/*

  *   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 <http://www.gnu.org/licenses/>.

  */

 /*

  *    SMO.java

  *    Copyright (C) 1999-2012 University of Waikato, Hamilton, New Zealand

  *

  */

 package weka.classifiers.functions;

 import java.io.Serializable;

 import java.util.Enumeration;

 import java.util.Random;

 import java.util.Vector;

 import weka.classifiers.AbstractClassifier;

 import weka.classifiers.functions.supportVector.Kernel;

 import weka.classifiers.functions.supportVector.PolyKernel;

 import weka.classifiers.functions.supportVector.SMOset;

 import weka.core.Attribute;

 import weka.core.Capabilities;

 import weka.core.Capabilities.Capability;

 import weka.core.DenseInstance;

 import weka.core.FastVector;

 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.TechnicalInformation;

 import weka.core.TechnicalInformation.Field;

 import weka.core.TechnicalInformation.Type;

 import weka.core.TechnicalInformationHandler;

 import weka.core.Utils;

 import weka.core.WeightedInstancesHandler;

 import weka.filters.Filter;

 import weka.filters.unsupervised.attribute.NominalToBinary;

 import weka.filters.unsupervised.attribute.Normalize;

 import weka.filters.unsupervised.attribute.ReplaceMissingValues;

 import weka.filters.unsupervised.attribute.Standardize;

 /**

  <!-- globalinfo-start -->

  * Implements John Platt's sequential minimal optimization algorithm for training a support vector classifier.<br/>

  * <br/>

  * This implementation globally replaces all missing values and transforms nominal attributes into binary ones. It also normalizes all attributes by default. (In that case the coefficients in the output are based on the normalized data, not the original data --- this is important for interpreting the classifier.)<br/>

  * <br/>

  * Multi-class problems are solved using pairwise classification (1-vs-1 and if logistic models are built pairwise coupling according to Hastie and Tibshirani, 1998).<br/>

  * <br/>

  * To obtain proper probability estimates, use the option that fits logistic regression models to the outputs of the support vector machine. In the multi-class case the predicted probabilities are coupled using Hastie and Tibshirani's pairwise coupling method.<br/>

  * <br/>

  * Note: for improved speed normalization should be turned off when operating on SparseInstances.<br/>

  * <br/>

  * For more information on the SMO algorithm, see<br/>

  * <br/>

  * J. Platt: Fast Training of Support Vector Machines using Sequential Minimal Optimization. In B. Schoelkopf and C. Burges and A. Smola, editors, Advances in Kernel Methods - Support Vector Learning, 1998.<br/>

  * <br/>

  * S.S. Keerthi, S.K. Shevade, C. Bhattacharyya, K.R.K. Murthy (2001). Improvements to Platt's SMO Algorithm for SVM Classifier Design. Neural Computation. 13(3):637-649.<br/>

  * <br/>

  * Trevor Hastie, Robert Tibshirani: Classification by Pairwise Coupling. In: Advances in Neural Information Processing Systems, 1998.

  * <p/>

  <!-- globalinfo-end -->

  *

  <!-- technical-bibtex-start -->

  * BibTeX:

  * <pre>

  * @incollection{Platt1998,

  *    author = {J. Platt},

  *    booktitle = {Advances in Kernel Methods - Support Vector Learning},

  *    editor = {B. Schoelkopf and C. Burges and A. Smola},

  *    publisher = {MIT Press},

  *    title = {Fast Training of Support Vector Machines using Sequential Minimal Optimization},

  *    year = {1998},

  *    URL = {http://research.microsoft.com/\~jplatt/smo.html},

  *    PS = {http://research.microsoft.com/\~jplatt/smo-book.ps.gz},

  *    PDF = {http://research.microsoft.com/\~jplatt/smo-book.pdf}

  * }

  * 

  * @article{Keerthi2001,

  *    author = {S.S. Keerthi and S.K. Shevade and C. Bhattacharyya and K.R.K. Murthy},

  *    journal = {Neural Computation},

  *    number = {3},

  *    pages = {637-649},

  *    title = {Improvements to Platt's SMO Algorithm for SVM Classifier Design},

  *    volume = {13},

  *    year = {2001},

  *    PS = {http://guppy.mpe.nus.edu.sg/\~mpessk/svm/smo_mod_nc.ps.gz}

  * }

  * 

  * @inproceedings{Hastie1998,

  *    author = {Trevor Hastie and Robert Tibshirani},

  *    booktitle = {Advances in Neural Information Processing Systems},

  *    editor = {Michael I. Jordan and Michael J. Kearns and Sara A. Solla},

  *    publisher = {MIT Press},

  *    title = {Classification by Pairwise Coupling},

  *    volume = {10},

  *    year = {1998},

  *    PS = {http://www-stat.stanford.edu/\~hastie/Papers/2class.ps}

  * }

  * </pre>

  * <p/>

  <!-- technical-bibtex-end -->

  *

  <!-- options-start -->

  * Valid options are: <p/>

  * 

  * <pre> -D

  *  If set, classifier is run in debug mode and

  *  may output additional info to the console</pre>

  * 

  * <pre> -no-checks

  *  Turns off all checks - use with caution!

  *  Turning them off assumes that data is purely numeric, doesn't

  *  contain any missing values, and has a nominal class. Turning them

  *  off also means that no header information will be stored if the

  *  machine is linear. Finally, it also assumes that no instance has

  *  a weight equal to 0.

  *  (default: checks on)</pre>

  * 

  * <pre> -C &lt;double&gt;

  *  The complexity constant C. (default 1)</pre>

  * 

  * <pre> -N

  *  Whether to 0=normalize/1=standardize/2=neither. (default 0=normalize)</pre>

  * 

  * <pre> -L &lt;double&gt;

  *  The tolerance parameter. (default 1.0e-3)</pre>

  * 

  * <pre> -P &lt;double&gt;

  *  The epsilon for round-off error. (default 1.0e-12)</pre>

  * 

  * <pre> -M

  *  Fit logistic models to SVM outputs. </pre>

  * 

  * <pre> -V &lt;double&gt;

  *  The number of folds for the internal

  *  cross-validation. (default -1, use training data)</pre>

  * 

  * <pre> -W &lt;double&gt;

  *  The random number seed. (default 1)</pre>

  * 

  * <pre> -K &lt;classname and parameters&gt;

  *  The Kernel to use.

  *  (default: weka.classifiers.functions.supportVector.PolyKernel)</pre>

  * 

  * <pre> 

  * Options specific to kernel weka.classifiers.functions.supportVector.PolyKernel:

  * </pre>

  * 

  * <pre> -D

  *  Enables debugging output (if available) to be printed.

  *  (default: off)</pre>

  * 

  * <pre> -no-checks

  *  Turns off all checks - use with caution!

  *  (default: checks on)</pre>

  * 

  * <pre> -C &lt;num&gt;

  *  The size of the cache (a prime number), 0 for full cache and 

  *  -1 to turn it off.

  *  (default: 250007)</pre>

  * 

  * <pre> -E &lt;num&gt;

  *  The Exponent to use.

  *  (default: 1.0)</pre>

  * 

  * <pre> -L

  *  Use lower-order terms.

  *  (default: no)</pre>

  * 

  <!-- options-end -->

  *

  * @author Eibe Frank (eibe@cs.waikato.ac.nz)

  * @author Shane Legg (shane@intelligenesis.net) (sparse vector code)

  * @author Stuart Inglis (stuart@reeltwo.com) (sparse vector code)

  * @version $Revision: 8034 $

  */

 public class SMO 

   extends AbstractClassifier 

   implements WeightedInstancesHandler, TechnicalInformationHandler {

   /** for serialization */

   static final long serialVersionUID = -6585883636378691736L;

   /**

    * Returns a string describing classifier

    * @return a description suitable for

    * displaying in the explorer/experimenter gui

    */

   public String globalInfo() {

     return  "Implements John Platt's sequential minimal optimization "

       + "algorithm for training a support vector classifier.\n\n"

       + "This implementation globally replaces all missing values and "

       + "transforms nominal attributes into binary ones. It also "

       + "normalizes all attributes by default. (In that case the coefficients "

       + "in the output are based on the normalized data, not the "

       + "original data --- this is important for interpreting the classifier.)\n\n"

       + "Multi-class problems are solved using pairwise classification "

       + "(1-vs-1 and if logistic models are built pairwise coupling "

       + "according to Hastie and Tibshirani, 1998).\n\n"

       + "To obtain proper probability estimates, use the option that fits "

       + "logistic regression models to the outputs of the support vector "

       + "machine. In the multi-class case the predicted probabilities "

       + "are coupled using Hastie and Tibshirani's pairwise coupling "

       + "method.\n\n"

       + "Note: for improved speed normalization should be turned off when "

       + "operating on SparseInstances.\n\n"

       + "For more information on the SMO algorithm, see\n\n"

       + getTechnicalInformation().toString();

   }

   /**

    * Returns an instance of a TechnicalInformation object, containing 

    * detailed information about the technical background of this class,

    * e.g., paper reference or book this class is based on.

    * 

    * @return the technical information about this class

    */

   public TechnicalInformation getTechnicalInformation() {

     TechnicalInformation         result;

     TechnicalInformation         additional;

     result = new TechnicalInformation(Type.INCOLLECTION);

     result.setValue(Field.AUTHOR, "J. Platt");

     result.setValue(Field.YEAR, "1998");

     result.setValue(Field.TITLE, "Fast Training of Support Vector Machines using Sequential Minimal Optimization");

     result.setValue(Field.BOOKTITLE, "Advances in Kernel Methods - Support Vector Learning");

     result.setValue(Field.EDITOR, "B. Schoelkopf and C. Burges and A. Smola");

     result.setValue(Field.PUBLISHER, "MIT Press");

     result.setValue(Field.URL, "http://research.microsoft.com/~jplatt/smo.html");

     result.setValue(Field.PDF, "http://research.microsoft.com/~jplatt/smo-book.pdf");

     result.setValue(Field.PS, "http://research.microsoft.com/~jplatt/smo-book.ps.gz");

     additional = result.add(Type.ARTICLE);

     additional.setValue(Field.AUTHOR, "S.S. Keerthi and S.K. Shevade and C. Bhattacharyya and K.R.K. Murthy");

     additional.setValue(Field.YEAR, "2001");

     additional.setValue(Field.TITLE, "Improvements to Platt's SMO Algorithm for SVM Classifier Design");

     additional.setValue(Field.JOURNAL, "Neural Computation");

     additional.setValue(Field.VOLUME, "13");

     additional.setValue(Field.NUMBER, "3");

     additional.setValue(Field.PAGES, "637-649");

     additional.setValue(Field.PS, "http://guppy.mpe.nus.edu.sg/~mpessk/svm/smo_mod_nc.ps.gz");

     additional = result.add(Type.INPROCEEDINGS);

     additional.setValue(Field.AUTHOR, "Trevor Hastie and Robert Tibshirani");

     additional.setValue(Field.YEAR, "1998");

     additional.setValue(Field.TITLE, "Classification by Pairwise Coupling");

     additional.setValue(Field.BOOKTITLE, "Advances in Neural Information Processing Systems");

     additional.setValue(Field.VOLUME, "10");

     additional.setValue(Field.PUBLISHER, "MIT Press");

     additional.setValue(Field.EDITOR, "Michael I. Jordan and Michael J. Kearns and Sara A. Solla");

     additional.setValue(Field.PS, "http://www-stat.stanford.edu/~hastie/Papers/2class.ps");

     return result;

   }

   /**

    * Class for building a binary support vector machine.

    */

   public class BinarySMO 

     implements Serializable {

     /** for serialization */

     static final long serialVersionUID = -8246163625699362456L;

     /** The Lagrange multipliers. */

     protected double[] m_alpha;

     /** The thresholds. */

     protected double m_b, m_bLow, m_bUp;

     /** The indices for m_bLow and m_bUp */

     protected int m_iLow, m_iUp;

     /** The training data. */

     protected Instances m_data;

     /** Weight vector for linear machine. */

     protected double[] m_weights;

     /** Variables to hold weight vector in sparse form.

         (To reduce storage requirements.) */

     protected double[] m_sparseWeights;

     protected int[] m_sparseIndices;

     /** Kernel to use **/

     protected Kernel m_kernel;

     /** The transformed class values. */

     protected double[] m_class;

     /** The current set of errors for all non-bound examples. */

     protected double[] m_errors;

     /* The five different sets used by the algorithm. */

     /** {i: 0 < m_alpha[i] < C} */

     protected SMOset m_I0;

     /**  {i: m_class[i] = 1, m_alpha[i] = 0} */

     protected SMOset m_I1; 

     /**  {i: m_class[i] = -1, m_alpha[i] =C} */

     protected SMOset m_I2; 

     /** {i: m_class[i] = 1, m_alpha[i] = C} */

     protected SMOset m_I3;

     /**  {i: m_class[i] = -1, m_alpha[i] = 0} */

     protected SMOset m_I4; 

     /** The set of support vectors */

     protected SMOset m_supportVectors; // {i: 0 < m_alpha[i]}

     /** Stores logistic regression model for probability estimate */

     protected Logistic m_logistic = null;

     /** Stores the weight of the training instances */

     protected double m_sumOfWeights = 0;

     /**

      * Fits logistic regression model to SVM outputs analogue

      * to John Platt's method.  

      *

      * @param insts the set of training instances

      * @param cl1 the first class' index

      * @param cl2 the second class' index

      * @param numFolds the number of folds for cross-validation

      * @param random for randomizing the data

      * @throws Exception if the sigmoid can't be fit successfully

      */

     protected void fitLogistic(Instances insts, int cl1, int cl2,

                              int numFolds, Random random) 

       throws Exception {

       // Create header of instances object

       FastVector atts = new FastVector(2);

       atts.addElement(new Attribute("pred"));

       FastVector attVals = new FastVector(2);

       attVals.addElement(insts.classAttribute().value(cl1));

       attVals.addElement(insts.classAttribute().value(cl2));

       atts.addElement(new Attribute("class", attVals));

       Instances data = new Instances("data", atts, insts.numInstances());

       data.setClassIndex(1);

       // Collect data for fitting the logistic model

       if (numFolds <= 0) {

         // Use training data

         for (int j = 0; j < insts.numInstances(); j++) {

           Instance inst = insts.instance(j);

           double[] vals = new double[2];

           vals[0] = SVMOutput(-1, inst);

           if (inst.classValue() == cl2) {

             vals[1] = 1;

           }

           data.add(new DenseInstance(inst.weight(), vals));

         }

       } else {

         // Check whether number of folds too large

         if (numFolds > insts.numInstances()) {

           numFolds = insts.numInstances();

         }

         // Make copy of instances because we will shuffle them around

         insts = new Instances(insts);

         // Perform three-fold cross-validation to collect

         // unbiased predictions

         insts.randomize(random);

         insts.stratify(numFolds);

         for (int i = 0; i < numFolds; i++) {

           Instances train = insts.trainCV(numFolds, i, random);

           /*          SerializedObject so = new SerializedObject(this);

                   BinarySMO smo = (BinarySMO)so.getObject(); */

           BinarySMO smo = new BinarySMO();

           smo.setKernel(Kernel.makeCopy(SMO.this.m_kernel));

           smo.buildClassifier(train, cl1, cl2, false, -1, -1);

           Instances test = insts.testCV(numFolds, i);

           for (int j = 0; j < test.numInstances(); j++) {

             double[] vals = new double[2];

             vals[0] = smo.SVMOutput(-1, test.instance(j));

             if (test.instance(j).classValue() == cl2) {

               vals[1] = 1;

             }

             data.add(new DenseInstance(test.instance(j).weight(), vals));

           }

         }

       }

       // Build logistic regression model

       m_logistic = new Logistic();

       m_logistic.buildClassifier(data);

     }

     /**

      * sets the kernel to use

      * 

      * @param value        the kernel to use

      */

     public void setKernel(Kernel value) {

       m_kernel = value;

     }

     /**

      * Returns the kernel to use

      * 

      * @return                 the current kernel

      */

     public Kernel getKernel() {

       return m_kernel;

     }

     /**

      * Method for building the binary classifier.

      *

      * @param insts the set of training instances

      * @param cl1 the first class' index

      * @param cl2 the second class' index

      * @param fitLogistic true if logistic model is to be fit

      * @param numFolds number of folds for internal cross-validation

      * @param randomSeed random number generator for cross-validation

      * @throws Exception if the classifier can't be built successfully

      */

     protected void buildClassifier(Instances insts, int cl1, int cl2,

                                  boolean fitLogistic, int numFolds,

                                  int randomSeed) throws Exception {

       // Initialize some variables

       m_bUp = -1; m_bLow = 1; m_b = 0; 

       m_alpha = null; m_data = null; m_weights = null; m_errors = null;

       m_logistic = null; m_I0 = null; m_I1 = null; m_I2 = null;

       m_I3 = null; m_I4 = null;        m_sparseWeights = null; m_sparseIndices = null;

       // Store the sum of weights

       m_sumOfWeights = insts.sumOfWeights();

       // Set class values

       m_class = new double[insts.numInstances()];

       m_iUp = -1; m_iLow = -1;

       for (int i = 0; i < m_class.length; i++) {

         if ((int) insts.instance(i).classValue() == cl1) {

           m_class[i] = -1; m_iLow = i;

         } else if ((int) insts.instance(i).classValue() == cl2) {

           m_class[i] = 1; m_iUp = i;

         } else {

           throw new Exception ("This should never happen!");

         }

       }

       // Check whether one or both classes are missing

       if ((m_iUp == -1) || (m_iLow == -1)) {

         if (m_iUp != -1) {

           m_b = -1;

         } else if (m_iLow != -1) {

           m_b = 1;

         } else {

           m_class = null;

           return;

         }

         if (m_KernelIsLinear) {

           m_sparseWeights = new double[0];

           m_sparseIndices = new int[0];

           m_class = null;

         } else {

           m_supportVectors = new SMOset(0);

           m_alpha = new double[0];

           m_class = new double[0];

         }

         // Fit sigmoid if requested

         if (fitLogistic) {

           fitLogistic(insts, cl1, cl2, numFolds, new Random(randomSeed));

         }

         return;

       }

       // Set the reference to the data

       m_data = insts;

       // If machine is linear, reserve space for weights

       if (m_KernelIsLinear) {

         m_weights = new double[m_data.numAttributes()];

       } else {

         m_weights = null;

       }

       // Initialize alpha array to zero

       m_alpha = new double[m_data.numInstances()];

       // Initialize sets

       m_supportVectors = new SMOset(m_data.numInstances());

       m_I0 = new SMOset(m_data.numInstances());

       m_I1 = new SMOset(m_data.numInstances());

       m_I2 = new SMOset(m_data.numInstances());

       m_I3 = new SMOset(m_data.numInstances());

       m_I4 = new SMOset(m_data.numInstances());

       // Clean out some instance variables

       m_sparseWeights = null;

       m_sparseIndices = null;

       // init kernel

       m_kernel.buildKernel(m_data);

       // Initialize error cache

       m_errors = new double[m_data.numInstances()];

       m_errors[m_iLow] = 1; m_errors[m_iUp] = -1;

       // Build up I1 and I4

       for (int i = 0; i < m_class.length; i++ ) {

         if (m_class[i] == 1) {

           m_I1.insert(i);

         } else {

           m_I4.insert(i);

         }

       }

       // Loop to find all the support vectors

       int numChanged = 0;

       boolean examineAll = true;

       while ((numChanged > 0) || examineAll) {

         numChanged = 0;

         if (examineAll) {

           for (int i = 0; i < m_alpha.length; i++) {

             if (examineExample(i)) {

               numChanged++;

             }

           }

         } else {

           // This code implements Modification 1 from Keerthi et al.'s paper

           for (int i = 0; i < m_alpha.length; i++) {

             if ((m_alpha[i] > 0) &&  

                 (m_alpha[i] < m_C * m_data.instance(i).weight())) {

               if (examineExample(i)) {

                 numChanged++;

               }

               // Is optimality on unbound vectors obtained?

               if (m_bUp > m_bLow - 2 * m_tol) {

                 numChanged = 0;

                 break;

               }

             }

           }

           //This is the code for Modification 2 from Keerthi et al.'s paper

           /*boolean innerLoopSuccess = true; 

             numChanged = 0;

             while ((m_bUp < m_bLow - 2 * m_tol) && (innerLoopSuccess == true)) {

             innerLoopSuccess = takeStep(m_iUp, m_iLow, m_errors[m_iLow]);

             }*/

         }

         if (examineAll) {

           examineAll = false;

         } else if (numChanged == 0) {

           examineAll = true;

         }

       }

       // Set threshold

       m_b = (m_bLow + m_bUp) / 2.0;

       // Save memory

       m_kernel.clean(); 

       m_errors = null;

       m_I0 = m_I1 = m_I2 = m_I3 = m_I4 = null;

       // If machine is linear, delete training data

       // and store weight vector in sparse format

       if (m_KernelIsLinear) {

         // We don't need to store the set of support vectors

         m_supportVectors = null;

         // We don't need to store the class values either

         m_class = null;

         // Clean out training data

         if (!m_checksTurnedOff) {

           m_data = new Instances(m_data, 0);

         } else {

           m_data = null;

         }

         // Convert weight vector

         double[] sparseWeights = new double[m_weights.length];

         int[] sparseIndices = new int[m_weights.length];

         int counter = 0;

         for (int i = 0; i < m_weights.length; i++) {

           if (m_weights[i] != 0.0) {

             sparseWeights[counter] = m_weights[i];

             sparseIndices[counter] = i;

             counter++;

           }

         }

         m_sparseWeights = new double[counter];

         m_sparseIndices = new int[counter];

         System.arraycopy(sparseWeights, 0, m_sparseWeights, 0, counter);

         System.arraycopy(sparseIndices, 0, m_sparseIndices, 0, counter);

         // Clean out weight vector

         m_weights = null;

         // We don't need the alphas in the linear case

         m_alpha = null;

       }

       // Fit sigmoid if requested

       if (fitLogistic) {

         fitLogistic(insts, cl1, cl2, numFolds, new Random(randomSeed));

       }

     }

     /**

      * Computes SVM output for given instance.

      *

      * @param index the instance for which output is to be computed

      * @param inst the instance 

      * @return the output of the SVM for the given instance

      * @throws Exception in case of an error

      */

     public double SVMOutput(int index, Instance inst) throws Exception {

       double result = 0;

       // Is the machine linear?

       if (m_KernelIsLinear) {

         // Is weight vector stored in sparse format?

         if (m_sparseWeights == null) {

           int n1 = inst.numValues(); 

           for (int p = 0; p < n1; p++) {

             if (inst.index(p) != m_classIndex) {

               result += m_weights[inst.index(p)] * inst.valueSparse(p);

             }

           }

         } else {

           int n1 = inst.numValues(); int n2 = m_sparseWeights.length;

           for (int p1 = 0, p2 = 0; p1 < n1 && p2 < n2;) {

             int ind1 = inst.index(p1); 

             int ind2 = m_sparseIndices[p2];

             if (ind1 == ind2) {

               if (ind1 != m_classIndex) {

                 result += inst.valueSparse(p1) * m_sparseWeights[p2];

               }

               p1++; p2++;

             } else if (ind1 > ind2) {

               p2++;

             } else { 

               p1++;

             }

           }

         }

       } else {

         for (int i = m_supportVectors.getNext(-1); i != -1; 

              i = m_supportVectors.getNext(i)) {

           result += m_class[i] * m_alpha[i] * m_kernel.eval(index, i, inst);

         }

       }

       result -= m_b;

       return result;

     }

     /**

      * Prints out the classifier.

      *

      * @return a description of the classifier as a string

      */

     public String toString() {

       StringBuffer text = new StringBuffer();

       int printed = 0;

       if ((m_alpha == null) && (m_sparseWeights == null)) {

         return "BinarySMO: No model built yet.\n";

       }

       try {

         text.append("BinarySMO\n\n");

         // If machine linear, print weight vector

         if (m_KernelIsLinear) {

           text.append("Machine linear: showing attribute weights, ");

           text.append("not support vectors.\n\n");

           // We can assume that the weight vector is stored in sparse

           // format because the classifier has been built

           for (int i = 0; i < m_sparseWeights.length; i++) {

             if (m_sparseIndices[i] != (int)m_classIndex) {

               if (printed > 0) {

                 text.append(" + ");

               } else {

                 text.append("   ");

               }

               text.append(Utils.doubleToString(m_sparseWeights[i], 12, 4) +

                           " * ");

               if (m_filterType == FILTER_STANDARDIZE) {

                 text.append("(standardized) ");

               } else if (m_filterType == FILTER_NORMALIZE) {

                 text.append("(normalized) ");

               }

               if (!m_checksTurnedOff) {

                 text.append(m_data.attribute(m_sparseIndices[i]).name()+"\n");

               } else {

                 text.append("attribute with index " + 

                             m_sparseIndices[i] +"\n");

               }

               printed++;

             }

           }

         } else {

           for (int i = 0; i < m_alpha.length; i++) {

             if (m_supportVectors.contains(i)) {

               double val = m_alpha[i];

               if (m_class[i] == 1) {

                 if (printed > 0) {

                   text.append(" + ");

                 }

               } else {

                 text.append(" - ");

               }

               text.append(Utils.doubleToString(val, 12, 4) 

                           + " * <");

               for (int j = 0; j < m_data.numAttributes(); j++) {

                 if (j != m_data.classIndex()) {

                   text.append(m_data.instance(i).toString(j));

                 }

                 if (j != m_data.numAttributes() - 1) {

                   text.append(" ");

                 }

               }

               text.append("> * X]\n");

               printed++;

             }

           }

         }

         if (m_b > 0) {

           text.append(" - " + Utils.doubleToString(m_b, 12, 4));

         } else {

           text.append(" + " + Utils.doubleToString(-m_b, 12, 4));

         }

         if (!m_KernelIsLinear) {

           text.append("\n\nNumber of support vectors: " + 

                       m_supportVectors.numElements());

         }

         int numEval = 0;

         int numCacheHits = -1;

         if (m_kernel != null) {

           numEval = m_kernel.numEvals();

           numCacheHits = m_kernel.numCacheHits();

         }

         text.append("\n\nNumber of kernel evaluations: " + numEval);

         if (numCacheHits >= 0 && numEval > 0) {

           double hitRatio = 1 - numEval*1.0/(numCacheHits+numEval);

           text.append(" (" + Utils.doubleToString(hitRatio*100, 7, 3).trim() + "% cached)");

         }

       } catch (Exception e) {

         e.printStackTrace();

         return "Can't print BinarySMO classifier.";

       }

       return text.toString();

     }

     /**

      * Examines instance.

      *

      * @param i2 index of instance to examine

      * @return true if examination was successfull

      * @throws Exception if something goes wrong

      */

     protected boolean examineExample(int i2) throws Exception {

       double y2, F2;

       int i1 = -1;

       y2 = m_class[i2];

       if (m_I0.contains(i2)) {

         F2 = m_errors[i2];

       } else {

         F2 = SVMOutput(i2, m_data.instance(i2)) + m_b - y2;

         m_errors[i2] = F2;

         // Update thresholds

         if ((m_I1.contains(i2) || m_I2.contains(i2)) && (F2 < m_bUp)) {

           m_bUp = F2; m_iUp = i2;

         } else if ((m_I3.contains(i2) || m_I4.contains(i2)) && (F2 > m_bLow)) {

           m_bLow = F2; m_iLow = i2;

         }

       }

       // Check optimality using current bLow and bUp and, if

       // violated, find an index i1 to do joint optimization

       // with i2...

       boolean optimal = true;

       if (m_I0.contains(i2) || m_I1.contains(i2) || m_I2.contains(i2)) {

         if (m_bLow - F2 > 2 * m_tol) {

           optimal = false; i1 = m_iLow;

         }

       }

       if (m_I0.contains(i2) || m_I3.contains(i2) || m_I4.contains(i2)) {

         if (F2 - m_bUp > 2 * m_tol) {

           optimal = false; i1 = m_iUp;

         }

       }

       if (optimal) {

         return false;

       }

       // For i2 unbound choose the better i1...

       if (m_I0.contains(i2)) {

         if (m_bLow - F2 > F2 - m_bUp) {

           i1 = m_iLow;

         } else {

           i1 = m_iUp;

         }

       }

       if (i1 == -1) {

         throw new Exception("This should never happen!");

       }

       return takeStep(i1, i2, F2);

     }

     /**

      * Method solving for the Lagrange multipliers for

      * two instances.

      *

      * @param i1 index of the first instance

      * @param i2 index of the second instance

      * @param F2

      * @return true if multipliers could be found

      * @throws Exception if something goes wrong

      */

     protected boolean takeStep(int i1, int i2, double F2) throws Exception {

       double alph1, alph2, y1, y2, F1, s, L, H, k11, k12, k22, eta,

         a1, a2, f1, f2, v1, v2, Lobj, Hobj;

       double C1 = m_C * m_data.instance(i1).weight();

       double C2 = m_C * m_data.instance(i2).weight();

       // Don't do anything if the two instances are the same

       if (i1 == i2) {

         return false;

       }

       // Initialize variables

       alph1 = m_alpha[i1]; alph2 = m_alpha[i2];

       y1 = m_class[i1]; y2 = m_class[i2];

       F1 = m_errors[i1];

       s = y1 * y2;

       // Find the constraints on a2

       if (y1 != y2) {

         L = Math.max(0, alph2 - alph1); 

         H = Math.min(C2, C1 + alph2 - alph1);

       } else {

         L = Math.max(0, alph1 + alph2 - C1);

         H = Math.min(C2, alph1 + alph2);

       }

       if (L >= H) {

         return false;

       }

       // Compute second derivative of objective function

       k11 = m_kernel.eval(i1, i1, m_data.instance(i1));

       k12 = m_kernel.eval(i1, i2, m_data.instance(i1));

       k22 = m_kernel.eval(i2, i2, m_data.instance(i2));

       eta = 2 * k12 - k11 - k22;

       // Check if second derivative is negative

       if (eta < 0) {

         // Compute unconstrained maximum

         a2 = alph2 - y2 * (F1 - F2) / eta;

         // Compute constrained maximum

         if (a2 < L) {

           a2 = L;

         } else if (a2 > H) {

           a2 = H;

         }

       } else {

         // Look at endpoints of diagonal

         f1 = SVMOutput(i1, m_data.instance(i1));

         f2 = SVMOutput(i2, m_data.instance(i2));

         v1 = f1 + m_b - y1 * alph1 * k11 - y2 * alph2 * k12; 

         v2 = f2 + m_b - y1 * alph1 * k12 - y2 * alph2 * k22; 

         double gamma = alph1 + s * alph2;

         Lobj = (gamma - s * L) + L - 0.5 * k11 * (gamma - s * L) * (gamma - s * L) - 

           0.5 * k22 * L * L - s * k12 * (gamma - s * L) * L - 

           y1 * (gamma - s * L) * v1 - y2 * L * v2;

         Hobj = (gamma - s * H) + H - 0.5 * k11 * (gamma - s * H) * (gamma - s * H) - 

           0.5 * k22 * H * H - s * k12 * (gamma - s * H) * H - 

           y1 * (gamma - s * H) * v1 - y2 * H * v2;

         if (Lobj > Hobj + m_eps) {

           a2 = L;

         } else if (Lobj < Hobj - m_eps) {

           a2 = H;

         } else {

           a2 = alph2;

         }

       }

       if (Math.abs(a2 - alph2) < m_eps * (a2 + alph2 + m_eps)) {

         return false;

       }

       // To prevent precision problems

       if (a2 > C2 - m_Del * C2) {

         a2 = C2;

       } else if (a2 <= m_Del * C2) {

         a2 = 0;

       }

       // Recompute a1

       a1 = alph1 + s * (alph2 - a2);

       // To prevent precision problems

       if (a1 > C1 - m_Del * C1) {

         a1 = C1;

       } else if (a1 <= m_Del * C1) {

         a1 = 0;

       }

       // Update sets

       if (a1 > 0) {

         m_supportVectors.insert(i1);

       } else {

         m_supportVectors.delete(i1);

       }

       if ((a1 > 0) && (a1 < C1)) {

         m_I0.insert(i1);

       } else {

         m_I0.delete(i1);

       }

       if ((y1 == 1) && (a1 == 0)) {

         m_I1.insert(i1);

       } else {

         m_I1.delete(i1);

       }

       if ((y1 == -1) && (a1 == C1)) {

         m_I2.insert(i1);

       } else {

         m_I2.delete(i1);

       }

       if ((y1 == 1) && (a1 == C1)) {

         m_I3.insert(i1);

       } else {

         m_I3.delete(i1);

       }

       if ((y1 == -1) && (a1 == 0)) {

         m_I4.insert(i1);

       } else {

         m_I4.delete(i1);

       }

       if (a2 > 0) {

         m_supportVectors.insert(i2);

       } else {

         m_supportVectors.delete(i2);

       }

       if ((a2 > 0) && (a2 < C2)) {

         m_I0.insert(i2);

       } else {

         m_I0.delete(i2);

       }

       if ((y2 == 1) && (a2 == 0)) {

         m_I1.insert(i2);

       } else {

         m_I1.delete(i2);

       }

       if ((y2 == -1) && (a2 == C2)) {

         m_I2.insert(i2);

       } else {

         m_I2.delete(i2);

       }

       if ((y2 == 1) && (a2 == C2)) {

         m_I3.insert(i2);

       } else {

         m_I3.delete(i2);

       }

       if ((y2 == -1) && (a2 == 0)) {

         m_I4.insert(i2);

       } else {

         m_I4.delete(i2);

       }

       // Update weight vector to reflect change a1 and a2, if linear SVM

       if (m_KernelIsLinear) {

         Instance inst1 = m_data.instance(i1);

         for (int p1 = 0; p1 < inst1.numValues(); p1++) {

           if (inst1.index(p1) != m_data.classIndex()) {

             m_weights[inst1.index(p1)] += 

               y1 * (a1 - alph1) * inst1.valueSparse(p1);

           }

         }

         Instance inst2 = m_data.instance(i2);

         for (int p2 = 0; p2 < inst2.numValues(); p2++) {

           if (inst2.index(p2) != m_data.classIndex()) {

             m_weights[inst2.index(p2)] += 

               y2 * (a2 - alph2) * inst2.valueSparse(p2);

           }

         }

       }

       // Update error cache using new Lagrange multipliers

       for (int j = m_I0.getNext(-1); j != -1; j = m_I0.getNext(j)) {

         if ((j != i1) && (j != i2)) {

           m_errors[j] += 

             y1 * (a1 - alph1) * m_kernel.eval(i1, j, m_data.instance(i1)) + 

             y2 * (a2 - alph2) * m_kernel.eval(i2, j, m_data.instance(i2));

         }

       }

       // Update error cache for i1 and i2

       m_errors[i1] += y1 * (a1 - alph1) * k11 + y2 * (a2 - alph2) * k12;

       m_errors[i2] += y1 * (a1 - alph1) * k12 + y2 * (a2 - alph2) * k22;

       // Update array with Lagrange multipliers

       m_alpha[i1] = a1;

       m_alpha[i2] = a2;

       // Update thresholds

       m_bLow = -Double.MAX_VALUE; m_bUp = Double.MAX_VALUE;

       m_iLow = -1; m_iUp = -1;

       for (int j = m_I0.getNext(-1); j != -1; j = m_I0.getNext(j)) {

         if (m_errors[j] < m_bUp) {

           m_bUp = m_errors[j]; m_iUp = j;

         }

         if (m_errors[j] > m_bLow) {

           m_bLow = m_errors[j]; m_iLow = j;

         }

       }

       if (!m_I0.contains(i1)) {

         if (m_I3.contains(i1) || m_I4.contains(i1)) {

           if (m_errors[i1] > m_bLow) {

             m_bLow = m_errors[i1]; m_iLow = i1;

           } 

         } else {

           if (m_errors[i1] < m_bUp) {

             m_bUp = m_errors[i1]; m_iUp = i1;

           }

         }

       }

       if (!m_I0.contains(i2)) {

         if (m_I3.contains(i2) || m_I4.contains(i2)) {

           if (m_errors[i2] > m_bLow) {

             m_bLow = m_errors[i2]; m_iLow = i2;

           }

         } else {

           if (m_errors[i2] < m_bUp) {

             m_bUp = m_errors[i2]; m_iUp = i2;

           }

         }

       }

       if ((m_iLow == -1) || (m_iUp == -1)) {

         throw new Exception("This should never happen!");

       }

       // Made some progress.

       return true;

     }

     /**

      * Quick and dirty check whether the quadratic programming problem is solved.

      * 

      * @throws Exception if checking fails

      */

     protected void checkClassifier() throws Exception {

       double sum = 0;

       for (int i = 0; i < m_alpha.length; i++) {

         if (m_alpha[i] > 0) {

           sum += m_class[i] * m_alpha[i];

         }

       }

       System.err.println("Sum of y(i) * alpha(i): " + sum);

       for (int i = 0; i < m_alpha.length; i++) {

         double output = SVMOutput(i, m_data.instance(i));

         if (Utils.eq(m_alpha[i], 0)) {

           if (Utils.sm(m_class[i] * output, 1)) {

             System.err.println("KKT condition 1 violated: " + m_class[i] * output);

           }

         } 

         if (Utils.gr(m_alpha[i], 0) && 

             Utils.sm(m_alpha[i], m_C * m_data.instance(i).weight())) {

           if (!Utils.eq(m_class[i] * output, 1)) {

             System.err.println("KKT condition 2 violated: " + m_class[i] * output);

           }

         } 

         if (Utils.eq(m_alpha[i], m_C * m_data.instance(i).weight())) {

           if (Utils.gr(m_class[i] * output, 1)) {

             System.err.println("KKT condition 3 violated: " + m_class[i] * output);

           }

         } 

       }

     }  

     /**

      * Returns the revision string.

      * 

      * @return                the revision

      */

     public String getRevision() {

       return RevisionUtils.extract("$Revision: 8034 $");

     }

   }

   /** filter: Normalize training data */

   public static final int FILTER_NORMALIZE = 0;

   /** filter: Standardize training data */

   public static final int FILTER_STANDARDIZE = 1;

   /** filter: No normalization/standardization */

   public static final int FILTER_NONE = 2;

   /** The filter to apply to the training data */

   public static final Tag [] TAGS_FILTER = {

     new Tag(FILTER_NORMALIZE, "Normalize training data"),

     new Tag(FILTER_STANDARDIZE, "Standardize training data"),

     new Tag(FILTER_NONE, "No normalization/standardization"),

   };

   /** The binary classifier(s) */

   protected BinarySMO[][] m_classifiers = null;

   /** The complexity parameter. */

   protected double m_C = 1.0;

   /** Epsilon for rounding. */

   protected double m_eps = 1.0e-12;

   /** Tolerance for accuracy of result. */

   protected double m_tol = 1.0e-3;

   /** Whether to normalize/standardize/neither */

   protected int m_filterType = FILTER_NORMALIZE;

   /** The filter used to make attributes numeric. */

   protected NominalToBinary m_NominalToBinary;

   /** The filter used to standardize/normalize all values. */

   protected Filter m_Filter = null;

   /** The filter used to get rid of missing values. */

   protected ReplaceMissingValues m_Missing;

   /** The class index from the training data */

   protected int m_classIndex = -1;

   /** The class attribute */

   protected Attribute m_classAttribute;

   /** whether the kernel is a linear one */

   protected boolean m_KernelIsLinear = false;

   /** Turn off all checks and conversions? Turning them off assumes

       that data is purely numeric, doesn't contain any missing values,

       and has a nominal class. Turning them off also means that

       no header information will be stored if the machine is linear. 

       Finally, it also assumes that no instance has a weight equal to 0.*/

   protected boolean m_checksTurnedOff;

   /** Precision constant for updating sets */

   protected static double m_Del = 1000 * Double.MIN_VALUE;

   /** Whether logistic models are to be fit */

   protected boolean m_fitLogisticModels = false;

   /** The number of folds for the internal cross-validation */

   protected int m_numFolds = -1;

   /** The random number seed  */

   protected int m_randomSeed = 1;

   /** the kernel to use */

   protected Kernel m_kernel = new PolyKernel();

   /**

    * Turns off checks for missing values, etc. Use with caution.

    */

   public void turnChecksOff() {

     m_checksTurnedOff = true;

   }

   /**

    * Turns on checks for missing values, etc.

    */

   public void turnChecksOn() {

     m_checksTurnedOff = false;

   }

   /**

    * Returns default capabilities of the classifier.

    *

    * @return      the capabilities of this classifier

    */

   public Capabilities getCapabilities() {

     Capabilities result = getKernel().getCapabilities();

     result.setOwner(this);

     // attribute

     result.enableAllAttributeDependencies();

     // with NominalToBinary we can also handle nominal attributes, but only

     // if the kernel can handle numeric attributes

     if (result.handles(Capability.NUMERIC_ATTRIBUTES))

       result.enable(Capability.NOMINAL_ATTRIBUTES);

     result.enable(Capability.MISSING_VALUES);

     // class

     result.disableAllClasses();

     result.disableAllClassDependencies();

     result.enable(Capability.NOMINAL_CLASS);

     result.enable(Capability.MISSING_CLASS_VALUES);

     return result;

   }

   /**

    * Method for building the classifier. Implements a one-against-one

    * wrapper for multi-class problems.

    *

    * @param insts the set of training instances

    * @throws Exception if the classifier can't be built successfully

    */

   public void buildClassifier(Instances insts) throws Exception {

     if (!m_checksTurnedOff) {

       // can classifier handle the data?

       getCapabilities().testWithFail(insts);