/*
* 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 2 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, write to the Free Software
* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
*/
/*
* LeastMedSq.java
*
* Copyright (C) 2001 University of Waikato
*/
package weka.classifiers.functions;
import weka.classifiers.Classifier;
import weka.core.Capabilities;
import weka.core.Instance;
import weka.core.Instances;
import weka.core.Option;
import weka.core.OptionHandler;
import weka.core.RevisionUtils;
import weka.core.TechnicalInformation;
import weka.core.TechnicalInformationHandler;
import weka.core.Utils;
import weka.core.Capabilities.Capability;
import weka.core.TechnicalInformation.Field;
import weka.core.TechnicalInformation.Type;
import weka.filters.Filter;
import weka.filters.supervised.attribute.NominalToBinary;
import weka.filters.unsupervised.attribute.ReplaceMissingValues;
import weka.filters.unsupervised.instance.RemoveRange;
import java.util.Enumeration;
import java.util.Random;
import java.util.Vector;
/**
<!-- globalinfo-start -->
* Implements a least median sqaured linear regression utilising the existing weka LinearRegression class to form predictions. <br/>
* Least squared regression functions are generated from random subsamples of the data. The least squared regression with the lowest meadian squared error is chosen as the final model.<br/>
* <br/>
* The basis of the algorithm is <br/>
* <br/>
* Peter J. Rousseeuw, Annick M. Leroy (1987). Robust regression and outlier detection. .
* <p/>
<!-- globalinfo-end -->
*
<!-- technical-bibtex-start -->
* BibTeX:
* <pre>
* @book{Rousseeuw1987,
* author = {Peter J. Rousseeuw and Annick M. Leroy},
* title = {Robust regression and outlier detection},
* year = {1987}
* }
* </pre>
* <p/>
<!-- technical-bibtex-end -->
*
<!-- options-start -->
* Valid options are: <p/>
*
* <pre> -S <sample size>
* Set sample size
* (default: 4)
* </pre>
*
* <pre> -G <seed>
* Set the seed used to generate samples
* (default: 0)
* </pre>
*
* <pre> -D
* Produce debugging output
* (default no debugging output)
* </pre>
*
<!-- options-end -->
*
* @author Tony Voyle (tv6@waikato.ac.nz)
* @version $Revision: 1.17 $
*/
public class LeastMedSq
extends Classifier
implements OptionHandler, TechnicalInformationHandler {
/** for serialization */
static final long serialVersionUID = 4288954049987652970L;
private double[] m_Residuals;
private double[] m_weight;
private double m_SSR;
private double m_scalefactor;
private double m_bestMedian = Double.POSITIVE_INFINITY;
private LinearRegression m_currentRegression;
private LinearRegression m_bestRegression;
private LinearRegression m_ls;
private Instances m_Data;
private Instances m_RLSData;
private Instances m_SubSample;
private ReplaceMissingValues m_MissingFilter;
private NominalToBinary m_TransformFilter;
private RemoveRange m_SplitFilter;
private int m_samplesize = 4;
private int m_samples;
private boolean m_israndom = false;
private boolean m_debug = false;
private Random m_random;
private long m_randomseed = 0;
/**
* Returns a string describing this classifier
* @return a description of the classifier suitable for
* displaying in the explorer/experimenter gui
*/
public String globalInfo() {
return "Implements a least median sqaured linear regression utilising the "
+"existing weka LinearRegression class to form predictions. \n"
+"Least squared regression functions are generated from random subsamples of "
+"the data. The least squared regression with the lowest meadian squared error "
+"is chosen as the final model.\n\n"
+"The basis of the algorithm is \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;
result = new TechnicalInformation(Type.BOOK);
result.setValue(Field.AUTHOR, "Peter J. Rousseeuw and Annick M. Leroy");
result.setValue(Field.YEAR, "1987");
result.setValue(Field.TITLE, "Robust regression and outlier detection");
return result;
}
/**
* Returns default capabilities of the classifier.
*
* @return the capabilities of this classifier
*/
public Capabilities getCapabilities() {
Capabilities result = super.getCapabilities();
// attributes
result.enable(Capability.NOMINAL_ATTRIBUTES);
result.enable(Capability.NUMERIC_ATTRIBUTES);
result.enable(Capability.DATE_ATTRIBUTES);
result.enable(Capability.MISSING_VALUES);
// class
result.enable(Capability.NUMERIC_CLASS);
result.enable(Capability.DATE_CLASS);
result.enable(Capability.MISSING_CLASS_VALUES);
return result;
}
/**
* Build lms regression
*
* @param data training data
* @throws Exception if an error occurs
*/
public void buildClassifier(Instances data)throws Exception{
// can classifier handle the data?
getCapabilities().testWithFail(data);
// remove instances with missing class
data = new Instances(data);
data.deleteWithMissingClass();
cleanUpData(data);
getSamples();
findBestRegression();
buildRLSRegression();
} // buildClassifier
/**
* Classify a given instance using the best generated
* LinearRegression Classifier.
*
* @param instance instance to be classified
* @return class value
* @throws Exception if an error occurs
*/
public double classifyInstance(Instance instance)throws Exception{
Instance transformedInstance = instance;
m_TransformFilter.input(transformedInstance);
transformedInstance = m_TransformFilter.output();
m_MissingFilter.input(transformedInstance);
transformedInstance = m_MissingFilter.output();
return m_ls.classifyInstance(transformedInstance);
} // classifyInstance
/**
* Cleans up data
*
* @param data data to be cleaned up
* @throws Exception if an error occurs
*/
private void cleanUpData(Instances data)throws Exception{
m_Data = data;
m_TransformFilter = new NominalToBinary();
m_TransformFilter.setInputFormat(m_Data);
m_Data = Filter.useFilter(m_Data, m_TransformFilter);
m_MissingFilter = new ReplaceMissingValues();
m_MissingFilter.setInputFormat(m_Data);
m_Data = Filter.useFilter(m_Data, m_MissingFilter);
m_Data.deleteWithMissingClass();
}
/**
* Gets the number of samples to use.
*
* @throws Exception if an error occurs
*/
private void getSamples()throws Exception{
int stuf[] = new int[] {500,50,22,17,15,14};
if ( m_samplesize < 7){
if ( m_Data.numInstances() < stuf[m_samplesize - 1])
m_samples = combinations(m_Data.numInstances(), m_samplesize);
else
m_samples = m_samplesize * 500;
} else m_samples = 3000;
if (m_debug){
System.out.println("m_samplesize: " + m_samplesize);
System.out.println("m_samples: " + m_samples);
System.out.println("m_randomseed: " + m_randomseed);
}
}
/**
* Set up the random number generator
*
*/
private void setRandom(){
m_random = new Random(getRandomSeed());
}
/**
* Finds the best regression generated from m_samples
* random samples from the training data
*
* @throws Exception if an error occurs
*/
private void findBestRegression()throws Exception{
setRandom();
m_bestMedian = Double.POSITIVE_INFINITY;
if (m_debug) {
System.out.println("Starting:");
}
for(int s = 0, r = 0; s < m_samples; s++, r++){
if (m_debug) {
if(s%(m_samples/100)==0)
System.out.print("*");
}
genRegression();
getMedian();
}
if (m_debug) {
System.out.println("");
}
m_currentRegression = m_bestRegression;
}
/**
* Generates a LinearRegression classifier from
* the current m_SubSample
*
* @throws Exception if an error occurs
*/
private void genRegression()throws Exception{
m_currentRegression = new LinearRegression();
m_currentRegression.setOptions(new String[]{"-S", "1"});
selectSubSample(m_Data);
m_currentRegression.buildClassifier(m_SubSample);
}
/**
* Finds residuals (squared) for the current
* regression.
*
* @throws Exception if an error occurs
*/
private void findResiduals()throws Exception{
m_SSR = 0;
m_Residuals = new double [m_Data.numInstances()];
for(int i = 0; i < m_Data.numInstances(); i++){
m_Residuals[i] = m_currentRegression.classifyInstance(m_Data.instance(i));
m_Residuals[i] -= m_Data.instance(i).value(m_Data.classAttribute());
m_Residuals[i] *= m_Residuals[i];
m_SSR += m_Residuals[i];
}
}
/**
* finds the median residual squared for the
* current regression
*
* @throws Exception if an error occurs
*/
private void getMedian()throws Exception{
findResiduals();
int p = m_Residuals.length;
select(m_Residuals, 0, p - 1, p / 2);
if(m_Residuals[p / 2] < m_bestMedian){
m_bestMedian = m_Residuals[p / 2];
m_bestRegression = m_currentRegression;
}
}
/**
* Returns a string representing the best
* LinearRegression classifier found.
*
* @return String representing the regression
*/
public String toString(){
if( m_ls == null){
return "model has not been built";
}
return m_ls.toString();
}
/**
* Builds a weight function removing instances with an
* abnormally high scaled residual
*
* @throws Exception if weight building fails
*/
private void buildWeight()throws Exception{
findResiduals();
m_scalefactor = 1.4826 * ( 1 + 5 / (m_Data.numInstances()
- m_Data.numAttributes()))
* Math.sqrt(m_bestMedian);
m_weight = new double[m_Residuals.length];
for (int i = 0; i < m_Residuals.length; i++)
m_weight[i] = ((Math.sqrt(m_Residuals[i])/m_scalefactor < 2.5)?1.0:0.0);
}
/**
* Builds a new LinearRegression without the 'bad' data
* found by buildWeight
*
* @throws Exception if building fails
*/
private void buildRLSRegression()throws Exception{
buildWeight();
m_RLSData = new Instances(m_Data);
int x = 0;
int y = 0;
int n = m_RLSData.numInstances();
while(y < n){
if (m_weight[x] == 0){
m_RLSData.delete(y);
n = m_RLSData.numInstances();
y--;
}
x++;
y++;
}
if ( m_RLSData.numInstances() == 0){
System.err.println("rls regression unbuilt");
m_ls = m_currentRegression;
}else{
m_ls = new LinearRegression();
m_ls.setOptions(new String[]{"-S", "1"});
m_ls.buildClassifier(m_RLSData);
m_currentRegression = m_ls;
}
}
/**
* Finds the kth number in an array
*
* @param a an array of numbers
* @param l left pointer
* @param r right pointer
* @param k position of number to be found
*/
private static void select( double [] a, int l, int r, int k){
if (r <=l) return;
int i = partition( a, l, r);
if (i > k) select(a, l, i-1, k);
if (i < k) select(a, i+1, r, k);
}
/**
* Partitions an array of numbers such that all numbers
* less than that at index r, between indexes l and r
* will have a smaller index and all numbers greater than
* will have a larger index
*
* @param a an array of numbers
* @param l left pointer
* @param r right pointer
* @return final index of number originally at r
*/
private static int partition( double [] a, int l, int r ){
int i = l-1, j = r;
double v = a[r], temp;
while(true){
while(a[++i] < v);
while(v < a[--j]) if(j == l) break;
if(i >= j) break;
temp = a[i];
a[i] = a[j];
a[j] = temp;
}
temp = a[i];
a[i] = a[r];
a[r] = temp;
return i;
}
/**
* Produces a random sample from m_Data
* in m_SubSample
*
* @param data data from which to take sample
* @throws Exception if an error occurs
*/
private void selectSubSample(Instances data)throws Exception{
m_SplitFilter = new RemoveRange();
m_SplitFilter.setInvertSelection(true);
m_SubSample = data;
m_SplitFilter.setInputFormat(m_SubSample);
m_SplitFilter.setInstancesIndices(selectIndices(m_SubSample));
m_SubSample = Filter.useFilter(m_SubSample, m_SplitFilter);
}
/**
* Returns a string suitable for passing to RemoveRange consisting
* of m_samplesize indices.
*
* @param data dataset from which to take indicese
* @return string of indices suitable for passing to RemoveRange
*/
private String selectIndices(Instances data){
StringBuffer text = new StringBuffer();
for(int i = 0, x = 0; i < m_samplesize; i++){
do{x = (int) (m_random.nextDouble() * data.numInstances());}
while(x==0);
text.append(Integer.toString(x));
if(i < m_samplesize - 1)
text.append(",");
else
text.append("\n");
}
return text.toString();
}
/**
* Returns the tip text for this property
* @return tip text for this property suitable for
* displaying in the explorer/experimenter gui
*/
public String sampleSizeTipText() {
return "Set the size of the random samples used to generate the least sqaured "
+"regression functions.";
}
/**
* sets number of samples
*
* @param samplesize value
*/
public void setSampleSize(int samplesize){
m_samplesize = samplesize;
}
/**
* gets number of samples
*
* @return value
*/
public int getSampleSize(){
return m_samplesize;
}
/**
* Returns the tip text for this property
* @return tip text for this property suitable for
* displaying in the explorer/experimenter gui
*/
public String randomSeedTipText() {
return "Set the seed for selecting random subsamples of the training data.";
}
/**
* Set the seed for the random number generator
*
* @param randomseed the seed
*/
public void setRandomSeed(long randomseed){
m_randomseed = randomseed;
}
/**
* get the seed for the random number generator
*
* @return the seed value
*/
public long getRandomSeed(){
return m_randomseed;
}
/**
* sets whether or not debugging output shouild be printed
*
* @param debug true if debugging output selected
*/
public void setDebug(boolean debug){
m_debug = debug;
}
/**
* Returns whether or not debugging output shouild be printed
*
* @return true if debuging output selected
*/
public boolean getDebug(){
return m_debug;
}
/**
* Returns an enumeration of all the available options..
*
* @return an enumeration of all available options.
*/
public Enumeration listOptions(){
Vector newVector = new Vector(1);
newVector.addElement(new Option("\tSet sample size\n"
+ "\t(default: 4)\n",
"S", 4, "-S <sample size>"));
newVector.addElement(new Option("\tSet the seed used to generate samples\n"
+ "\t(default: 0)\n",
"G", 0, "-G <seed>"));
newVector.addElement(new Option("\tProduce debugging output\n"
+ "\t(default no debugging output)\n",
"D", 0, "-D"));
return newVector.elements();
}
/**
* Sets the OptionHandler's options using the given list. All options
* will be set (or reset) during this call (i.e. incremental setting
* of options is not possible).
*
<!-- options-start -->
* Valid options are: <p/>
*
* <pre> -S <sample size>
* Set sample size
* (default: 4)
* </pre>
*
* <pre> -G <seed>
* Set the seed used to generate samples
* (default: 0)
* </pre>
*
* <pre> -D
* Produce debugging output
* (default no debugging output)
* </pre>
*
<!-- options-end -->
*
* @param options the list of options as an array of strings
* @throws Exception if an option is not supported
*/
public void setOptions(String[] options) throws Exception {
String curropt = Utils.getOption('S', options);
if ( curropt.length() != 0){
setSampleSize(Integer.parseInt(curropt));
} else
setSampleSize(4);
curropt = Utils.getOption('G', options);
if ( curropt.length() != 0){
setRandomSeed(Long.parseLong(curropt));
} else {
setRandomSeed(0);
}
setDebug(Utils.getFlag('D', options));
}
/**
* Gets the current option settings for the OptionHandler.
*
* @return the list of current option settings as an array of strings
*/
public String[] getOptions(){
String options[] = new String[9];
int current = 0;
options[current++] = "-S";
options[current++] = "" + getSampleSize();
options[current++] = "-G";
options[current++] = "" + getRandomSeed();
if (getDebug()) {
options[current++] = "-D";
}
while (current < options.length) {
options[current++] = "";
}
return options;
}
/**
* Produces the combination nCr
*
* @param n
* @param r
* @return the combination
* @throws Exception if r is greater than n
*/
public static int combinations (int n, int r)throws Exception {
int c = 1, denom = 1, num = 1, i,orig=r;
if (r > n) throw new Exception("r must be less that or equal to n.");
r = Math.min( r , n - r);
for (i = 1 ; i <= r; i++){
num *= n-i+1;
denom *= i;
}
c = num / denom;
if(false)
System.out.println( "n: "+n+" r: "+orig+" num: "+num+
" denom: "+denom+" c: "+c);
return c;
}
/**
* Returns the revision string.
*
* @return the revision
*/
public String getRevision() {
return RevisionUtils.extract("$Revision: 1.17 $");
}
/**
* generate a Linear regression predictor for testing
*
* @param argv options
*/
public static void main(String [] argv){
runClassifier(new LeastMedSq(), argv);
} // main
} // lmr