source: trunk/CrossPare/src/de/ugoe/cs/cpdp/training/WekaLocalFQTraining.java @ 52

// Copyright 2015 Georg-August-Universität Göttingen, Germany
//
//   Licensed under the Apache License, Version 2.0 (the "License");
//   you may not use this file except in compliance with the License.
//   You may obtain a copy of the License at
//
//       http://www.apache.org/licenses/LICENSE-2.0
//
//   Unless required by applicable law or agreed to in writing, software
//   distributed under the License is distributed on an "AS IS" BASIS,
//   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
//   See the License for the specific language governing permissions and
//   limitations under the License.

package de.ugoe.cs.cpdp.training;

import java.io.PrintStream;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.Random;
import java.util.Set;
import java.util.logging.Level;

import org.apache.commons.io.output.NullOutputStream;

import de.ugoe.cs.cpdp.training.QuadTree;
import de.ugoe.cs.util.console.Console;
import weka.classifiers.AbstractClassifier;
import weka.classifiers.Classifier;
import weka.core.DenseInstance;
import weka.core.EuclideanDistance;
import weka.core.Instance;
import weka.core.Instances;
import weka.filters.Filter;
import weka.filters.unsupervised.attribute.Remove;

/**
 * Trainer with reimplementation of WHERE clustering algorithm from: Tim Menzies, Andrew Butcher,
 * David Cok, Andrian Marcus, Lucas Layman, Forrest Shull, Burak Turhan, Thomas Zimmermann,
 * "Local versus Global Lessons for Defect Prediction and Effort Estimation," IEEE Transactions on
 * Software Engineering, vol. 39, no. 6, pp. 822-834, June, 2013
 * 
 * With WekaLocalFQTraining we do the following: 1) Run the Fastmap algorithm on all training data,
 * let it calculate the 2 most significant dimensions and projections of each instance to these
 * dimensions 2) With these 2 dimensions we span a QuadTree which gets recursively split on
 * median(x) and median(y) values. 3) We cluster the QuadTree nodes together if they have similar
 * density (50%) 4) We save the clusters and their training data 5) We only use clusters with >
 * ALPHA instances (currently Math.sqrt(SIZE)), rest is discarded with the training data of this
 * cluster 6) We train a Weka classifier for each cluster with the clusters training data 7) We
 * recalculate Fastmap distances for a single instance with the old pivots and then try to find a
 * cluster containing the coords of the instance. 7.1.) If we can not find a cluster (due to coords
 * outside of all clusters) we find the nearest cluster. 8) We classify the Instance with the
 * classifier and traindata from the Cluster we found in 7.
 */
public class WekaLocalFQTraining extends WekaBaseTraining implements ITrainingStrategy {

    private final TraindatasetCluster classifier = new TraindatasetCluster();

    @Override
    public Classifier getClassifier() {
        return classifier;
    }

    @Override
    public void apply(Instances traindata) {
        PrintStream errStr = System.err;
        System.setErr(new PrintStream(new NullOutputStream()));
        try {
            classifier.buildClassifier(traindata);
        }
        catch (Exception e) {
            throw new RuntimeException(e);
        }
        finally {
            System.setErr(errStr);
        }
    }

    public class TraindatasetCluster extends AbstractClassifier {

        private static final long serialVersionUID = 1L;

        /* classifier per cluster */
        private HashMap<Integer, Classifier> cclassifier;

        /* instances per cluster */
        private HashMap<Integer, Instances> ctraindata;

        /*
         * holds the instances and indices of the pivot objects of the Fastmap calculation in
         * buildClassifier
         */
        private HashMap<Integer, Instance> cpivots;

        /* holds the indices of the pivot objects for x,y and the dimension [x,y][dimension] */
        private int[][] cpivotindices;

        /* holds the sizes of the cluster multiple "boxes" per cluster */
        private HashMap<Integer, ArrayList<Double[][]>> csize;

        /* debug vars */
        @SuppressWarnings("unused")
        private boolean show_biggest = true;

        @SuppressWarnings("unused")
        private int CFOUND = 0;
        @SuppressWarnings("unused")
        private int CNOTFOUND = 0;

        private Instance createInstance(Instances instances, Instance instance) {
            // attributes for feeding instance to classifier
            Set<String> attributeNames = new HashSet<>();
            for (int j = 0; j < instances.numAttributes(); j++) {
                attributeNames.add(instances.attribute(j).name());
            }

            double[] values = new double[instances.numAttributes()];
            int index = 0;
            for (int j = 0; j < instance.numAttributes(); j++) {
                if (attributeNames.contains(instance.attribute(j).name())) {
                    values[index] = instance.value(j);
                    index++;
                }
            }

            Instances tmp = new Instances(instances);
            tmp.clear();
            Instance instCopy = new DenseInstance(instance.weight(), values);
            instCopy.setDataset(tmp);

            return instCopy;
        }

        /**
         * Because Fastmap saves only the image not the values of the attributes it used we can not
         * use the old data directly to classify single instances to clusters.
         * 
         * To classify a single instance we do a new fastmap computation with only the instance and
         * the old pivot elements.
         * 
         * After that we find the cluster with our fastmap result for x and y.
         */
        @Override
        public double classifyInstance(Instance instance) {

            double ret = 0;
            try {
                // classinstance gets passed to classifier
                Instances traindata = ctraindata.get(0);
                Instance classInstance = createInstance(traindata, instance);

                // this one keeps the class attribute
                Instances traindata2 = ctraindata.get(1);

                // remove class attribute before clustering
                Remove filter = new Remove();
                filter.setAttributeIndices("" + (traindata.classIndex() + 1));
                filter.setInputFormat(traindata);
                traindata = Filter.useFilter(traindata, filter);
                Instance clusterInstance = createInstance(traindata, instance);

                Fastmap FMAP = new Fastmap(2);
                EuclideanDistance dist = new EuclideanDistance(traindata);

                // we set our pivot indices [x=0,y=1][dimension]
                int[][] npivotindices = new int[2][2];
                npivotindices[0][0] = 1;
                npivotindices[1][0] = 2;
                npivotindices[0][1] = 3;
                npivotindices[1][1] = 4;

                // build temp dist matrix (2 pivots per dimension + 1 instance we want to classify)
                // the instance we want to classify comes first after that the pivot elements in the
                // order defined above
                double[][] distmat = new double[2 * FMAP.target_dims + 1][2 * FMAP.target_dims + 1];
                distmat[0][0] = 0;
                distmat[0][1] =
                    dist.distance(clusterInstance,
                                  this.cpivots.get((Integer) this.cpivotindices[0][0]));
                distmat[0][2] =
                    dist.distance(clusterInstance,
                                  this.cpivots.get((Integer) this.cpivotindices[1][0]));
                distmat[0][3] =
                    dist.distance(clusterInstance,
                                  this.cpivots.get((Integer) this.cpivotindices[0][1]));
                distmat[0][4] =
                    dist.distance(clusterInstance,
                                  this.cpivots.get((Integer) this.cpivotindices[1][1]));

                distmat[1][0] =
                    dist.distance(this.cpivots.get((Integer) this.cpivotindices[0][0]),
                                  clusterInstance);
                distmat[1][1] = 0;
                distmat[1][2] =
                    dist.distance(this.cpivots.get((Integer) this.cpivotindices[0][0]),
                                  this.cpivots.get((Integer) this.cpivotindices[1][0]));
                distmat[1][3] =
                    dist.distance(this.cpivots.get((Integer) this.cpivotindices[0][0]),
                                  this.cpivots.get((Integer) this.cpivotindices[0][1]));
                distmat[1][4] =
                    dist.distance(this.cpivots.get((Integer) this.cpivotindices[0][0]),
                                  this.cpivots.get((Integer) this.cpivotindices[1][1]));

                distmat[2][0] =
                    dist.distance(this.cpivots.get((Integer) this.cpivotindices[1][0]),
                                  clusterInstance);
                distmat[2][1] =
                    dist.distance(this.cpivots.get((Integer) this.cpivotindices[1][0]),
                                  this.cpivots.get((Integer) this.cpivotindices[0][0]));
                distmat[2][2] = 0;
                distmat[2][3] =
                    dist.distance(this.cpivots.get((Integer) this.cpivotindices[1][0]),
                                  this.cpivots.get((Integer) this.cpivotindices[0][1]));
                distmat[2][4] =
                    dist.distance(this.cpivots.get((Integer) this.cpivotindices[1][0]),
                                  this.cpivots.get((Integer) this.cpivotindices[1][1]));

                distmat[3][0] =
                    dist.distance(this.cpivots.get((Integer) this.cpivotindices[0][1]),
                                  clusterInstance);
                distmat[3][1] =
                    dist.distance(this.cpivots.get((Integer) this.cpivotindices[0][1]),
                                  this.cpivots.get((Integer) this.cpivotindices[0][0]));
                distmat[3][2] =
                    dist.distance(this.cpivots.get((Integer) this.cpivotindices[0][1]),
                                  this.cpivots.get((Integer) this.cpivotindices[1][0]));
                distmat[3][3] = 0;
                distmat[3][4] =
                    dist.distance(this.cpivots.get((Integer) this.cpivotindices[0][1]),
                                  this.cpivots.get((Integer) this.cpivotindices[1][1]));

                distmat[4][0] =
                    dist.distance(this.cpivots.get((Integer) this.cpivotindices[1][1]),
                                  clusterInstance);
                distmat[4][1] =
                    dist.distance(this.cpivots.get((Integer) this.cpivotindices[1][1]),
                                  this.cpivots.get((Integer) this.cpivotindices[0][0]));
                distmat[4][2] =
                    dist.distance(this.cpivots.get((Integer) this.cpivotindices[1][1]),
                                  this.cpivots.get((Integer) this.cpivotindices[1][0]));
                distmat[4][3] =
                    dist.distance(this.cpivots.get((Integer) this.cpivotindices[1][1]),
                                  this.cpivots.get((Integer) this.cpivotindices[0][1]));
                distmat[4][4] = 0;

                /*
                 * debug output: show biggest distance found within the new distance matrix double
                 * biggest = 0; for(int i=0; i < distmat.length; i++) { for(int j=0; j <
                 * distmat[0].length; j++) { if(biggest < distmat[i][j]) { biggest = distmat[i][j];
                 * } } } if(this.show_biggest) { Console.traceln(Level.INFO,
                 * String.format(""+clusterInstance)); Console.traceln(Level.INFO,
                 * String.format("biggest distances: "+ biggest)); this.show_biggest = false; }
                 */

                FMAP.setDistmat(distmat);
                FMAP.setPivots(npivotindices);
                FMAP.calculate();
                double[][] x = FMAP.getX();
                double[] proj = x[0];

                // debug output: show the calculated distance matrix, our result vektor for the
                // instance and the complete result matrix
                /*
                 * Console.traceln(Level.INFO, "distmat:"); for(int i=0; i<distmat.length; i++){
                 * for(int j=0; j<distmat[0].length; j++){ Console.trace(Level.INFO,
                 * String.format("%20s", distmat[i][j])); } Console.traceln(Level.INFO, ""); }
                 * 
                 * Console.traceln(Level.INFO, "vector:"); for(int i=0; i < proj.length; i++) {
                 * Console.trace(Level.INFO, String.format("%20s", proj[i])); }
                 * Console.traceln(Level.INFO, "");
                 * 
                 * Console.traceln(Level.INFO, "resultmat:"); for(int i=0; i<x.length; i++){ for(int
                 * j=0; j<x[0].length; j++){ Console.trace(Level.INFO, String.format("%20s",
                 * x[i][j])); } Console.traceln(Level.INFO, ""); }
                 */

                // now we iterate over all clusters (well, boxes of sizes per cluster really) and
                // save the number of the
                // cluster in which we are
                int cnumber;
                int found_cnumber = -1;
                Iterator<Integer> clusternumber = this.csize.keySet().iterator();
                while (clusternumber.hasNext() && found_cnumber == -1) {
                    cnumber = clusternumber.next();

                    // now iterate over the boxes of the cluster and hope we find one (cluster could
                    // have been removed)
                    // or we are too far away from any cluster because of the fastmap calculation
                    // with the initial pivot objects
                    for (int box = 0; box < this.csize.get(cnumber).size(); box++) {
                        Double[][] current = this.csize.get(cnumber).get(box);

                        if (proj[0] >= current[0][0] && proj[0] <= current[0][1] && // x
                            proj[1] >= current[1][0] && proj[1] <= current[1][1])
                        { // y
                            found_cnumber = cnumber;
                        }
                    }
                }

                // we want to count how often we are really inside a cluster
                // if ( found_cnumber == -1 ) {
                // CNOTFOUND += 1;
                // }else {
                // CFOUND += 1;
                // }

                // now it can happen that we do not find a cluster because we deleted it previously
                // (too few instances)
                // or we get bigger distance measures from weka so that we are completely outside of
                // our clusters.
                // in these cases we just find the nearest cluster to our instance and use it for
                // classification.
                // to do that we use the EuclideanDistance again to compare our distance to all
                // other Instances
                // then we take the cluster of the closest weka instance
                dist = new EuclideanDistance(traindata2);
                if (!this.ctraindata.containsKey(found_cnumber)) {
                    double min_distance = Double.MAX_VALUE;
                    clusternumber = ctraindata.keySet().iterator();
                    while (clusternumber.hasNext()) {
                        cnumber = clusternumber.next();
                        for (int i = 0; i < ctraindata.get(cnumber).size(); i++) {
                            if (dist.distance(instance, ctraindata.get(cnumber).get(i)) <= min_distance)
                            {
                                found_cnumber = cnumber;
                                min_distance =
                                    dist.distance(instance, ctraindata.get(cnumber).get(i));
                            }
                        }
                    }
                }

                // here we have the cluster where an instance has the minimum distance between
                // itself and the
                // instance we want to classify
                // if we still have not found a cluster we exit because something is really wrong
                if (found_cnumber == -1) {
                    Console.traceln(Level.INFO, String
                        .format("ERROR matching instance to cluster with full search!"));
                    throw new RuntimeException("cluster not found with full search");
                }

                // classify the passed instance with the cluster we found and its training data
                ret = cclassifier.get(found_cnumber).classifyInstance(classInstance);

            }
            catch (Exception e) {
                Console.traceln(Level.INFO, String.format("ERROR matching instance to cluster!"));
                throw new RuntimeException(e);
            }
            return ret;
        }

        @Override
        public void buildClassifier(Instances traindata) throws Exception {

            // Console.traceln(Level.INFO, String.format("found: "+ CFOUND + ", notfound: " +
            // CNOTFOUND));
            this.show_biggest = true;

            cclassifier = new HashMap<Integer, Classifier>();
            ctraindata = new HashMap<Integer, Instances>();
            cpivots = new HashMap<Integer, Instance>();
            cpivotindices = new int[2][2];

            // 1. copy traindata
            Instances train = new Instances(traindata);
            Instances train2 = new Instances(traindata); // this one keeps the class attribute

            // 2. remove class attribute for clustering
            Remove filter = new Remove();
            filter.setAttributeIndices("" + (train.classIndex() + 1));
            filter.setInputFormat(train);
            train = Filter.useFilter(train, filter);

            // 3. calculate distance matrix (needed for Fastmap because it starts at dimension 1)
            double biggest = 0;
            EuclideanDistance dist = new EuclideanDistance(train);
            double[][] distmat = new double[train.size()][train.size()];
            for (int i = 0; i < train.size(); i++) {
                for (int j = 0; j < train.size(); j++) {
                    distmat[i][j] = dist.distance(train.get(i), train.get(j));
                    if (distmat[i][j] > biggest) {
                        biggest = distmat[i][j];
                    }
                }
            }
            // Console.traceln(Level.INFO, String.format("biggest distances: "+ biggest));

            // 4. run fastmap for 2 dimensions on the distance matrix
            Fastmap FMAP = new Fastmap(2);
            FMAP.setDistmat(distmat);
            FMAP.calculate();

            cpivotindices = FMAP.getPivots();

            double[][] X = FMAP.getX();
            distmat = new double[0][0];
            System.gc();

            // quadtree payload generation
            ArrayList<QuadTreePayload<Instance>> qtp = new ArrayList<QuadTreePayload<Instance>>();

            // we need these for the sizes of the quadrants
            double[] big =
                { 0, 0 };
            double[] small =
                { Double.MAX_VALUE, Double.MAX_VALUE };

            // set quadtree payload values and get max and min x and y values for size
            for (int i = 0; i < X.length; i++) {
                if (X[i][0] >= big[0]) {
                    big[0] = X[i][0];
                }
                if (X[i][1] >= big[1]) {
                    big[1] = X[i][1];
                }
                if (X[i][0] <= small[0]) {
                    small[0] = X[i][0];
                }
                if (X[i][1] <= small[1]) {
                    small[1] = X[i][1];
                }
                QuadTreePayload<Instance> tmp =
                    new QuadTreePayload<Instance>(X[i][0], X[i][1], train2.get(i));
                qtp.add(tmp);
            }

            // Console.traceln(Level.INFO,
            // String.format("size for cluster ("+small[0]+","+small[1]+") - ("+big[0]+","+big[1]+")"));

            // 5. generate quadtree
            QuadTree TREE = new QuadTree(null, qtp);
            QuadTree.size = train.size();
            QuadTree.alpha = Math.sqrt(train.size());
            QuadTree.ccluster = new ArrayList<ArrayList<QuadTreePayload<Instance>>>();
            QuadTree.csize = new HashMap<Integer, ArrayList<Double[][]>>();

            // Console.traceln(Level.INFO, String.format("Generate QuadTree with "+ QuadTree.size +
            // " size, Alpha: "+ QuadTree.alpha+ ""));

            // set the size and then split the tree recursively at the median value for x, y
            TREE.setSize(new double[]
                { small[0], big[0] }, new double[]
                { small[1], big[1] });

            // recursive split und grid clustering eher static
            TREE.recursiveSplit(TREE);

            // generate list of nodes sorted by density (childs only)
            ArrayList<QuadTree> l = new ArrayList<QuadTree>(TREE.getList(TREE));

            // recursive grid clustering (tree pruning), the values are stored in ccluster
            TREE.gridClustering(l);

            // wir iterieren durch die cluster und sammeln uns die instanzen daraus
            // ctraindata.clear();
            for (int i = 0; i < QuadTree.ccluster.size(); i++) {
                ArrayList<QuadTreePayload<Instance>> current = QuadTree.ccluster.get(i);

                // i is the clusternumber
                // we only allow clusters with Instances > ALPHA, other clusters are not considered!
                // if(current.size() > QuadTree.alpha) {
                if (current.size() > 4) {
                    for (int j = 0; j < current.size(); j++) {
                        if (!ctraindata.containsKey(i)) {
                            ctraindata.put(i, new Instances(train2));
                            ctraindata.get(i).delete();
                        }
                        ctraindata.get(i).add(current.get(j).getInst());
                    }
                }
                else {
                    Console.traceln(Level.INFO,
                                    String.format("drop cluster, only: " + current.size() +
                                        " instances"));
                }
            }

            // here we keep things we need later on
            // QuadTree sizes for later use (matching new instances)
            this.csize = new HashMap<Integer, ArrayList<Double[][]>>(QuadTree.csize);

            // pivot elements
            // this.cpivots.clear();
            for (int i = 0; i < FMAP.PA[0].length; i++) {
                this.cpivots.put(FMAP.PA[0][i], (Instance) train.get(FMAP.PA[0][i]).copy());
            }
            for (int j = 0; j < FMAP.PA[0].length; j++) {
                this.cpivots.put(FMAP.PA[1][j], (Instance) train.get(FMAP.PA[1][j]).copy());
            }

            /*
             * debug output int pnumber; Iterator<Integer> pivotnumber =
             * cpivots.keySet().iterator(); while ( pivotnumber.hasNext() ) { pnumber =
             * pivotnumber.next(); Console.traceln(Level.INFO, String.format("pivot: "+pnumber+
             * " inst: "+cpivots.get(pnumber))); }
             */

            // train one classifier per cluster, we get the cluster number from the traindata
            int cnumber;
            Iterator<Integer> clusternumber = ctraindata.keySet().iterator();
            // cclassifier.clear();

            // int traindata_count = 0;
            while (clusternumber.hasNext()) {
                cnumber = clusternumber.next();
                cclassifier.put(cnumber, setupClassifier()); // this is the classifier used for the
                                                             // cluster
                cclassifier.get(cnumber).buildClassifier(ctraindata.get(cnumber));
                // Console.traceln(Level.INFO, String.format("classifier in cluster "+cnumber));
                // traindata_count += ctraindata.get(cnumber).size();
                // Console.traceln(Level.INFO,
                // String.format("building classifier in cluster "+cnumber +"  with "+
                // ctraindata.get(cnumber).size() +" traindata instances"));
            }

            // add all traindata
            // Console.traceln(Level.INFO, String.format("traindata in all clusters: " +
            // traindata_count));
        }
    }

    /**
     * Payload for the QuadTree. x and y are the calculated Fastmap values. T is a weka instance.
     */
    public class QuadTreePayload<T> {

        public double x;
        public double y;
        private T inst;

        public QuadTreePayload(double x, double y, T value) {
            this.x = x;
            this.y = y;
            this.inst = value;
        }

        public T getInst() {
            return this.inst;
        }
    }

    /**
     * Fastmap implementation
     * 
     * Faloutsos, C., & Lin, K. I. (1995). FastMap: A fast algorithm for indexing, data-mining and
     * visualization of traditional and multimedia datasets (Vol. 24, No. 2, pp. 163-174). ACM.
     */
    public class Fastmap {

        /* N x k Array, at the end, the i-th row will be the image of the i-th object */
        private double[][] X;

        /* 2 x k pivot Array one pair per recursive call */
        private int[][] PA;

        /* Objects we got (distance matrix) */
        private double[][] O;

        /* column of X currently updated (also the dimension) */
        private int col = 0;

        /* number of dimensions we want */
        private int target_dims = 0;

        // if we already have the pivot elements
        private boolean pivot_set = false;

        public Fastmap(int k) {
            this.target_dims = k;
        }

        /**
         * Sets the distance matrix and params that depend on this
         * 
         * @param O
         */
        public void setDistmat(double[][] O) {
            this.O = O;
            int N = O.length;
            this.X = new double[N][this.target_dims];
            this.PA = new int[2][this.target_dims];
        }

        /**
         * Set pivot elements, we need that to classify instances after the calculation is complete
         * (because we then want to reuse only the pivot elements).
         * 
         * @param pi
         */
        public void setPivots(int[][] pi) {
            this.pivot_set = true;
            this.PA = pi;
        }

        /**
         * Return the pivot elements that were chosen during the calculation
         * 
         * @return
         */
        public int[][] getPivots() {
            return this.PA;
        }

        /**
         * The distance function for euclidean distance
         * 
         * Acts according to equation 4 of the fastmap paper
         * 
         * @param x
         *            x index of x image (if k==0 x object)
         * @param y
         *            y index of y image (if k==0 y object)
         * @param kdimensionality
         * @return distance
         */
        private double dist(int x, int y, int k) {

            // basis is object distance, we get this from our distance matrix
            double tmp = this.O[x][y] * this.O[x][y];

            // decrease by projections
            for (int i = 0; i < k; i++) {
                double tmp2 = (this.X[x][i] - this.X[y][i]);
                tmp -= tmp2 * tmp2;
            }

            return Math.abs(tmp);
        }

        /**
         * Find the object farthest from the given index This method is a helper Method for
         * findDistandObjects
         * 
         * @param index
         *            of the object
         * @return index of the farthest object from the given index
         */
        private int findFarthest(int index) {
            double furthest = Double.MIN_VALUE;
            int ret = 0;

            for (int i = 0; i < O.length; i++) {
                double dist = this.dist(i, index, this.col);
                if (i != index && dist > furthest) {
                    furthest = dist;
                    ret = i;
                }
            }
            return ret;
        }

        /**
         * Finds the pivot objects
         * 
         * This method is basically algorithm 1 of the fastmap paper.
         * 
         * @return 2 indexes of the choosen pivot objects
         */
        private int[] findDistantObjects() {
            // 1. choose object randomly
            Random r = new Random();
            int obj = r.nextInt(this.O.length);

            // 2. find farthest object from randomly chosen object
            int idx1 = this.findFarthest(obj);

            // 3. find farthest object from previously farthest object
            int idx2 = this.findFarthest(idx1);

            return new int[]
                { idx1, idx2 };
        }

        /**
         * Calculates the new k-vector values (projections)
         * 
         * This is basically algorithm 2 of the fastmap paper. We just added the possibility to
         * pre-set the pivot elements because we need to classify single instances after the
         * computation is already done.
         * 
         * @param dims
         *            dimensionality
         */
        public void calculate() {

            for (int k = 0; k < this.target_dims; k++) {
                // 2) choose pivot objects
                if (!this.pivot_set) {
                    int[] pivots = this.findDistantObjects();

                    // 3) record ids of pivot objects
                    this.PA[0][this.col] = pivots[0];
                    this.PA[1][this.col] = pivots[1];
                }

                // 4) inter object distances are zero (this.X is initialized with 0 so we just
                // continue)
                if (this.dist(this.PA[0][this.col], this.PA[1][this.col], this.col) == 0) {
                    continue;
                }

                // 5) project the objects on the line between the pivots
                double dxy = this.dist(this.PA[0][this.col], this.PA[1][this.col], this.col);
                for (int i = 0; i < this.O.length; i++) {

                    double dix = this.dist(i, this.PA[0][this.col], this.col);
                    double diy = this.dist(i, this.PA[1][this.col], this.col);

                    double tmp = (dix + dxy - diy) / (2 * Math.sqrt(dxy));

                    // save the projection
                    this.X[i][this.col] = tmp;
                }

                this.col += 1;
            }
        }

        /**
         * returns the result matrix of the projections
         * 
         * @return calculated result
         */
        public double[][] getX() {
            return this.X;
        }
    }
}