package de.lmu.ifi.dbs.elki.math.linearalgebra.pca;

/*
 This file is part of ELKI:
 Environment for Developing KDD-Applications Supported by Index-Structures

 Copyright (C) 2015
 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 de.lmu.ifi.dbs.elki.math.linearalgebra.EigenPair;
import de.lmu.ifi.dbs.elki.math.linearalgebra.SortedEigenPairs;
import de.lmu.ifi.dbs.elki.utilities.documentation.Description;
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.constraints.CommonConstraints;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameterization.Parameterization;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameters.DoubleParameter;

/**
 * The SignificantEigenPairFilter sorts the eigenpairs in descending order of
 * their eigenvalues and chooses the contrast of an Eigenvalue to the remaining
 * Eigenvalues is maximal.
 *
 * It is closely related to the WeakEigenPairFilter and RelativeEigenPairFilter.
 * But while the RelativeEigenPairFilter chooses the highest dimensionality that
 * satisfies the relative alpha levels, the SignificantEigenPairFilter will
 * chose the local dimensionality such that the 'contrast' is maximal.
 *
 * There are some situations where one or the other is superior, especially when
 * it comes to handling nested clusters and strong global correlations that are
 * not too interesting. These benefits usually only make a difference at higher
 * dimensionalities.
 *
 * @author Erich Schubert
 * @since 0.2
 */
@Title("Significant EigenPair Filter")
@Description("Sorts the eigenpairs in decending order of their eigenvalues and looks for the maxmimum contrast of current Eigenvalue / average of remaining Eigenvalues.")
public class SignificantEigenPairFilter implements EigenPairFilter {
  /**
   * The default value for walpha. Not used by default, we're going for maximum
   * contrast only.
   */
  public static final double DEFAULT_WALPHA = 0.0;

  /**
   * The noise tolerance level for weak eigenvectors
   */
  private double walpha;

  /**
   * Constructor.
   *
   * @param walpha
   */
  public SignificantEigenPairFilter(double walpha) {
    super();
    this.walpha = walpha;
  }

  @Override
  public FilteredEigenPairs filter(SortedEigenPairs eigenPairs) {
    // init strong and weak eigenpairs
    List<EigenPair> strongEigenPairs = new ArrayList<>();
    List<EigenPair> weakEigenPairs = new ArrayList<>();

    // default value is "all strong".
    int contrastMaximum = eigenPairs.size() - 1;
    double maxContrast = 0.0;
    // calc the eigenvalue sum.
    double eigenValueSum = 0.0;
    for(int i = 0; i < eigenPairs.size(); i++) {
      EigenPair eigenPair = eigenPairs.getEigenPair(i);
      eigenValueSum += eigenPair.getEigenvalue();
    }
    double weakEigenvalue = eigenValueSum / eigenPairs.size() * walpha;
    // now find the maximum contrast.
    double currSum = eigenPairs.getEigenPair(eigenPairs.size() - 1).getEigenvalue();
    for(int i = eigenPairs.size() - 2; i >= 0; i--) {
      EigenPair eigenPair = eigenPairs.getEigenPair(i);
      currSum += eigenPair.getEigenvalue();
      // weak?
      if(eigenPair.getEigenvalue() < weakEigenvalue) {
        continue;
      }
      double contrast = eigenPair.getEigenvalue() / (currSum / (eigenPairs.size() - i));
      if(contrast > maxContrast) {
        maxContrast = contrast;
        contrastMaximum = i;
      }
    }

    for(int i = 0; i <= contrastMaximum /* && i < eigenPairs.size() */; i++) {
      EigenPair eigenPair = eigenPairs.getEigenPair(i);
      strongEigenPairs.add(eigenPair);
    }
    for(int i = contrastMaximum + 1; i < eigenPairs.size(); i++) {
      EigenPair eigenPair = eigenPairs.getEigenPair(i);
      weakEigenPairs.add(eigenPair);
    }

    return new FilteredEigenPairs(weakEigenPairs, strongEigenPairs);
  }

  /**
   * Parameterization class.
   *
   * @author Erich Schubert
   *
   * @apiviz.exclude
   */
  public static class Parameterizer extends AbstractParameterizer {
    private double walpha;

    @Override
    protected void makeOptions(Parameterization config) {
      super.makeOptions(config);
      DoubleParameter walphaP = new DoubleParameter(WeakEigenPairFilter.Parameterizer.EIGENPAIR_FILTER_WALPHA, DEFAULT_WALPHA);
      walphaP.addConstraint(CommonConstraints.GREATER_EQUAL_ZERO_DOUBLE);
      if(config.grab(walphaP)) {
        walpha = walphaP.getValue();
      }
    }

    @Override
    protected SignificantEigenPairFilter makeInstance() {
      return new SignificantEigenPairFilter(walpha);
    }
  }
}
