunc.distance(ci2.getCenter(), obj)) > 0) {
+ ci = ci2;
+ }
+ }
+ // logger.debug("level:" + (ci != null ? ci.getLevel() : -1) +" l:"+l);
+ if(ci == null) {
+ break; // no matching tree for this level.
+ }
+
+ // Find the closest C_j
+ Node cj = null;
+ for(int i = 0; i < g; i++) {
+ Node cj2 = qts.get(i).findClosestNode(ci.getCenter(), l - alpha);
+ // TODO: allow higher levels or not?
+ if(cj != null && cj2.getLevel() < cj.getLevel()) {
+ continue;
+ }
+ // TODO: always use manhattan?
+ if(cj == null || distFunc.distance(cj.getCenter(), ci.getCenter()).compareTo(distFunc.distance(cj2.getCenter(), ci.getCenter())) > 0) {
+ cj = cj2;
+ }
+ }
+ // logger.debug("level:" + (cj != null ? cj.getLevel() : -1) +" l:"+l);
+ if(cj == null) {
+ continue; // no matching tree for this level.
+ }
+ double mdefnorm = calculate_MDEF_norm(cj, ci);
+ // logger.warning("level:" + ci.getLevel() + "/" + cj.getLevel() +
+ // " mdef: " + mdefnorm);
+ maxmdefnorm = Math.max(maxmdefnorm, mdefnorm);
+ }
+ // Store results
+ mdef_norm.putDouble(iditer, maxmdefnorm);
+ minmax.put(maxmdefnorm);
+ if(progressLOCI != null) {
+ progressLOCI.incrementProcessed(LOG);
+ }
+ }
+ if(progressLOCI != null) {
+ progressLOCI.ensureCompleted(LOG);
+ }
+ Relation<Double> scoreResult = new MaterializedRelation<>("aLOCI normalized MDEF", "aloci-mdef-outlier", TypeUtil.DOUBLE, mdef_norm, relation.getDBIDs());
+ OutlierScoreMeta scoreMeta = new QuotientOutlierScoreMeta(minmax.getMin(), minmax.getMax(), 0.0, Double.POSITIVE_INFINITY);
+ OutlierResult result = new OutlierResult(scoreMeta, scoreResult);
+ return result;
+ }
+
+ /**
+ * Method for the MDEF calculation
+ *
+ * @param sn Sampling Neighborhood
+ * @param cg Counting Neighborhood
+ *
+ * @return MDEF norm
+ */
+ private static double calculate_MDEF_norm(Node sn, Node cg) {
+ // get the square sum of the counting neighborhoods box counts
+ long sq = sn.getSquareSum(cg.getLevel() - sn.getLevel());
+ /*
+ * if the square sum is equal to box count of the sampling Neighborhood then
+ * n_hat is equal one, and as cg needs to have at least one Element mdef
+ * would get zero or lower than zero. This is the case when all of the
+ * counting Neighborhoods contain one or zero Objects. Additionally, the
+ * cubic sum, square sum and sampling Neighborhood box count are all equal,
+ * which leads to sig_n_hat being zero and thus mdef_norm is either negative
+ * infinite or undefined. As the distribution of the Objects seem quite
+ * uniform, a mdef_norm value of zero ( = no outlier) is appropriate and
+ * circumvents the problem of undefined values.
+ */
+ if(sq == sn.getCount()) {
+ return 0.0;
+ }
+ // calculation of mdef according to the paper and standardization as done in
+ // LOCI
+ long cb = sn.getCubicSum(cg.getLevel() - sn.getLevel());
+ double n_hat = (double) sq / sn.getCount();
+ double sig_n_hat = java.lang.Math.sqrt(cb * sn.getCount() - (sq * sq)) / sn.getCount();
+ // Avoid NaN - correct result 0.0?
+ if(sig_n_hat < Double.MIN_NORMAL) {
+ return 0.0;
+ }
+ double mdef = n_hat - cg.getCount();
+ return mdef / sig_n_hat;
+ }
+
+ @Override
+ protected Logging getLogger() {
+ return LOG;
+ }
+
+ @Override
+ public TypeInformation[] getInputTypeRestriction() {
+ return TypeUtil.array(distFunc.getInputTypeRestriction());
+ }
+
+ /**
+ * Simple quadtree for ALOCI. Not storing the actual objects, just the counts.
+ *
+ * Furthermore, the quadtree can be shifted by a specified vector, wrapping
+ * around min/max
+ *
+ * @author Jonathan von Brünken
+ * @author Erich Schubert
+ *
+ * @apiviz.composedOf Node
+ */
+ static class ALOCIQuadTree {
+ /**
+ * Tree parameters
+ */
+ private double[] shift, min, width;
+
+ /**
+ * Maximum fill for a page before splitting
+ */
+ private int nmin;
+
+ /**
+ * Tree root
+ */
+ Node root;
+
+ /**
+ * Relation indexed.
+ */
+ private Relation<? extends NumberVector<?>> relation;
+
+ /**
+ * Constructor.
+ *
+ * @param min Minimum coordinates
+ * @param max Maximum coordinates
+ * @param shift Tree shift offset
+ * @param nmin Maximum size for a page to split
+ * @param relation Relation to index
+ */
+ public ALOCIQuadTree(double[] min, double[] max, double[] shift, int nmin, Relation<? extends NumberVector<?>> relation) {
+ super();
+ assert (min.length <= 32) : "Quadtrees are only supported for up to 32 dimensions";
+ this.shift = shift;
+ this.nmin = nmin;
+ this.min = min;
+ this.width = new double[min.length];
+ for(int d = 0; d < min.length; d++) {
+ width[d] = max[d] - min[d];
+ if(width[d] <= 0) {
+ width[d] = 1;
+ }
+ }
+ double[] center = new double[min.length];
+ for(int d = 0; d < min.length; d++) {
+ if(shift[d] < width[d] * .5) {
+ center[d] = min[d] + shift[d] + width[d] * .5;
+ }
+ else {
+ center[d] = min[d] + shift[d] - width[d] * .5;
+ }
+ }
+ this.relation = relation;
+ ArrayModifiableDBIDs ids = DBIDUtil.newArray(relation.getDBIDs());
+ List<Node> children = new ArrayList<>();
+ bulkLoad(min.clone(), max.clone(), children, ids, 0, ids.size(), 0, 0, 0);
+ this.root = new Node(0, new Vector(center), ids.size(), -1, children);
+ }
+
+ /**
+ * Bulk load the tree
+ *
+ * @param lmin Subtree minimum (unshifted, will be modified)
+ * @param lmax Subtree maximum (unshifted, will be modified)
+ * @param children List of children for current parent
+ * @param ids IDs to process
+ * @param start Start of ids subinterval
+ * @param end End of ids subinterval
+ * @param dim Current dimension
+ * @param level Current tree level
+ * @param code Bit code of node position
+ */
+ private void bulkLoad(double[] lmin, double[] lmax, List<Node> children, ArrayModifiableDBIDs ids, int start, int end, int dim, int level, int code) {
+ // logger.warning(FormatUtil.format(lmin)+" "+FormatUtil.format(lmax)+" "+start+"->"+end+" "+(end-start));
+ // Hack: Check degenerate cases that won't split
+ if(dim == 0) {
+ DBIDArrayIter iter = ids.iter();
+ iter.seek(start);
+ NumberVector<?> first = relation.get(iter);
+ iter.advance();
+ boolean degenerate = true;
+ loop: for(; iter.getOffset() < end; iter.advance()) {
+ NumberVector<?> other = relation.get(iter);
+ for(int d = 0; d < lmin.length; d++) {
+ if(Math.abs(first.doubleValue(d) - other.doubleValue(d)) > 1E-15) {
+ degenerate = false;
+ break loop;
+ }
+ }
+ }
+ if(degenerate) {
+ double[] center = new double[lmin.length];
+ for(int d = 0; d < lmin.length; d++) {
+ center[d] = lmin[d] * .5 + lmax[d] * .5 + shift[d];
+ if(center[d] > min[d] + width[d]) {
+ center[d] -= width[d];
+ }
+ }
+ children.add(new Node(code, new Vector(center), end - start, level, null));
+ return;
+ }
+ }
+ // Complete level
+ if(dim == lmin.length) {
+ double[] center = new double[lmin.length];
+ for(int d = 0; d < lmin.length; d++) {
+ center[d] = lmin[d] * .5 + lmax[d] * .5 + shift[d];
+ if(center[d] > min[d] + width[d]) {
+ center[d] -= width[d];
+ }
+ }
+ if(end - start < nmin) {
+ children.add(new Node(code, new Vector(center), end - start, level, null));
+ return;
+ }
+ else {
+ List<Node> newchildren = new ArrayList<>();
+ bulkLoad(lmin, lmax, newchildren, ids, start, end, 0, level + 1, 0);
+ children.add(new Node(code, new Vector(center), end - start, level, newchildren));
+ return;
+ }
+ }
+ else {
+ // Partially sort data, by dimension dim < mid
+ DBIDArrayIter siter = ids.iter(), eiter = ids.iter();
+ siter.seek(start);
+ eiter.seek(end - 1);
+ while(siter.getOffset() < eiter.getOffset()) {
+ if(getShiftedDim(relation.get(siter), dim, level) <= .5) {
+ siter.advance();
+ continue;
+ }
+ if(getShiftedDim(relation.get(eiter), dim, level) > 0.5) {
+ eiter.retract();
+ continue;
+ }
+ ids.swap(siter.getOffset(), eiter.getOffset() - 1);
+ siter.advance();
+ eiter.retract();
+ }
+ final int spos = siter.getOffset();
+ if(start < spos) {
+ final double tmp = lmax[dim];
+ lmax[dim] = lmax[dim] * .5 + lmin[dim] * .5;
+ bulkLoad(lmin, lmax, children, ids, start, spos, dim + 1, level, code);
+ lmax[dim] = tmp; // Restore
+ }
+ if(spos < end) {
+ final double tmp = lmin[dim];
+ lmin[dim] = lmax[dim] * .5 + lmin[dim] * .5;
+ bulkLoad(lmin, lmax, children, ids, spos, end, dim + 1, level, code | (1 << dim));
+ lmin[dim] = tmp; // Restore
+ }
+ }
+ }
+
+ /**
+ * Shift and wrap a single dimension.
+ *
+ * @param obj Object
+ * @param dim Dimension
+ * @param level Level (controls scaling/wraping!)
+ * @return Shifted position
+ */
+ private double getShiftedDim(NumberVector<?> obj, int dim, int level) {
+ double pos = obj.doubleValue(dim) + shift[dim];
+ pos = (pos - min[dim]) / width[dim] * (1 + level);
+ return pos - Math.floor(pos);
+ }
+
+ /**
+ * Find the closest node (of depth tlevel or above, if there is no node at
+ * this depth) for the given vector.
+ *
+ * @param vec Query vector
+ * @param tlevel Target level
+ * @return Node
+ */
+ public Node findClosestNode(NumberVector<?> vec, int tlevel) {
+ Node cur = root;
+ for(int level = 0; level <= tlevel; level++) {
+ if(cur.children == null) {
+ break;
+ }
+ int code = 0;
+ for(int d = 0; d < min.length; d++) {
+ if(getShiftedDim(vec, d, level) > .5) {
+ code |= 1 << d;
+ }
+ }
+ boolean found = false;
+ for(Node child : cur.children) {
+ if(child.code == code) {
+ cur = child;
+ found = true;
+ break;
+ }
+ }
+ if(!found) {
+ break; // Do not descend
+ }
+ }
+ return cur;
+ }
+ }
+
+ /**
+ * Node of the ALOCI Quadtree
+ *
+ * @author Erich Schubert
+ */
+ static class Node {
+ /**
+ * Position code
+ */
+ final int code;
+
+ /**
+ * Number of elements
+ */
+ final int count;
+
+ /**
+ * Level of node
+ */
+ final int level;
+
+ /**
+ * Child nodes, may be null
+ */
+ List<Node> children;
+
+ /**
+ * Parent node
+ */
+ Node parent = null;
+
+ /**
+ * Center vector
+ */
+ Vector center;
+
+ /**
+ * Constructor.
+ *
+ * @param code Node code
+ * @param center Center vector
+ * @param count Element count
+ * @param level Node level
+ * @param children Children list
+ */
+ protected Node(int code, Vector center, int count, int level, List<Node> children) {
+ this.code = code;
+ this.center = center;
+ this.count = count;
+ this.level = level;
+ this.children = children;
+ if(children != null) {
+ for(Node child : children) {
+ child.parent = this;
+ }
+ }
+ }
+
+ /**
+ * Get level of node.
+ *
+ * @return Level of node
+ */
+ public int getLevel() {
+ return level;
+ }
+
+ /**
+ * Get count of subtree
+ *
+ * @return subtree count
+ */
+ public int getCount() {
+ return count;
+ }
+
+ /**
+ * Return center vector
+ *
+ * @return center vector
+ */
+ public Vector getCenter() {
+ return center;
+ }
+
+ /**
+ * Get sum of squares, recursively
+ *
+ * @param levels Depth to collect
+ * @return Sum of squares
+ */
+ public long getSquareSum(int levels) {
+ if(levels <= 0 || children == null) {
+ return ((long) count) * ((long) count);
+ }
+ long agg = 0;
+ for(Node child : children) {
+ agg += child.getSquareSum(levels - 1);
+ }
+ return agg;
+ }
+
+ /**
+ * Get cubic sum.
+ *
+ * @param levels Level to collect
+ * @return sum of cubes
+ */
+ public long getCubicSum(int levels) {
+ if(levels <= 0 || children == null) {
+ return ((long) count) * ((long) count) * ((long) count);
+ }
+ long agg = 0;
+ for(Node child : children) {
+ agg += child.getCubicSum(levels - 1);
+ }
+ return agg;
+ }
+ }
+
+ /**
+ * Parameterization class.
+ *
+ * @author Erich Schubert
+ *
+ * @apiviz.exclude
+ */
+ public static class Parameterizer<O extends NumberVector<?>, D extends NumberDistance<D, ?>> extends AbstractParameterizer {
+ /**
+ * Parameter to specify the minimum neighborhood size
+ */
+ public static final OptionID NMIN_ID = new OptionID("loci.nmin", "Minimum neighborhood size to be considered.");
+
+ /**
+ * Parameter to specify the averaging neighborhood scaling.
+ */
+ public static final OptionID ALPHA_ID = new OptionID("loci.alpha", "Scaling factor for averaging neighborhood");
+
+ /**
+ * Parameter to specify the number of Grids to use.
+ */
+ public static final OptionID GRIDS_ID = new OptionID("loci.g", "The number of Grids to use.");
+
+ /**
+ * Parameter to specify the seed to initialize Random.
+ */
+ public static final OptionID SEED_ID = new OptionID("loci.seed", "The seed to use for initializing Random.");
+
+ /**
+ * Neighborhood minimum size
+ */
+ protected int nmin = 0;
+
+ /**
+ * Alpha: number of levels difference to use in comparison
+ */
+ protected int alpha = 4;
+
+ /**
+ * G: number of shifted trees to create.
+ */
+ protected int g = 1;
+
+ /**
+ * Random generator
+ */
+ protected RandomFactory rnd;
+
+ /**
+ * The distance function
+ */
+ private NumberVectorDistanceFunction<D> distanceFunction;
+
+ @Override
+ protected void makeOptions(Parameterization config) {
+ super.makeOptions(config);
+
+ ObjectParameter<NumberVectorDistanceFunction<D>> distanceFunctionP = makeParameterDistanceFunction(EuclideanDistanceFunction.class, NumberVectorDistanceFunction.class);
+ if(config.grab(distanceFunctionP)) {
+ distanceFunction = distanceFunctionP.instantiateClass(config);
+ }
+
+ final IntParameter nminP = new IntParameter(NMIN_ID, 20);
+ if(config.grab(nminP)) {
+ nmin = nminP.getValue();
+ }
+
+ final IntParameter g = new IntParameter(GRIDS_ID, 1);
+ if(config.grab(g)) {
+ this.g = g.getValue();
+ }
+
+ final RandomParameter rndP = new RandomParameter(SEED_ID);
+ if(config.grab(rndP)) {
+ this.rnd = rndP.getValue();
+ }
+
+ final IntParameter alphaP = new IntParameter(ALPHA_ID, 4);
+ if(config.grab(alphaP)) {
+ this.alpha = alphaP.getValue();
+ if(this.alpha < 1) {
+ this.alpha = 1;
+ }
+ }
+ }
+
+ @Override
+ protected ALOCI<O, D> makeInstance() {
+ return new ALOCI<>(distanceFunction, nmin, alpha, g, rnd);
+ }
+ }
+}