ClustreamKernel.java

package org.apache.samoa.moa.clusterers.clustream;

/*
 * #%L
 * SAMOA
 * %%
 * Copyright (C) 2014 - 2015 Apache Software Foundation
 * %%
 * 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.
 * #L%
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import java.util.List;

import org.apache.samoa.instances.Instance;
import org.apache.samoa.moa.cluster.CFCluster;

public class ClustreamKernel extends CFCluster {
  private static final long serialVersionUID = 1L;

  private final static double EPSILON = 0.00005;
  public static final double MIN_VARIANCE = 1e-50;

  protected double LST;
  protected double SST;

  int m;
  double t;

  public ClustreamKernel(Instance instance, int dimensions, long timestamp, double t, int m) {
    super(instance, dimensions);
    this.t = t;
    this.m = m;
    this.LST = timestamp;
    this.SST = timestamp * timestamp;
  }

  public ClustreamKernel(ClustreamKernel cluster, double t, int m) {
    super(cluster);
    this.t = t;
    this.m = m;
    this.LST = cluster.LST;
    this.SST = cluster.SST;
  }

  public void insert(Instance instance, long timestamp) {
    N++;
    LST += timestamp;
    SST += timestamp * timestamp;

    for (int i = 0; i < instance.numValues(); i++) {
      LS[i] += instance.value(i);
      SS[i] += instance.value(i) * instance.value(i);
    }
  }

  @Override
  public void add(CFCluster other2) {
    ClustreamKernel other = (ClustreamKernel) other2;
    assert (other.LS.length == this.LS.length);
    this.N += other.N;
    this.LST += other.LST;
    this.SST += other.SST;

    for (int i = 0; i < LS.length; i++) {
      this.LS[i] += other.LS[i];
      this.SS[i] += other.SS[i];
    }
  }

  public double getRelevanceStamp() {
    if (N < 2 * m)
      return getMuTime();

    return getMuTime() + getSigmaTime() * getQuantile(((double) m) / (2 * N));
  }

  private double getMuTime() {
    return LST / N;
  }

  private double getSigmaTime() {
    return Math.sqrt(SST / N - (LST / N) * (LST / N));
  }

  private double getQuantile(double z) {
    assert (z >= 0 && z <= 1);
    return Math.sqrt(2) * inverseError(2 * z - 1);
  }

  @Override
  public double getRadius() {
    // trivial cluster
    if (N == 1)
      return 0;
    if (t == 1)
      t = 1;

    return getDeviation() * radiusFactor;
  }

  @Override
  public CFCluster getCF() {
    return this;
  }

  private double getDeviation() {
    double[] variance = getVarianceVector();
    double sumOfDeviation = 0.0;
    for (double aVariance : variance) {
      double d = Math.sqrt(aVariance);
      sumOfDeviation += d;
    }
    return sumOfDeviation / variance.length;
  }

  /**
   * @return this kernels' center
   */
  @Override
  public double[] getCenter() {
    assert (!this.isEmpty());
    double res[] = new double[this.LS.length];
    for (int i = 0; i < res.length; i++) {
      res[i] = this.LS[i] / N;
    }
    return res;
  }

  /**
   * See interface <code>Cluster</code>
   * 
   * @param instance
   * @return double value
   */
  @Override
  public double getInclusionProbability(Instance instance) {
    // trivial cluster
    if (N == 1) {
      double distance = 0.0;
      for (int i = 0; i < LS.length; i++) {
        double d = LS[i] - instance.value(i);
        distance += d * d;
      }
      distance = Math.sqrt(distance);
      if (distance < EPSILON)
        return 1.0;
      return 0.0;
    }
    else {
      double dist = calcNormalizedDistance(instance.toDoubleArray());
      if (dist <= getRadius()) {
        return 1;
      }
      else {
        return 0;
      }
      // double res = AuxiliaryFunctions.distanceProbabilty(dist, LS.length);
      // return res;
    }
  }

  private double[] getVarianceVector() {
    double[] res = new double[this.LS.length];
    for (int i = 0; i < this.LS.length; i++) {
      double ls = this.LS[i];
      double ss = this.SS[i];

      double lsDivN = ls / this.getWeight();
      double lsDivNSquared = lsDivN * lsDivN;
      double ssDivN = ss / this.getWeight();
      res[i] = ssDivN - lsDivNSquared;

      // Due to numerical errors, small negative values can occur.
      // We correct this by settings them to almost zero.
      if (res[i] <= 0.0) {
        if (res[i] > -EPSILON) {
          res[i] = MIN_VARIANCE;
        }
      }
    }
    return res;
  }

  /**
   * Check if this cluster is empty or not.
   * 
   * @return <code>true</code> if the cluster has no data points, <code>false</code> otherwise.
   */
  public boolean isEmpty() {
    return this.N == 0;
  }

  /**
   * Calculate the normalized euclidean distance (Mahalanobis distance for distribution w/o covariances) to a point.
   * 
   * @param point
   *          The point to which the distance is calculated.
   * @return The normalized distance to the cluster center.
   * 
   *         TODO: check whether WEIGHTING is correctly applied to variances
   */
  // ???????
  private double calcNormalizedDistance(double[] point) {
    double[] center = getCenter();
    double res = 0.0;

    for (int i = 0; i < center.length; i++) {
      double diff = center[i] - point[i];
      res += (diff * diff);// variance[i];
    }
    return Math.sqrt(res);
  }

  /**
   * Approximates the inverse error function. Clustream needs this.
   * 
   * @param x
   */
  public static double inverseError(double x) {
    double z = Math.sqrt(Math.PI) * x;
    double res = (z) / 2;

    double z2 = z * z;
    double zProd = z * z2; // z^3
    res += (1.0 / 24) * zProd;

    zProd *= z2; // z^5
    res += (7.0 / 960) * zProd;

    zProd *= z2; // z^7
    res += (127 * zProd) / 80640;

    zProd *= z2; // z^9
    res += (4369 * zProd) / 11612160;

    zProd *= z2; // z^11
    res += (34807 * zProd) / 364953600;

    zProd *= z2; // z^13
    res += (20036983 * zProd) / 797058662400d;

    return res;
  }

  @Override
  protected void getClusterSpecificInfo(List<String> infoTitle, List<String> infoValue) {
    super.getClusterSpecificInfo(infoTitle, infoValue);
    infoTitle.add("Deviation");

    double[] variance = getVarianceVector();
    double sumOfDeviation = 0.0;
    for (double aVariance : variance) {
      double d = Math.sqrt(aVariance);
      sumOfDeviation += d;
    }

    sumOfDeviation /= variance.length;

    infoValue.add(Double.toString(sumOfDeviation));
  }
}