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weka.classifiers.functions.SGD Maven / Gradle / Ivy

/*
 *   This program is free software: you can redistribute it and/or modify
 *   it under the terms of the GNU 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 General Public License for more details.
 *
 *   You should have received a copy of the GNU General Public License
 *   along with this program.  If not, see .
 */

/*
 *    SGD.java
 *    Copyright (C) 2009-2012 University of Waikato, Hamilton, New Zealand
 *
 */

package weka.classifiers.functions;

import java.util.ArrayList;
import java.util.Collections;
import java.util.Enumeration;
import java.util.Random;
import java.util.Vector;

import weka.classifiers.RandomizableClassifier;
import weka.classifiers.UpdateableClassifier;
import weka.core.Capabilities;
import weka.core.Capabilities.Capability;
import weka.core.Aggregateable;
import weka.core.Instance;
import weka.core.Instances;
import weka.core.Option;
import weka.core.OptionHandler;
import weka.core.RevisionUtils;
import weka.core.SelectedTag;
import weka.core.Tag;
import weka.core.Utils;
import weka.filters.Filter;
import weka.filters.unsupervised.attribute.Normalize;
import weka.filters.unsupervised.attribute.ReplaceMissingValues;

/**
 
 * Implements stochastic gradient descent for learning various linear models (binary class SVM, binary class logistic regression, squared loss, Huber loss and epsilon-insensitive loss linear regression). Globally replaces all missing values and transforms nominal attributes into binary ones. It also normalizes all attributes, so the coefficients in the output are based on the normalized data.

 * For numeric class attributes, the squared, Huber or epsilon-insensitve loss function must be used. Epsilon-insensitive and Huber loss may require a much higher learning rate.
 * 

 
 * 
 
 * Valid options are: 

 * 
 * 
 -F
 *  Set the loss function to minimize.
 *  0 = hinge loss (SVM), 1 = log loss (logistic regression),
 *  2 = squared loss (regression), 3 = epsilon insensitive loss (regression),
 *  4 = Huber loss (regression).
 *  (default = 0)
 * 
 * 
 -L
 *  The learning rate. If normalization is
 *  turned off (as it is automatically for streaming data), then the
 *  default learning rate will need to be reduced (try 0.0001).
 *  (default = 0.01).
 * 
 * 
 -R <double>
 *  The lambda regularization constant (default = 0.0001)
 * 
 * 
 -E <integer>
 *  The number of epochs to perform (batch learning only, default = 500)
 * 
 * 
 -C <double>
 *  The epsilon threshold (epsilon-insenstive and Huber loss only, default = 1e-3)
 * 
 * 
 -N
 *  Don't normalize the data
 * 
 * 
 -M
 *  Don't replace missing values
 * 
 * 
 -S <num>
 *  Random number seed.
 *  (default 1)
 * 
 * 
 -output-debug-info
 *  If set, classifier is run in debug mode and
 *  may output additional info to the console
 * 
 * 
 -do-not-check-capabilities
 *  If set, classifier capabilities are not checked before classifier is built
 *  (use with caution).
 * 
 
 * 
 * @author Eibe Frank (eibe{[at]}cs{[dot]}waikato{[dot]}ac{[dot]}nz)
 * @author Mark Hall (mhall{[at]}pentaho{[dot]}com)
 * @version $Revision: 15519 $
 * 
 */
public class SGD extends RandomizableClassifier implements
    UpdateableClassifier, OptionHandler, Aggregateable {

  /** For serialization */
  private static final long serialVersionUID = -3732968666673530290L;

  /** Replace missing values */
  protected ReplaceMissingValues m_replaceMissing;

  /**
   * Convert nominal attributes to numerically coded binary ones. Uses
   * supervised NominalToBinary in the batch learning case
   */
  protected Filter m_nominalToBinary;

  /** Normalize the training data */
  protected Normalize m_normalize;

  /** The regularization parameter */
  protected double m_lambda = 0.0001;

  /** The learning rate */
  protected double m_learningRate = 0.01;

  /** Stores the weights (+ bias in the last element) */
  protected double[] m_weights;

  /** The epsilon parameter for epsilon insensitive and Huber loss */
  protected double m_epsilon = 1e-3;

  /** Holds the current iteration number */
  protected double m_t;

  /** The number of training instances */
  protected double m_numInstances;

  /**
   * The number of epochs to perform (batch learning). Total iterations is
   * m_epochs * num instances
   */
  protected int m_epochs = 500;

  /**
   * Turn off normalization of the input data. This option gets forced for
   * incremental training.
   */
  protected boolean m_dontNormalize = false;

  /**
   * Turn off global replacement of missing values. Missing values will be
   * ignored instead. This option gets forced for incremental training.
   */
  protected boolean m_dontReplaceMissing = false;

  /** Holds the header of the training data */
  protected Instances m_data;

  /**
   * Returns default capabilities of the classifier.
   * 
   * @return the capabilities of this classifier
   */
  @Override
  public Capabilities getCapabilities() {
    Capabilities result = super.getCapabilities();
    result.disableAll();

    // attributes
    result.enable(Capability.NOMINAL_ATTRIBUTES);
    result.enable(Capability.NUMERIC_ATTRIBUTES);
    result.enable(Capability.MISSING_VALUES);

    // class
    if (m_loss == SQUAREDLOSS || m_loss == EPSILON_INSENSITIVE
        || m_loss == HUBER)
      result.enable(Capability.NUMERIC_CLASS);
    else
      result.enable(Capability.BINARY_CLASS);
    result.enable(Capability.MISSING_CLASS_VALUES);

    // instances
    result.setMinimumNumberInstances(0);

    return result;
  }

  /**
   * Returns the tip text for this property
   * 
   * @return tip text for this property suitable for displaying in the
   *         explorer/experimenter gui
   */
  public String epsilonTipText() {
    return "The epsilon threshold for epsilon insensitive and Huber "
        + "loss. An error with absolute value less that this "
        + "threshold has loss of 0 for epsilon insensitive loss. "
        + "For Huber loss this is the boundary between the quadratic "
        + "and linear parts of the loss function.";
  }

  /**
   * Set the epsilon threshold on the error for epsilon insensitive and Huber
   * loss functions
   * 
   * @param e the value of epsilon to use
   */
  public void setEpsilon(double e) {
    m_epsilon = e;
  }

  /**
   * Get the epsilon threshold on the error for epsilon insensitive and Huber
   * loss functions
   * 
   * @return the value of epsilon to use
   */
  public double getEpsilon() {
    return m_epsilon;
  }

  /**
   * Returns the tip text for this property
   * 
   * @return tip text for this property suitable for displaying in the
   *         explorer/experimenter gui
   */
  public String lambdaTipText() {
    return "The regularization constant. (default = 0.0001)";
  }

  /**
   * Set the value of lambda to use
   * 
   * @param lambda the value of lambda to use
   */
  public void setLambda(double lambda) {
    m_lambda = lambda;
  }

  /**
   * Get the current value of lambda
   * 
   * @return the current value of lambda
   */
  public double getLambda() {
    return m_lambda;
  }

  /**
   * Set the learning rate.
   * 
   * @param lr the learning rate to use.
   */
  public void setLearningRate(double lr) {
    m_learningRate = lr;
  }

  /**
   * Get the learning rate.
   * 
   * @return the learning rate
   */
  public double getLearningRate() {
    return m_learningRate;
  }

  /**
   * Returns the tip text for this property
   * 
   * @return tip text for this property suitable for displaying in the
   *         explorer/experimenter gui
   */
  public String learningRateTipText() {
    return "The learning rate. If normalization is turned off "
        + "(as it is automatically for streaming data), then"
        + "the default learning rate will need to be reduced ("
        + "try 0.0001).";
  }

  /**
   * Returns the tip text for this property
   * 
   * @return tip text for this property suitable for displaying in the
   *         explorer/experimenter gui
   */
  public String epochsTipText() {
    return "The number of epochs to perform (batch learning). "
        + "The total number of iterations is epochs * num" + " instances.";
  }

  /**
   * Set the number of epochs to use
   * 
   * @param e the number of epochs to use
   */
  public void setEpochs(int e) {
    m_epochs = e;
  }

  /**
   * Get current number of epochs
   * 
   * @return the current number of epochs
   */
  public int getEpochs() {
    return m_epochs;
  }

  /**
   * Turn normalization off/on.
   * 
   * @param m true if normalization is to be disabled.
   */
  public void setDontNormalize(boolean m) {
    m_dontNormalize = m;
  }

  /**
   * Get whether normalization has been turned off.
   * 
   * @return true if normalization has been disabled.
   */
  public boolean getDontNormalize() {
    return m_dontNormalize;
  }

  /**
   * Returns the tip text for this property
   * 
   * @return tip text for this property suitable for displaying in the
   *         explorer/experimenter gui
   */
  public String dontNormalizeTipText() {
    return "Turn normalization off";
  }

  /**
   * Turn global replacement of missing values off/on. If turned off, then
   * missing values are effectively ignored.
   * 
   * @param m true if global replacement of missing values is to be turned off.
   */
  public void setDontReplaceMissing(boolean m) {
    m_dontReplaceMissing = m;
  }

  /**
   * Get whether global replacement of missing values has been disabled.
   * 
   * @return true if global replacement of missing values has been turned off
   */
  public boolean getDontReplaceMissing() {
    return m_dontReplaceMissing;
  }

  /**
   * Returns the tip text for this property
   * 
   * @return tip text for this property suitable for displaying in the
   *         explorer/experimenter gui
   */
  public String dontReplaceMissingTipText() {
    return "Turn off global replacement of missing values";
  }

  /**
   * Set the loss function to use.
   * 
   * @param function the loss function to use.
   */
  public void setLossFunction(SelectedTag function) {
    if (function.getTags() == TAGS_SELECTION) {
      m_loss = function.getSelectedTag().getID();
    }
  }

  /**
   * Get the current loss function.
   * 
   * @return the current loss function.
   */
  public SelectedTag getLossFunction() {
    return new SelectedTag(m_loss, TAGS_SELECTION);
  }

  /**
   * Returns the tip text for this property
   * 
   * @return tip text for this property suitable for displaying in the
   *         explorer/experimenter gui
   */
  public String lossFunctionTipText() {
    return "The loss function to use. Hinge loss (SVM), "
        + "log loss (logistic regression) or " + "squared loss (regression).";
  }

  /**
   * Returns an enumeration describing the available options.
   * 
   * @return an enumeration of all the available options.
   */
  @Override
  public Enumeration listOptions() {

    Vector newVector = new Vector();
    newVector.add(new Option("\tSet the loss function to minimize.\n\t0 = "
        + "hinge loss (SVM), 1 = log loss (logistic regression),\n\t"
        + "2 = squared loss (regression), 3 = epsilon insensitive loss (regression)," +
        "\n\t4 = Huber loss (regression).\n\t(default = 0)", "F", 1, "-F"));
    newVector
        .add(new Option(
            "\tThe learning rate. If normalization is\n"
                + "\tturned off (as it is automatically for streaming data), then the\n\t"
                + "default learning rate will need to be reduced "
                + "(try 0.0001).\n\t(default = 0.01).", "L", 1, "-L"));
    newVector.add(new Option("\tThe lambda regularization constant "
        + "(default = 0.0001)", "R", 1, "-R "));
    newVector.add(new Option("\tThe number of epochs to perform ("
        + "batch learning only, default = 500)", "E", 1, "-E "));
    newVector.add(new Option("\tThe epsilon threshold ("
        + "epsilon-insenstive and Huber loss only, default = 1e-3)", "C", 1,
        "-C "));
    newVector.add(new Option("\tDon't normalize the data", "N", 0, "-N"));
    newVector.add(new Option("\tDon't replace missing values", "M", 0, "-M"));

    newVector.addAll(Collections.list(super.listOptions()));
    
    return newVector.elements();
  }

  /**
   * 
   * Parses a given list of options.
   * 

   * 
   
   * Valid options are: 

   * 
   * 
 -F
   *  Set the loss function to minimize.
   *  0 = hinge loss (SVM), 1 = log loss (logistic regression),
   *  2 = squared loss (regression), 3 = epsilon insensitive loss (regression),
   *  4 = Huber loss (regression).
   *  (default = 0)
   * 
   * 
 -L
   *  The learning rate. If normalization is
   *  turned off (as it is automatically for streaming data), then the
   *  default learning rate will need to be reduced (try 0.0001).
   *  (default = 0.01).
   * 
   * 
 -R <double>
   *  The lambda regularization constant (default = 0.0001)
   * 
   * 
 -E <integer>
   *  The number of epochs to perform (batch learning only, default = 500)
   * 
   * 
 -C <double>
   *  The epsilon threshold (epsilon-insenstive and Huber loss only, default = 1e-3)
   * 
   * 
 -N
   *  Don't normalize the data
   * 
   * 
 -M
   *  Don't replace missing values
   * 
   * 
 -S <num>
   *  Random number seed.
   *  (default 1)
   * 
   * 
 -output-debug-info
   *  If set, classifier is run in debug mode and
   *  may output additional info to the console
   * 
   * 
 -do-not-check-capabilities
   *  If set, classifier capabilities are not checked before classifier is built
   *  (use with caution).
   * 
   
   * 
   * @param options the list of options as an array of strings
   * @throws Exception if an option is not supported
   */
  @Override
  public void setOptions(String[] options) throws Exception {
    reset();

    String lossString = Utils.getOption('F', options);
    if (lossString.length() != 0) {
      setLossFunction(new SelectedTag(Integer.parseInt(lossString),
          TAGS_SELECTION));
    }

    String lambdaString = Utils.getOption('R', options);
    if (lambdaString.length() > 0) {
      setLambda(Double.parseDouble(lambdaString));
    }

    String learningRateString = Utils.getOption('L', options);
    if (learningRateString.length() > 0) {
      setLearningRate(Double.parseDouble(learningRateString));
    }

    String epochsString = Utils.getOption("E", options);
    if (epochsString.length() > 0) {
      setEpochs(Integer.parseInt(epochsString));
    }

    String epsilonString = Utils.getOption("C", options);
    if (epsilonString.length() > 0) {
      setEpsilon(Double.parseDouble(epsilonString));
    }

    setDontNormalize(Utils.getFlag("N", options));
    setDontReplaceMissing(Utils.getFlag('M', options));

    super.setOptions(options);
  }

  /**
   * Gets the current settings of the classifier.
   * 
   * @return an array of strings suitable for passing to setOptions
   */
  @Override
  public String[] getOptions() {
    ArrayList options = new ArrayList();

    options.add("-F");
    options.add("" + getLossFunction().getSelectedTag().getID());
    options.add("-L");
    options.add("" + getLearningRate());
    options.add("-R");
    options.add("" + getLambda());
    options.add("-E");
    options.add("" + getEpochs());
    options.add("-C");
    options.add("" + getEpsilon());
    if (getDontNormalize()) {
      options.add("-N");
    }
    if (getDontReplaceMissing()) {
      options.add("-M");
    }

    Collections.addAll(options, super.getOptions());
    
    return options.toArray(new String[1]);
  }

  /**
   * Returns a string describing classifier
   * 
   * @return a description suitable for displaying in the explorer/experimenter
   *         gui
   */
  public String globalInfo() {
    return "Implements stochastic gradient descent for learning"
        + " various linear models (binary class SVM, binary class"
        + " logistic regression, squared loss, Huber loss and "
        + "epsilon-insensitive loss linear regression)."
        + " Globally replaces all missing values and transforms nominal"
        + " attributes into binary ones. It also normalizes all attributes,"
        + " so the coefficients in the output are based on the normalized"
        + " data.\n" + "For numeric class attributes, the squared, Huber or "
        + "epsilon-insensitve loss function must be used. Epsilon-insensitive "
        + "and Huber loss may require a much higher learning rate.";
  }

  /**
   * Reset the classifier.
   */
  public void reset() {
    m_t = 1;
    m_weights = null;
  }

  /**
   * Method for building the classifier.
   * 
   * @param data the set of training instances.
   * @throws Exception if the classifier can't be built successfully.
   */
  @Override
  public void buildClassifier(Instances data) throws Exception {
    reset();

    // can classifier handle the data?
    getCapabilities().testWithFail(data);

    data = new Instances(data);
    data.deleteWithMissingClass();

    if (data.numInstances() > 0 && !m_dontReplaceMissing) {
      m_replaceMissing = new ReplaceMissingValues();
      m_replaceMissing.setInputFormat(data);
      data = Filter.useFilter(data, m_replaceMissing);
    }

    // check for only numeric attributes
    boolean onlyNumeric = true;
    for (int i = 0; i < data.numAttributes(); i++) {
      if (i != data.classIndex()) {
        if (!data.attribute(i).isNumeric()) {
          onlyNumeric = false;
          break;
        }
      }
    }

    if (!onlyNumeric) {
      if (data.numInstances() > 0) {
        m_nominalToBinary = new weka.filters.supervised.attribute.NominalToBinary();
      } else {
        m_nominalToBinary = new weka.filters.unsupervised.attribute.NominalToBinary();
      }
      m_nominalToBinary.setInputFormat(data);
      data = Filter.useFilter(data, m_nominalToBinary);
    }

    if (!m_dontNormalize && data.numInstances() > 0) {

      m_normalize = new Normalize();
      m_normalize.setInputFormat(data);
      data = Filter.useFilter(data, m_normalize);
    }

    m_numInstances = data.numInstances();

    m_weights = new double[data.numAttributes() + 1];
    m_data = new Instances(data, 0);

    if (data.numInstances() > 0) {
      data.randomize(new Random(getSeed())); // randomize the data
      train(data);
    }
  }

  /** the hinge loss function. */
  public static final int HINGE = 0;

  /** the log loss function. */
  public static final int LOGLOSS = 1;

  /** the squared loss function. */
  public static final int SQUAREDLOSS = 2;

  /** The epsilon insensitive loss function */
  public static final int EPSILON_INSENSITIVE = 3;

  /** The Huber loss function */
  public static final int HUBER = 4;

  /** The current loss function to minimize */
  protected int m_loss = HINGE;

  /** Loss functions to choose from */
  public static final Tag[] TAGS_SELECTION = {
      new Tag(HINGE, "Hinge loss (SVM)"),
      new Tag(LOGLOSS, "Log loss (logistic regression)"),
      new Tag(SQUAREDLOSS, "Squared loss (regression)"),
      new Tag(EPSILON_INSENSITIVE, "Epsilon-insensitive loss (SVM regression)"),
      new Tag(HUBER, "Huber loss (robust regression)") };

  protected double dloss(double z) {
    if (m_loss == HINGE) {
      return (z < 1) ? 1 : 0;
    }

    if (m_loss == LOGLOSS) {
      // log loss
      if (z < 0) {
        return 1.0 / (Math.exp(z) + 1.0);
      } else {
        double t = Math.exp(-z);
        return t / (t + 1);
      }
    }

    if (m_loss == EPSILON_INSENSITIVE) {
      if (z > m_epsilon) {
        return 1.0;
      }

      if (-z > m_epsilon) {
        return -1.0;
      }

      return 0;
    }

    if (m_loss == HUBER) {
      if (Math.abs(z) <= m_epsilon) {
        return z;
      } else if (z > 0.0) {
        return m_epsilon;
      } else {
        return -m_epsilon;
      }
    }

    // squared loss
    return z;
  }

  private void train(Instances data) throws Exception {
    for (int e = 0; e < m_epochs; e++) {
      for (int i = 0; i < data.numInstances(); i++) {
        updateClassifier(data.instance(i), false);
      }
    }
  }

  protected static double dotProd(Instance inst1, double[] weights,
      int classIndex) {
    double result = 0;

    int n1 = inst1.numValues();
    int n2 = weights.length - 1;

    for (int p1 = 0, p2 = 0; p1 < n1 && p2 < n2;) {
      int ind1 = inst1.index(p1);
      int ind2 = p2;
      if (ind1 == ind2) {
        if (ind1 != classIndex && !inst1.isMissingSparse(p1)) {
          result += inst1.valueSparse(p1) * weights[p2];
        }
        p1++;
        p2++;
      } else if (ind1 > ind2) {
        p2++;
      } else {
        p1++;
      }
    }
    return (result);
  }

  /**
   * Updates the classifier with the given instance.
   * 
   * @param instance the new training instance to include in the model
   * @param filter true if the instance should pass through any of the filters
   *          set up in buildClassifier(). When batch training buildClassifier()
   *          already batch filters all training instances so don't need to
   *          filter them again here.
   * @exception Exception if the instance could not be incorporated in the
   *              model.
   */
  protected void updateClassifier(Instance instance, boolean filter)
      throws Exception {

    if (!instance.classIsMissing()) {
      if (filter) {
        if (m_replaceMissing != null) {
          m_replaceMissing.input(instance);
          instance = m_replaceMissing.output();
        }

        if (m_nominalToBinary != null) {
          m_nominalToBinary.input(instance);
          instance = m_nominalToBinary.output();
        }

        if (m_normalize != null) {
          m_normalize.input(instance);
          instance = m_normalize.output();
        }
      }

      double wx = dotProd(instance, m_weights, instance.classIndex());

      double y;
      double z;
      if (instance.classAttribute().isNominal()) {
        y = (instance.classValue() == 0) ? -1 : 1;
        z = y * (wx + m_weights[m_weights.length - 1]);
      } else {
        y = instance.classValue();
        z = y - (wx + m_weights[m_weights.length - 1]);
        y = 1;
      }

      // Compute multiplier for weight decay
      double multiplier = 1.0;
      if (m_numInstances == 0) {
        multiplier = 1.0 - (m_learningRate * m_lambda) / m_t;
      } else {
        multiplier = 1.0 - (m_learningRate * m_lambda) / m_numInstances;
      }
      for (int i = 0; i < m_weights.length - 1; i++) {
        m_weights[i] *= multiplier;
      }

      // Only need to do the following if the loss is non-zero
      // if (m_loss != HINGE || (z < 1)) {
      if (m_loss == SQUAREDLOSS || m_loss == LOGLOSS || m_loss == HUBER
          || (m_loss == HINGE && (z < 1))
          || (m_loss == EPSILON_INSENSITIVE && Math.abs(z) > m_epsilon)) {

        // Compute Factor for updates
        double factor = m_learningRate * y * dloss(z);

        // Update coefficients for attributes
        int n1 = instance.numValues();
        for (int p1 = 0; p1 < n1; p1++) {
          int indS = instance.index(p1);
          if (indS != instance.classIndex() && !instance.isMissingSparse(p1)) {
            m_weights[indS] += factor * instance.valueSparse(p1);
          }
        }

        // update the bias
        m_weights[m_weights.length - 1] += factor;
      }
      m_t++;
    }
  }

  /**
   * Updates the classifier with the given instance.
   * 
   * @param instance the new training instance to include in the model
   * @exception Exception if the instance could not be incorporated in the
   *              model.
   */
  @Override
  public void updateClassifier(Instance instance) throws Exception {
    updateClassifier(instance, true);
  }

  /**
   * Computes the distribution for a given instance
   * 
   * @param inst the instance for which distribution is computed
   * @return the distribution
   * @throws Exception if the distribution can't be computed successfully
   */
  @Override
  public double[] distributionForInstance(Instance inst) throws Exception {
    double[] result = (inst.classAttribute().isNominal()) ? new double[2]
        : new double[1];

    if (m_replaceMissing != null) {
      m_replaceMissing.input(inst);
      inst = m_replaceMissing.output();
    }

    if (m_nominalToBinary != null) {
      m_nominalToBinary.input(inst);
      inst = m_nominalToBinary.output();
    }

    if (m_normalize != null) {
      m_normalize.input(inst);
      inst = m_normalize.output();
    }

    double wx = dotProd(inst, m_weights, inst.classIndex());// * m_wScale;
    double z = (wx + m_weights[m_weights.length - 1]);

    if (inst.classAttribute().isNumeric()) {
      result[0] = z;
      return result;
    }

    if (z <= 0) {
      // z = 0;
      if (m_loss == LOGLOSS) {
        result[0] = 1.0 / (1.0 + Math.exp(z));
        result[1] = 1.0 - result[0];
      } else {
        result[0] = 1;
      }
    } else {
      if (m_loss == LOGLOSS) {
        result[1] = 1.0 / (1.0 + Math.exp(-z));
        result[0] = 1.0 - result[1];
      } else {
        result[1] = 1;
      }
    }
    return result;
  }

  public double[] getWeights() {
    return m_weights;
  }

  /**
   * Prints out the classifier.
   * 
   * @return a description of the classifier as a string
   */
  @Override
  public String toString() {
    if (m_weights == null) {
      return "SGD: No model built yet.\n";
    }
    StringBuffer buff = new StringBuffer();
    buff.append("Loss function: ");
    if (m_loss == HINGE) {
      buff.append("Hinge loss (SVM)\n\n");
    } else if (m_loss == LOGLOSS) {
      buff.append("Log loss (logistic regression)\n\n");
    } else if (m_loss == EPSILON_INSENSITIVE) {
      buff.append("Epsilon insensitive loss (SVM regression)\n\n");
    } else if (m_loss == HUBER) {
      buff.append("Huber loss (robust regression)\n\n");
    } else {
      buff.append("Squared loss (linear regression)\n\n");
    }

    buff.append(m_data.classAttribute().name() + " = \n\n");
    int printed = 0;

    for (int i = 0; i < m_weights.length - 1; i++) {
      if (i != m_data.classIndex()) {
        if (printed > 0) {
          buff.append(" + ");
        } else {
          buff.append("   ");
        }

        buff.append(Utils.doubleToString(m_weights[i], 12, 4) + " "
            + ((m_normalize != null) ? "(normalized) " : "")
            + m_data.attribute(i).name() + "\n");

        printed++;
      }
    }

    if (m_weights[m_weights.length - 1] > 0) {
      buff.append(" + "
          + Utils.doubleToString(m_weights[m_weights.length - 1], 12, 4));
    } else {
      buff.append(" - "
          + Utils.doubleToString(-m_weights[m_weights.length - 1], 12, 4));
    }

    return buff.toString();
  }

  /**
   * Returns the revision string.
   * 
   * @return the revision
   */
  @Override
  public String getRevision() {
    return RevisionUtils.extract("$Revision: 15519 $");
  }

  protected int m_numModels = 0;

  /**
   * Aggregate an object with this one
   * 
   * @param toAggregate the object to aggregate
   * @return the result of aggregation
   * @throws Exception if the supplied object can't be aggregated for some
   *           reason
   */
  @Override
  public SGD aggregate(SGD toAggregate) throws Exception {

    if (m_weights == null) {
      throw new Exception("No model built yet, can't aggregate");
    }
    
    if (!m_data.equalHeaders(toAggregate.m_data)) {
      throw new Exception("Can't aggregate - data headers dont match: "
          + m_data.equalHeadersMsg(toAggregate.m_data));
    }
    
    if (m_weights.length != toAggregate.getWeights().length) {
      throw new Exception(
          "Can't aggregate - SDG to aggregate has weight vector "
              + "that differs in length from ours.");
    }        
    
    for (int i = 0; i < m_weights.length; i++) {
      m_weights[i] += toAggregate.getWeights()[i];
    }

    m_numModels++;

    return this;
  }

  /**
   * Call to complete the aggregation process. Allows implementers to do any
   * final processing based on how many objects were aggregated.
   * 
   * @throws Exception if the aggregation can't be finalized for some reason
   */
  @Override
  public void finalizeAggregation() throws Exception {    
    if (m_numModels == 0) {
      throw new Exception("Unable to finalize aggregation - " +
                "haven't seen any models to aggregate");
    }
    
    for (int i = 0; i < m_weights.length; i++) {
      m_weights[i] /= (m_numModels + 1); // plus one for us
    }

    // aggregation complete
    m_numModels = 0;
  }
  
  /**
   * Main method for testing this class.
   */
  public static void main(String[] args) {
    runClassifier(new SGD(), args);
  }
}