/*
* 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.
*/
/*
* PrincipalComponents.java
* Copyright (C) 2000 Mark Hall
*
*/
package weka.attributeSelection;
import java.io.*;
import java.util.*;
import weka.core.*;
import weka.filters.unsupervised.attribute.ReplaceMissingValues;
import weka.filters.unsupervised.attribute.Normalize;
import weka.filters.unsupervised.attribute.NominalToBinary;
import weka.filters.unsupervised.attribute.Remove;
import weka.filters.Filter;
/**
* Class for performing principal components analysis/transformation. <p>
*
* Valid options are:<p>
* -N <br>
* Don't normalize the input data. <p>
*
* -R <variance> <br>
* Retain enough pcs to account for this proportion of the variance. <p>
*
* -T <br>
* Transform through the PC space and back to the original space. <p>
*
* @author Mark Hall (mhall@cs.waikato.ac.nz)
* @author Gabi Schmidberger (gabi@cs.waikato.ac.nz)
* @version $Revision: 1.1.1.1 $
*/
public class PrincipalComponents extends UnsupervisedAttributeEvaluator
implements AttributeTransformer, OptionHandler {
/** The data to transform analyse/transform */
private Instances m_trainInstances;
/** Keep a copy for the class attribute (if set) */
private Instances m_trainCopy;
/** The header for the transformed data format */
private Instances m_transformedFormat;
/** The header for data transformed back to the original space */
private Instances m_originalSpaceFormat;
/** Data has a class set */
private boolean m_hasClass;
/** Class index */
private int m_classIndex;
/** Number of attributes */
private int m_numAttribs;
/** Number of instances */
private int m_numInstances;
/** Correlation matrix for the original data */
private double [][] m_correlation;
/** Will hold the unordered linear transformations of the (normalized)
original data */
private double [][] m_eigenvectors;
/** Eigenvalues for the corresponding eigenvectors */
private double [] m_eigenvalues = null;
/** Sorted eigenvalues */
private int [] m_sortedEigens;
/** sum of the eigenvalues */
private double m_sumOfEigenValues = 0.0;
/** Filters for original data */
private ReplaceMissingValues m_replaceMissingFilter;
private Normalize m_normalizeFilter;
private NominalToBinary m_nominalToBinFilter;
private Remove m_attributeFilter;
/** used to remove the class column if a class column is set */
private Remove m_attribFilter;
/** The number of attributes in the pc transformed data */
private int m_outputNumAtts = -1;
/** normalize the input data? */
private boolean m_normalize = true;
/** the amount of varaince to cover in the original data when
retaining the best n PC's */
private double m_coverVariance = 0.95;
/** transform the data through the pc space and back to the original
space ? */
private boolean m_transBackToOriginal = false;
/** holds the transposed eigenvectors for converting back to the
original space */
private double [][] m_eTranspose;
/**
* Returns a string describing this attribute transformer
* @return a description of the evaluator suitable for
* displaying in the explorer/experimenter gui
*/
public String globalInfo() {
return "Performs a principal components analysis and transformation of "
+"the data. Use in conjunction with a Ranker search. Dimensionality "
+"reduction is accomplished by choosing enough eigenvectors to "
+"account for some percentage of the variance in the original data---"
+"default 0.95 (95%). Attribute noise can be filtered by transforming "
+"to the PC space, eliminating some of the worst eigenvectors, and "
+"then transforming back to the original space.";
}
/**
* Returns an enumeration describing the available options. <p>
*
* @return an enumeration of all the available options.
**/
public Enumeration listOptions () {
Vector newVector = new Vector(3);
newVector.addElement(new Option("\tDon't normalize input data."
, "D", 0, "-D"));
newVector.addElement(new Option("\tRetain enough PC attributes to account "
+"\n\tfor this proportion of variance in "
+"the original data. (default = 0.95)",
"R",1,"-R"));
newVector.addElement(new Option("\tTransform through the PC space and "
+"\n\tback to the original space."
, "O", 0, "-O"));
return newVector.elements();
}
/**
* Parses a given list of options.
*
* Valid options are:<p>
* -N <br>
* Don't normalize the input data. <p>
*
* -R <variance> <br>
* Retain enough pcs to account for this proportion of the variance. <p>
*
* -T <br>
* Transform through the PC space and back to the original space. <p>
*
* @param options the list of options as an array of strings
* @exception Exception if an option is not supported
*/
public void setOptions (String[] options)
throws Exception {
resetOptions();
String optionString;
optionString = Utils.getOption('R', options);
if (optionString.length() != 0) {
Double temp;
temp = Double.valueOf(optionString);
setVarianceCovered(temp.doubleValue());
}
setNormalize(!Utils.getFlag('D', options));
setTransformBackToOriginal(Utils.getFlag('O', options));
}
/**
* Reset to defaults
*/
private void resetOptions() {
m_coverVariance = 0.95;
m_normalize = true;
m_sumOfEigenValues = 0.0;
m_transBackToOriginal = false;
}
/**
* Returns the tip text for this property
* @return tip text for this property suitable for
* displaying in the explorer/experimenter gui
*/
public String normalizeTipText() {
return "Normalize input data.";
}
/**
* Set whether input data will be normalized.
* @param n true if input data is to be normalized
*/
public void setNormalize(boolean n) {
m_normalize = n;
}
/**
* Gets whether or not input data is to be normalized
* @return true if input data is to be normalized
*/
public boolean getNormalize() {
return m_normalize;
}
/**
* Returns the tip text for this property
* @return tip text for this property suitable for
* displaying in the explorer/experimenter gui
*/
public String varianceCoveredTipText() {
return "Retain enough PC attributes to account for this proportion of "
+"variance.";
}
/**
* Sets the amount of variance to account for when retaining
* principal components
* @param vc the proportion of total variance to account for
*/
public void setVarianceCovered(double vc) {
m_coverVariance = vc;
}
/**
* Gets the proportion of total variance to account for when
* retaining principal components
* @return the proportion of variance to account for
*/
public double getVarianceCovered() {
return m_coverVariance;
}
/**
* Returns the tip text for this property
* @return tip text for this property suitable for
* displaying in the explorer/experimenter gui
*/
public String transformBackToOriginalTipText() {
return "Transform through the PC space and back to the original space. "
+"If only the best n PCs are retained (by setting varianceCovered < 1) "
+"then this option will give a dataset in the original space but with "
+"less attribute noise.";
}
/**
* Sets whether the data should be transformed back to the original
* space
* @param b true if the data should be transformed back to the
* original space
*/
public void setTransformBackToOriginal(boolean b) {
m_transBackToOriginal = b;
}
/**
* Gets whether the data is to be transformed back to the original
* space.
* @return true if the data is to be transformed back to the original space
*/
public boolean getTransformBackToOriginal() {
return m_transBackToOriginal;
}
/**
* Gets the current settings of PrincipalComponents
*
* @return an array of strings suitable for passing to setOptions()
*/
public String[] getOptions () {
String[] options = new String[4];
int current = 0;
if (!getNormalize()) {
options[current++] = "-D";
}
options[current++] = "-R"; options[current++] = ""+getVarianceCovered();
if (getTransformBackToOriginal()) {
options[current++] = "-O";
}
while (current < options.length) {
options[current++] = "";
}
return options;
}
/**
* Initializes principal components and performs the analysis
* @param data the instances to analyse/transform
* @exception Exception if analysis fails
*/
public void buildEvaluator(Instances data) throws Exception {
buildAttributeConstructor(data);
}
private void buildAttributeConstructor (Instances data) throws Exception {
m_eigenvalues = null;
m_outputNumAtts = -1;
m_attributeFilter = null;
m_nominalToBinFilter = null;
m_sumOfEigenValues = 0.0;
if (data.checkForStringAttributes()) {
throw new UnsupportedAttributeTypeException("Can't handle string attributes!");
}
m_trainInstances = data;
// make a copy of the training data so that we can get the class
// column to append to the transformed data (if necessary)
m_trainCopy = new Instances(m_trainInstances);
m_replaceMissingFilter = new ReplaceMissingValues();
m_replaceMissingFilter.setInputFormat(m_trainInstances);
m_trainInstances = Filter.useFilter(m_trainInstances,
m_replaceMissingFilter);
if (m_normalize) {
m_normalizeFilter = new Normalize();
m_normalizeFilter.setInputFormat(m_trainInstances);
m_trainInstances = Filter.useFilter(m_trainInstances, m_normalizeFilter);
}
m_nominalToBinFilter = new NominalToBinary();
m_nominalToBinFilter.setInputFormat(m_trainInstances);
m_trainInstances = Filter.useFilter(m_trainInstances,
m_nominalToBinFilter);
// delete any attributes with only one distinct value or are all missing
Vector deleteCols = new Vector();
for (int i=0;i<m_trainInstances.numAttributes();i++) {
if (m_trainInstances.numDistinctValues(i) <=1) {
deleteCols.addElement(new Integer(i));
}
}
if (m_trainInstances.classIndex() >=0) {
// get rid of the class column
m_hasClass = true;
m_classIndex = m_trainInstances.classIndex();
deleteCols.addElement(new Integer(m_classIndex));
}
// remove columns from the data if necessary
if (deleteCols.size() > 0) {
m_attributeFilter = new Remove();
int [] todelete = new int [deleteCols.size()];
for (int i=0;i<deleteCols.size();i++) {
todelete[i] = ((Integer)(deleteCols.elementAt(i))).intValue();
}
m_attributeFilter.setAttributeIndicesArray(todelete);
m_attributeFilter.setInvertSelection(false);
m_attributeFilter.setInputFormat(m_trainInstances);
m_trainInstances = Filter.useFilter(m_trainInstances, m_attributeFilter);
}
m_numInstances = m_trainInstances.numInstances();
m_numAttribs = m_trainInstances.numAttributes();
fillCorrelation();
double [] d = new double[m_numAttribs];
double [][] v = new double[m_numAttribs][m_numAttribs];
Matrix corr = new Matrix(m_correlation);
corr.eigenvalueDecomposition(v, d);
//if (debug) {
// Matrix V = new Matrix(v);
// boolean b = corr.testEigen(V, d, true);
// if (!b)
// System.out.println("Problem with eigenvektors!!!");
// else
// System.out.println("***** everything's fine !!!");
// }
m_eigenvectors = (double [][])v.clone();
m_eigenvalues = (double [])d.clone();
// any eigenvalues less than 0 are not worth anything --- change to 0
for (int i = 0; i < m_eigenvalues.length; i++) {
if (m_eigenvalues[i] < 0) {
m_eigenvalues[i] = 0.0;
}
}
m_sortedEigens = Utils.sort(m_eigenvalues);
m_sumOfEigenValues = Utils.sum(m_eigenvalues);
m_transformedFormat = setOutputFormat();
if (m_transBackToOriginal) {
m_originalSpaceFormat = setOutputFormatOriginal();
// new ordered eigenvector matrix
int numVectors = (m_transformedFormat.classIndex() < 0)
? m_transformedFormat.numAttributes()
: m_transformedFormat.numAttributes() - 1;
double [][] orderedVectors =
new double [m_eigenvectors.length][numVectors + 1];
// try converting back to the original space
for (int i = m_numAttribs - 1; i > (m_numAttribs - numVectors - 1); i--) {
for (int j = 0; j < m_numAttribs; j++) {
orderedVectors[j][m_numAttribs - i] =
m_eigenvectors[j][m_sortedEigens[i]];
}
}
// transpose the matrix
int nr = orderedVectors.length;
int nc = orderedVectors[0].length;
m_eTranspose =
new double [nc][nr];
for (int i = 0; i < nc; i++) {
for (int j = 0; j < nr; j++) {
m_eTranspose[i][j] = orderedVectors[j][i];
}
}
}
}
/**
* Returns just the header for the transformed data (ie. an empty
* set of instances. This is so that AttributeSelection can
* determine the structure of the transformed data without actually
* having to get all the transformed data through getTransformedData().
* @return the header of the transformed data.
* @exception Exception if the header of the transformed data can't
* be determined.
*/
public Instances transformedHeader() throws Exception {
if (m_eigenvalues == null) {
throw new Exception("Principal components hasn't been built yet");
}
if (m_transBackToOriginal) {
return m_originalSpaceFormat;
} else {
return m_transformedFormat;
}
}
/**
* Gets the transformed training data.
* @return the transformed training data
* @exception Exception if transformed data can't be returned
*/
public Instances transformedData() throws Exception {
if (m_eigenvalues == null) {
throw new Exception("Principal components hasn't been built yet");
}
Instances output;
if (m_transBackToOriginal) {
output = new Instances(m_originalSpaceFormat);
} else {
output = new Instances(m_transformedFormat);
}
for (int i=0;i<m_trainCopy.numInstances();i++) {
Instance converted = convertInstance(m_trainCopy.instance(i));
output.add(converted);
}
return output;
}
/**
* Evaluates the merit of a transformed attribute. This is defined
* to be 1 minus the cumulative variance explained. Merit can't
* be meaningfully evaluated if the data is to be transformed back
* to the original space.
* @param att the attribute to be evaluated
* @return the merit of a transformed attribute
* @exception Exception if attribute can't be evaluated
*/
public double evaluateAttribute(int att) throws Exception {
if (m_eigenvalues == null) {
throw new Exception("Principal components hasn't been built yet!");
}
if (m_transBackToOriginal) {
return 1.0; // can't evaluate back in the original space!
}
// return 1-cumulative variance explained for this transformed att
double cumulative = 0.0;
for (int i = m_numAttribs - 1; i >= m_numAttribs - att - 1; i--) {
cumulative += m_eigenvalues[m_sortedEigens[i]];
}
return 1.0 - cumulative / m_sumOfEigenValues;
}
/**
* Fill the correlation matrix
*/
private void fillCorrelation() {
m_correlation = new double[m_numAttribs][m_numAttribs];
double [] att1 = new double [m_numInstances];
double [] att2 = new double [m_numInstances];
double corr;
for (int i = 0; i < m_numAttribs; i++) {
for (int j = 0; j < m_numAttribs; j++) {
if (i == j) {
m_correlation[i][j] = 1.0;
} else {
for (int k = 0; k < m_numInstances; k++) {
att1[k] = m_trainInstances.instance(k).value(i);
att2[k] = m_trainInstances.instance(k).value(j);
}
corr = Utils.correlation(att1,att2,m_numInstances);
m_correlation[i][j] = corr;
m_correlation[i][j] = corr;
}
}
}
}
/**
* Return a summary of the analysis
* @return a summary of the analysis.
*/
private String principalComponentsSummary() {
StringBuffer result = new StringBuffer();
double cumulative = 0.0;
Instances output = null;
int numVectors=0;
try {
output = setOutputFormat();
numVectors = (output.classIndex() < 0)
? output.numAttributes()
: output.numAttributes()-1;
} catch (Exception ex) {
}
//tomorrow
result.append("Correlation matrix\n"+matrixToString(m_correlation)
+"\n\n");
result.append("eigenvalue\tproportion\tcumulative\n");
for (int i = m_numAttribs - 1; i > (m_numAttribs - numVectors - 1); i--) {
cumulative+=m_eigenvalues[m_sortedEigens[i]];
result.append(Utils.doubleToString(m_eigenvalues[m_sortedEigens[i]],9,5)
+"\t"+Utils.
doubleToString((m_eigenvalues[m_sortedEigens[i]] /
m_sumOfEigenValues),
9,5)
+"\t"+Utils.doubleToString((cumulative /
m_sumOfEigenValues),9,5)
+"\t"+output.attribute(m_numAttribs - i - 1).name()+"\n");
}
result.append("\nEigenvectors\n");
for (int j = 1;j <= numVectors;j++) {
result.append(" V"+j+'\t');
}
result.append("\n");
for (int j = 0; j < m_numAttribs; j++) {
for (int i = m_numAttribs - 1; i > (m_numAttribs - numVectors - 1); i--) {
result.append(Utils.
doubleToString(m_eigenvectors[j][m_sortedEigens[i]],7,4)
+"\t");
}
result.append(m_trainInstances.attribute(j).name()+'\n');
}
if (m_transBackToOriginal) {
result.append("\nPC space transformed back to original space.\n"
+"(Note: can't evaluate attributes in the original "
+"space)\n");
}
return result.toString();
}
/**
* Returns a description of this attribute transformer
* @return a String describing this attribute transformer
*/
public String toString() {
if (m_eigenvalues == null) {
return "Principal components hasn't been built yet!";
} else {
return "\tPrincipal Components Attribute Transformer\n\n"
+principalComponentsSummary();
}
}
/**
* Return a matrix as a String
* @param matrix that is decribed as a string
* @return a String describing a matrix
*/
private String matrixToString(double [][] matrix) {
StringBuffer result = new StringBuffer();
int last = matrix.length - 1;
for (int i = 0; i <= last; i++) {
for (int j = 0; j <= last; j++) {
result.append(Utils.doubleToString(matrix[i][j],6,2)+" ");
if (j == last) {
result.append('\n');
}
}
}
return result.toString();
}
/**
* Convert a pc transformed instance back to the original space
*/
private Instance convertInstanceToOriginal(Instance inst)
throws Exception {
double[] newVals = null;
if (m_hasClass) {
newVals = new double[m_numAttribs+1];
} else {
newVals = new double[m_numAttribs];
}
if (m_hasClass) {
// class is always appended as the last attribute
newVals[m_numAttribs] = inst.value(inst.numAttributes() - 1);
}
for (int i = 0; i < m_eTranspose[0].length; i++) {
double tempval = 0.0;
for (int j = 1; j < m_eTranspose.length; j++) {
tempval += (m_eTranspose[j][i] *
inst.value(j - 1));
}
newVals[i] = tempval;
}
if (inst instanceof SparseInstance) {
return new SparseInstance(inst.weight(), newVals);
} else {
return new Instance(inst.weight(), newVals);
}
}
/**
* Transform an instance in original (unormalized) format. Convert back
* to the original space if requested.
* @param instance an instance in the original (unormalized) format
* @return a transformed instance
* @exception Exception if instance cant be transformed
*/
public Instance convertInstance(Instance instance) throws Exception {
if (m_eigenvalues == null) {
throw new Exception("convertInstance: Principal components not "
+"built yet");
}
double[] newVals = new double[m_outputNumAtts];
Instance tempInst = (Instance)instance.copy();
if (!instance.equalHeaders(m_trainCopy.instance(0))) {
throw new Exception("Can't convert instance: header's don't match: "
+"PrincipalComponents");
}
m_replaceMissingFilter.input(tempInst);
m_replaceMissingFilter.batchFinished();
tempInst = m_replaceMissingFilter.output();
if (m_normalize) {
m_normalizeFilter.input(tempInst);
m_normalizeFilter.batchFinished();
tempInst = m_normalizeFilter.output();
}
m_nominalToBinFilter.input(tempInst);
m_nominalToBinFilter.batchFinished();
tempInst = m_nominalToBinFilter.output();
if (m_attributeFilter != null) {
m_attributeFilter.input(tempInst);
m_attributeFilter.batchFinished();
tempInst = m_attributeFilter.output();
}
if (m_hasClass) {
newVals[m_outputNumAtts - 1] = instance.value(instance.classIndex());
}
double cumulative = 0;
for (int i = m_numAttribs - 1; i >= 0; i--) {
double tempval = 0.0;
for (int j = 0; j < m_numAttribs; j++) {
tempval += (m_eigenvectors[j][m_sortedEigens[i]] *
tempInst.value(j));
}
newVals[m_numAttribs - i - 1] = tempval;
cumulative+=m_eigenvalues[m_sortedEigens[i]];
if ((cumulative / m_sumOfEigenValues) >= m_coverVariance) {
break;
}
}
if (!m_transBackToOriginal) {
if (instance instanceof SparseInstance) {
return new SparseInstance(instance.weight(), newVals);
} else {
return new Instance(instance.weight(), newVals);
}
} else {
if (instance instanceof SparseInstance) {
return convertInstanceToOriginal(new SparseInstance(instance.weight(),
newVals));
} else {
return convertInstanceToOriginal(new Instance(instance.weight(),
newVals));
}
}
}
/**
* Set up the header for the PC->original space dataset
*/
private Instances setOutputFormatOriginal() throws Exception {
FastVector attributes = new FastVector();
for (int i = 0; i < m_numAttribs; i++) {
String att = m_trainInstances.attribute(i).name();
attributes.addElement(new Attribute(att));
}
if (m_hasClass) {
attributes.addElement(m_trainCopy.classAttribute().copy());
}
Instances outputFormat =
new Instances(m_trainCopy.relationName()+"->PC->original space",
attributes, 0);
// set the class to be the last attribute if necessary
if (m_hasClass) {
outputFormat.setClassIndex(outputFormat.numAttributes()-1);
}
return outputFormat;
}
/**
* Set the format for the transformed data
* @return a set of empty Instances (header only) in the new format
* @exception Exception if the output format can't be set
*/
private Instances setOutputFormat() throws Exception {
if (m_eigenvalues == null) {
return null;
}
double cumulative = 0.0;
FastVector attributes = new FastVector();
for (int i = m_numAttribs - 1; i >= 0; i--) {
StringBuffer attName = new StringBuffer();
for (int j = 0; j < m_numAttribs; j++) {
attName.append(Utils.
doubleToString(m_eigenvectors[j][m_sortedEigens[i]],
5,3)
+m_trainInstances.attribute(j).name());
if (j != m_numAttribs - 1) {
if (m_eigenvectors[j+1][m_sortedEigens[i]] >= 0) {
attName.append("+");
}
}
}
attributes.addElement(new Attribute(attName.toString()));
cumulative+=m_eigenvalues[m_sortedEigens[i]];
if ((cumulative / m_sumOfEigenValues) >= m_coverVariance) {
break;
}
}
if (m_hasClass) {
attributes.addElement(m_trainCopy.classAttribute().copy());
}
Instances outputFormat =
new Instances(m_trainInstances.relationName()+"_principal components",
attributes, 0);
// set the class to be the last attribute if necessary
if (m_hasClass) {
outputFormat.setClassIndex(outputFormat.numAttributes()-1);
}
m_outputNumAtts = outputFormat.numAttributes();
return outputFormat;
}
/**
* Main method for testing this class
* @param argv should contain the command line arguments to the
* evaluator/transformer (see AttributeSelection)
*/
public static void main(String [] argv) {
try {
System.out.println(AttributeSelection.
SelectAttributes(new PrincipalComponents(), argv));
}
catch (Exception e) {
e.printStackTrace();
System.out.println(e.getMessage());
}
}
}