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+package de.lmu.ifi.dbs.elki.math.statistics.dependence;
+
+/*
+ This file is part of ELKI:
+ Environment for Developing KDD-Applications Supported by Index-Structures
+
+ Copyright (C) 2014
+ 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 de.lmu.ifi.dbs.elki.utilities.datastructures.arraylike.NumberArrayAdapter;
+import de.lmu.ifi.dbs.elki.utilities.datastructures.heap.DoubleMinHeap;
+import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
+import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
+
+/**
+ * Compute the similarity of dimensions using the SURFING score. The parameter k
+ * for the k nearest neighbors is currently hard-coded to 10% of the set size.
+ *
+ * Note that the complexity is roughly O(n n k), so this is a rather slow
+ * method, and with k at 10% of n, is actually cubic: O(0.1 * n^3).
+ *
+ * This version cannot use index support, as the API operates without database
+ * attachment. However, it should be possible to implement some trivial
+ * sorted-list indexes to get a reasonable speedup!
+ *
+ * Reference:
+ * <p>
+ * Elke Achtert, Hans-Peter Kriegel, Erich Schubert, Arthur Zimek:<br />
+ * Interactive Data Mining with 3D-Parallel-Coordinate-Trees.<br />
+ * Proceedings of the 2013 ACM International Conference on Management of Data
+ * (SIGMOD), New York City, NY, 2013.
+ * </p>
+ *
+ * Based on:
+ * <p>
+ * Christian Baumgartner, Claudia Plant, Karin Kailing, Hans-Peter Kriegel, and
+ * Peer Kröger<br />
+ * Subspace Selection for Clustering High-Dimensional Data<br />
+ * In IEEE International Conference on Data Mining, 2004.
+ * </p>
+ *
+ * TODO: make the subspace distance function and k parameterizable.
+ *
+ * @author Robert Rödler
+ * @author Erich Schubert
+ *
+ * @apiviz.uses SubspaceEuclideanDistanceFunction
+ */
+@Reference(authors = "Elke Achtert, Hans-Peter Kriegel, Erich Schubert, Arthur Zimek", //
+title = "Interactive Data Mining with 3D-Parallel-Coordinate-Trees", //
+booktitle = "Proc. of the 2013 ACM International Conference on Management of Data (SIGMOD)", //
+url = "http://dx.doi.org/10.1145/2463676.2463696")
+public class SURFINGDependenceMeasure extends AbstractDependenceMeasure {
+ /**
+ * Static instance.
+ */
+ public static final SURFINGDependenceMeasure STATIC = new SURFINGDependenceMeasure();
+
+ /**
+ * Constructor. Use static instance instead!
+ */
+ protected SURFINGDependenceMeasure() {
+ super();
+ }
+
+ @Reference(authors = "Christian Baumgartner, Claudia Plant, Karin Kailing, Hans-Peter Kriegel, and Peer Kröger", //
+ title = "Subspace Selection for Clustering High-Dimensional Data", //
+ booktitle = "IEEE International Conference on Data Mining, 2004", //
+ url = "http://dx.doi.org/10.1109/ICDM.2004.10112")
+ @Override
+ public <A, B> double dependence(NumberArrayAdapter<?, A> adapter1, A data1, NumberArrayAdapter<?, B> adapter2, B data2) {
+ final int len = size(adapter1, data1, adapter2, data2);
+ final int k = Math.max(1, len / 10);
+
+ double[] knns = new double[len];
+
+ DoubleMinHeap heap = new DoubleMinHeap(k);
+ double kdistmean = 0.;
+ for(int i = 0; i < len; ++i) {
+ double ix = adapter1.getDouble(data1, i), iy = adapter2.getDouble(data2, i);
+ heap.clear();
+ for(int j = 0; j < len; ++j) {
+ double jx = adapter1.getDouble(data1, j), jy = adapter2.getDouble(data2, j);
+ double dx = ix - jx, dy = iy - jy;
+ heap.add(dx * dx + dy * dy); // Squared Euclidean.
+ }
+ double kdist = Math.sqrt(heap.peek()); // Euclidean
+ knns[i] = kdist;
+ kdistmean += kdist;
+ }
+ kdistmean /= len;
+ // Deviation from mean:
+ double diff = 0.;
+ int below = 0;
+ for(int l = 0; l < knns.length; l++) {
+ diff += Math.abs(kdistmean - knns[l]);
+ if(knns[l] < kdistmean) {
+ below++;
+ }
+ }
+ return (below > 0) ? diff / (2. * kdistmean * below) : 0;
+ }
+
+ /**
+ * Parameterization class.
+ *
+ * @author Erich Schubert
+ *
+ * @apiviz.exclude
+ */
+ public static class Parameterizer extends AbstractParameterizer {
+ @Override
+ protected SURFINGDependenceMeasure makeInstance() {
+ return STATIC;
+ }
+ }
+}