/*
* 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/>.
*/
/*
* GaussianProcesses.java
* Copyright (C) 2005-2012 University of Waikato
*/
package weka.classifiers.functions;
import java.util.Enumeration;
import java.util.Vector;
import weka.classifiers.AbstractClassifier;
import weka.classifiers.ConditionalDensityEstimator;
import weka.classifiers.IntervalEstimator;
import weka.classifiers.functions.supportVector.CachedKernel;
import weka.classifiers.functions.supportVector.Kernel;
import weka.classifiers.functions.supportVector.PolyKernel;
import weka.core.Capabilities;
import weka.core.Capabilities.Capability;
import weka.core.Instance;
import weka.core.Instances;
import weka.core.Option;
import weka.core.OptionHandler;
import weka.core.SelectedTag;
import weka.core.Statistics;
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.core.matrix.Matrix;
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 Gaussian processes for
* regression without hyperparameter-tuning. To make choosing an
* appropriate noise level easier, this implementation applies
* normalization/standardization to the target attribute as well (if
* normalization/standardizaton is turned on). Missing values
* are replaced by the global mean/mode. Nominal attributes are
* converted to binary ones.
* <!-- globalinfo-end -->
*
* <!-- technical-bibtex-start --> BibTeX:
*
* <pre>
* @misc{Mackay1998,
* address = {Dept. of Physics, Cambridge University, UK},
* author = {David J.C. Mackay},
* title = {Introduction to Gaussian Processes},
* year = {1998},
* PS = {http://wol.ra.phy.cam.ac.uk/mackay/gpB.ps.gz}
* }
* </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>
* -L <double>
* Level of Gaussian Noise. (default 0.1)
* </pre>
*
* <pre>
* -N
* Whether to 0=normalize/1=standardize/2=neither. (default 0=normalize)
* </pre>
*
* <pre>
* -K <classname and parameters>
* The Kernel to use.
* (default: weka.classifiers.functions.supportVector.PolyKernel)
* </pre>
*
* <pre>
*
* Options specific to kernel weka.classifiers.functions.supportVector.RBFKernel:
* </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 <num>
* The size of the cache (a prime number).
* (default: 250007)
* </pre>
*
* <pre>
* -G <num>
* The Gamma parameter.
* (default: 0.01)
* </pre>
*
* <!-- options-end -->
*
* @author Kurt Driessens (kurtd@cs.waikato.ac.nz)
* @author Remco Bouckaert (remco@cs.waikato.ac.nz)
* @version $Revision: 9562 $
*/
public class GaussianProcesses extends AbstractClassifier implements OptionHandler, IntervalEstimator,
ConditionalDensityEstimator,
TechnicalInformationHandler, WeightedInstancesHandler {
/** for serialization */
static final long serialVersionUID = -8620066949967678545L;
/** The filter used to make attributes numeric. */
protected NominalToBinary m_NominalToBinary;
/** normalizes the data */
public static final int FILTER_NORMALIZE = 0;
/** standardizes the data */
public static final int FILTER_STANDARDIZE = 1;
/** no filter */
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 filter used to standardize/normalize all values. */
protected Filter m_Filter = null;
/** Whether to normalize/standardize/neither */
protected int m_filterType = FILTER_NORMALIZE;
/** The filter used to get rid of missing values. */
protected ReplaceMissingValues m_Missing;
/**
* Turn off all checks and conversions? Turning them off assumes that data
* is purely numeric, doesn't contain any missing values, and has a numeric
* class.
*/
protected boolean m_checksTurnedOff = false;
/** Gaussian Noise Value. */
protected double m_delta = 1;
/**
* The parameters of the linear transforamtion realized by the filter on the
* class attribute
*/
protected double m_Alin;
protected double m_Blin;
/** Kernel to use * */
protected Kernel m_kernel = new PolyKernel();
/** The number of training instances */
protected int m_NumTrain = 0;
/** The training data. */
protected double m_avg_target;
/** (negative) covariance matrix in symmetric matrix representation **/
public double[][] m_L;
/** The vector of target values. */
protected Matrix m_t;
/**
* Returns a string describing classifier
*
* @return a description suitable for displaying in the
* explorer/experimenter gui
*/
public String globalInfo() {
return " Implements Gaussian processes for "
+ "regression without hyperparameter-tuning. To make choosing an "
+ "appropriate noise level easier, this implementation applies "
+ "normalization/standardization to the target attribute as well "
+ "as the other attributes (if "
+ " normalization/standardizaton is turned on). Missing values "
+ "are replaced by the global mean/mode. Nominal attributes are "
+ "converted to binary ones. Note that kernel caching is turned off "
+ "if the kernel used implements CachedKernel.";
}
/**
* 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.MISC);
result.setValue(Field.AUTHOR, "David J.C. Mackay");
result.setValue(Field.YEAR, "1998");
result.setValue(Field.TITLE, "Introduction to Gaussian Processes");
result.setValue(Field.ADDRESS, "Dept. of Physics, Cambridge University, UK");
result.setValue(Field.PS, "http://wol.ra.phy.cam.ac.uk/mackay/gpB.ps.gz");
return result;
}
/**
* 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.NUMERIC_CLASS);
result.enable(Capability.DATE_CLASS);
result.enable(Capability.MISSING_CLASS_VALUES);
return result;
}
/**
* Method for building the classifier.
*
* @param insts
* the set of training instances
* @throws Exception
* if the classifier can't be built successfully
*/
public void buildClassifier(Instances insts) throws Exception {
/* check the set of training instances */
if (!m_checksTurnedOff) {
// can classifier handle the data?
getCapabilities().testWithFail(insts);
// remove instances with missing class
insts = new Instances(insts);
insts.deleteWithMissingClass();
}
if (!m_checksTurnedOff) {
m_Missing = new ReplaceMissingValues();
m_Missing.setInputFormat(insts);
insts = Filter.useFilter(insts, m_Missing);
} else {
m_Missing = null;
}
if (getCapabilities().handles(Capability.NUMERIC_ATTRIBUTES)) {
boolean onlyNumeric = true;
if (!m_checksTurnedOff) {
for (int i = 0; i < insts.numAttributes(); i++) {
if (i != insts.classIndex()) {
if (!insts.attribute(i).isNumeric()) {
onlyNumeric = false;
break;
}
}
}
}
if (!onlyNumeric) {
m_NominalToBinary = new NominalToBinary();
m_NominalToBinary.setInputFormat(insts);
insts = Filter.useFilter(insts, m_NominalToBinary);
} else {
m_NominalToBinary = null;
}
} else {
m_NominalToBinary = null;
}
if (m_filterType == FILTER_STANDARDIZE) {
m_Filter = new Standardize();
((Standardize)m_Filter).setIgnoreClass(true);
m_Filter.setInputFormat(insts);
insts = Filter.useFilter(insts, m_Filter);
} else if (m_filterType == FILTER_NORMALIZE) {
m_Filter = new Normalize();
((Normalize)m_Filter).setIgnoreClass(true);
m_Filter.setInputFormat(insts);
insts = Filter.useFilter(insts, m_Filter);
} else {
m_Filter = null;
}
m_NumTrain = insts.numInstances();
// determine which linear transformation has been
// applied to the class by the filter
if (m_Filter != null) {
Instance witness = (Instance) insts.instance(0).copy();
witness.setValue(insts.classIndex(), 0);
m_Filter.input(witness);
m_Filter.batchFinished();
Instance res = m_Filter.output();
m_Blin = res.value(insts.classIndex());
witness.setValue(insts.classIndex(), 1);
m_Filter.input(witness);
m_Filter.batchFinished();
res = m_Filter.output();
m_Alin = res.value(insts.classIndex()) - m_Blin;
} else {
m_Alin = 1.0;
m_Blin = 0.0;
}
// Initialize kernel
try {
CachedKernel cachedKernel = (CachedKernel) m_kernel;
cachedKernel.setCacheSize(0);
} catch (Exception e) {
// ignore
}
m_kernel.buildKernel(insts);
// Compute average target value
double sum = 0.0;
for (int i = 0; i < insts.numInstances(); i++) {
sum += insts.instance(i).classValue();
}
m_avg_target = sum / insts.numInstances();
// initialize kernel matrix/covariance matrix
int n = insts.numInstances();
m_L = new double[n][];
for (int i = 0; i < n; i++) {
m_L[i] = new double[i+1];
}
double kv = 0;
for (int i = 0; i < n; i++) {
for (int j = 0; j < i; j++) {
kv = m_kernel.eval(i, j, insts.instance(i));
m_L[i][j] = kv;
}
kv = m_kernel.eval(i, i, insts.instance(i));
m_L[i][i] = kv + m_delta * m_delta;
}
// Save memory (can't use Kernel.clean() because of polynominal kernel with exponent 1)
if (m_kernel instanceof CachedKernel) {
m_kernel = Kernel.makeCopy(m_kernel);
((CachedKernel)m_kernel).setCacheSize(-1);
m_kernel.buildKernel(insts);
}
// Calculate inverse matrix exploiting symmetry of covariance matrix
// NB this replaces the kernel matrix with (the negative of) its inverse and does
// not require any extra memory for a solution matrix
double [] tmprow = new double [n];
double tmp2 = 0, tmp = 0;
for (int i = 0; i < n; i++) {
tmp = -m_L[i][i];
m_L[i][i] = 1.0 / tmp;
for (int j = 0; j < n; j++) {
if (j != i) {
if (j < i) {
tmprow[j] = m_L[i][j];
m_L[i][j] /= tmp;
tmp2 = m_L[i][j];
m_L[j][j] += tmp2 * tmp2 * tmp;
} else if (j > i) {
tmprow[j] = m_L[j][i];
m_L[j][i] /= tmp;
tmp2 = m_L[j][i];
m_L[j][j] += tmp2 * tmp2 * tmp;
}
}
}
for (int j = 0; j < n; j++) {
if (j != i) {
if (i < j) {
for (int k = 0; k < i; k++) {
m_L[j][k] += tmprow[j] * m_L[i][k];
}
} else {
for (int k = 0; k < j; k++) {
m_L[j][k] += tmprow[j] * m_L[i][k];
}
}
for (int k = i + 1; k < j; k++) {
m_L[j][k] += tmprow[j] * m_L[k][i];
}
}
}
}
m_t = new Matrix(insts.numInstances(), 1);
double [] tt = new double[n];
for (int i = 0; i < n; i++) {
tt[i] = insts.instance(i).classValue() - m_avg_target;
}
// calculate m_t = tt . m_L
for (int i = 0; i < n; i++) {
double s = 0;
for (int k = 0; k < i; k++) {
s -= m_L[i][k] * tt[k];
}
for (int k = i; k < n; k++) {
s -= m_L[k][i] * tt[k];
}
m_t.set(i, 0, s);
}
} // buildClassifier
/**
* Classifies a given instance.
*
* @param inst
* the instance to be classified
* @return the classification
* @throws Exception
* if instance could not be classified successfully
*/
public double classifyInstance(Instance inst) throws Exception {
// Filter instance
inst = filterInstance(inst);
// Build K vector
Matrix k = new Matrix(m_NumTrain, 1);
for (int i = 0; i < m_NumTrain; i++) {
k.set(i, 0, m_kernel.eval(-1, i, inst));
}
double result = k.transpose().times(m_t).get(0, 0) + m_avg_target;
result = (result - m_Blin) / m_Alin;
return result;
}
/**
* Filters an instance.
*/
protected Instance filterInstance(Instance inst) throws Exception {
if (!m_checksTurnedOff) {
m_Missing.input(inst);
m_Missing.batchFinished();
inst = m_Missing.output();
}
if (m_NominalToBinary != null) {
m_NominalToBinary.input(inst);
m_NominalToBinary.batchFinished();
inst = m_NominalToBinary.output();
}
if (m_Filter != null) {
m_Filter.input(inst);
m_Filter.batchFinished();
inst = m_Filter.output();
}
return inst;
}
/**
* Computes standard deviation for given instance, without
* transforming target back into original space.
*/
protected double computeStdDev(Instance inst, Matrix k) throws Exception {
double kappa = m_kernel.eval(-1, -1, inst) + m_delta * m_delta;
double s = 0;
int n = m_L.length;
for (int i = 0; i < n; i++) {
double t = 0;
for (int j = 0; j < n; j++) {
t -= k.get(j,0) * (i>j? m_L[i][j] : m_L[j][i]);
}
s += t * k.get(i,0);
}
double sigma = m_delta;
if (kappa > s) {
sigma = Math.sqrt(kappa - s);
}
return sigma;
}
/**
* Computes a prediction interval for the given instance and confidence
* level.
*
* @param inst
* the instance to make the prediction for
* @param confidenceLevel
* the percentage of cases the interval should cover
* @return a 1*2 array that contains the boundaries of the interval
* @throws Exception
* if interval could not be estimated successfully
*/
public double[][] predictIntervals(Instance inst, double confidenceLevel) throws Exception {
inst = filterInstance(inst);
// Build K vector (and Kappa)
Matrix k = new Matrix(m_NumTrain, 1);
for (int i = 0; i < m_NumTrain; i++) {
k.set(i, 0, m_kernel.eval(-1, i, inst));
}
double estimate = k.transpose().times(m_t).get(0, 0) + m_avg_target;
double sigma = computeStdDev(inst, k);
confidenceLevel = 1.0 - ((1.0 - confidenceLevel) / 2.0);
double z = Statistics.normalInverse(confidenceLevel);
double[][] interval = new double[1][2];
interval[0][0] = estimate - z * sigma;
interval[0][1] = estimate + z * sigma;
interval[0][0] = (interval[0][0] - m_Blin) / m_Alin;
interval[0][1] = (interval[0][1] - m_Blin) / m_Alin;
return interval;
}
/**
* Gives standard deviation of the prediction at the given instance.
*
* @param inst
* the instance to get the standard deviation for
* @return the standard deviation
* @throws Exception
* if computation fails
*/
public double getStandardDeviation(Instance inst) throws Exception {
inst = filterInstance(inst);
// Build K vector (and Kappa)
Matrix k = new Matrix(m_NumTrain, 1);
for (int i = 0; i < m_NumTrain; i++) {
k.set(i, 0, m_kernel.eval(-1, i, inst));
}
return computeStdDev(inst, k) / m_Alin;
}
/**
* Returns natural logarithm of density estimate for given value based on given instance.
*
* @param instance the instance to make the prediction for.
* @param value the value to make the prediction for.
* @return the natural logarithm of the density estimate
* @exception Exception if the density cannot be computed
*/
public double logDensity(Instance inst, double value) throws Exception {
inst = filterInstance(inst);
// Build K vector (and Kappa)
Matrix k = new Matrix(m_NumTrain, 1);
for (int i = 0; i < m_NumTrain; i++) {
k.set(i, 0, m_kernel.eval(-1, i, inst));
}
double estimate = k.transpose().times(m_t).get(0, 0) + m_avg_target;
double sigma = computeStdDev(inst, k);
// transform to GP space
value = value * m_Alin + m_Blin;
// center around estimate
value = value - estimate;
double z = -Math.log(sigma * Math.sqrt(2 * Math.PI))
- value * value /(2.0*sigma*sigma);
return z + Math.log(m_Alin);
}
/**
* Returns an enumeration describing the available options.
*
* @return an enumeration of all the available options.
*/
public Enumeration listOptions() {
Vector<Option> result = new Vector<Option>();
Enumeration enm = super.listOptions();
while (enm.hasMoreElements())
result.addElement((Option)enm.nextElement());
result.addElement(new Option("\tLevel of Gaussian Noise wrt transformed target." + " (default 1)", "L", 1, "-L <double>"));
result.addElement(new Option("\tWhether to 0=normalize/1=standardize/2=neither. " + "(default 0=normalize)",
"N", 1, "-N"));
result.addElement(new Option("\tThe Kernel to use.\n"
+ "\t(default: weka.classifiers.functions.supportVector.PolyKernel)", "K", 1,
"-K <classname and parameters>"));
result.addElement(new Option("", "", 0, "\nOptions specific to kernel " + getKernel().getClass().getName()
+ ":"));
enm = ((OptionHandler) getKernel()).listOptions();
while (enm.hasMoreElements())
result.addElement((Option)enm.nextElement());
return result.elements();
}
/**
* Parses a given list of options. <p/>
*
* <!-- 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>
* -L <double>
* Level of Gaussian Noise. (default 0.1)
* </pre>
*
* <pre>
* -M <double>
* Level of Gaussian Noise for the class. (default 0.1)
* </pre>
*
* <pre>
* -N
* Whether to 0=normalize/1=standardize/2=neither. (default 0=normalize)
* </pre>
*
* <pre>
* -K <classname and parameters>
* The Kernel to use.
* (default: weka.classifiers.functions.supportVector.PolyKernel)
* </pre>
*
* <pre>
*
* Options specific to kernel weka.classifiers.functions.supportVector.RBFKernel:
* </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 <num>
* The size of the cache (a prime number).
* (default: 250007)
* </pre>
*
* <pre>
* -G <num>
* The Gamma parameter.
* (default: 0.01)
* </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 tmpStr;
String[] tmpOptions;
tmpStr = Utils.getOption('L', options);
if (tmpStr.length() != 0)
setNoise(Double.parseDouble(tmpStr));
else
setNoise(1);
tmpStr = Utils.getOption('N', options);
if (tmpStr.length() != 0)
setFilterType(new SelectedTag(Integer.parseInt(tmpStr), TAGS_FILTER));
else
setFilterType(new SelectedTag(FILTER_NORMALIZE, TAGS_FILTER));
tmpStr = Utils.getOption('K', options);
tmpOptions = Utils.splitOptions(tmpStr);
if (tmpOptions.length != 0) {
tmpStr = tmpOptions[0];
tmpOptions[0] = "";
setKernel(Kernel.forName(tmpStr, tmpOptions));
}
super.setOptions(options);
}
/**
* Gets the current settings of the classifier.
*
* @return an array of strings suitable for passing to setOptions
*/
public String[] getOptions() {
int i;
Vector<String> result;
String[] options;
result = new Vector<String>();
options = super.getOptions();
for (i = 0; i < options.length; i++)
result.addElement(options[i]);
result.addElement("-L");
result.addElement("" + getNoise());
result.addElement("-N");
result.addElement("" + m_filterType);
result.addElement("-K");
result.addElement("" + m_kernel.getClass().getName() + " " + Utils.joinOptions(m_kernel.getOptions()));
return (String[]) result.toArray(new String[result.size()]);
}
/**
* Returns the tip text for this property
*
* @return tip text for this property suitable for displaying in the
* explorer/experimenter gui
*/
public String kernelTipText() {
return "The kernel to use.";
}
/**
* Gets the kernel to use.
*
* @return the kernel
*/
public Kernel getKernel() {
return m_kernel;
}
/**
* Sets the kernel to use.
*
* @param value
* the new kernel
*/
public void setKernel(Kernel value) {
m_kernel = value;
}
/**
* Returns the tip text for this property
*
* @return tip text for this property suitable for displaying in the
* explorer/experimenter gui
*/
public String filterTypeTipText() {
return "Determines how/if the data will be transformed.";
}
/**
* Gets how the training data will be transformed. Will be one of
* FILTER_NORMALIZE, FILTER_STANDARDIZE, FILTER_NONE.
*
* @return the filtering mode
*/
public SelectedTag getFilterType() {
return new SelectedTag(m_filterType, TAGS_FILTER);
}
/**
* Sets how the training data will be transformed. Should be one of
* FILTER_NORMALIZE, FILTER_STANDARDIZE, FILTER_NONE.
*
* @param newType
* the new filtering mode
*/
public void setFilterType(SelectedTag newType) {
if (newType.getTags() == TAGS_FILTER) {
m_filterType = newType.getSelectedTag().getID();
}
}
/**
* Returns the tip text for this property
*
* @return tip text for this property suitable for displaying in the
* explorer/experimenter gui
*/
public String noiseTipText() {
return "The level of Gaussian Noise (added to the diagonal of the Covariance Matrix), after the " +
"target has been normalized/standardized/left unchanged).";
}
/**
* Get the value of noise.
*
* @return Value of noise.
*/
public double getNoise() {
return m_delta;
}
/**
* Set the level of Gaussian Noise.
*
* @param v
* Value to assign to noise.
*/
public void setNoise(double v) {
m_delta = v;
}
/**
* Prints out the classifier.
*
* @return a description of the classifier as a string
*/
public String toString() {
StringBuffer text = new StringBuffer();
if (m_t == null)
return "Gaussian Processes: No model built yet.";
try {
text.append("Gaussian Processes\n\n");
text.append("Kernel used:\n " + m_kernel.toString() + "\n\n");
text.append("All values shown based on: " +
TAGS_FILTER[m_filterType].getReadable() + "\n\n");
text.append("Average Target Value : " + m_avg_target + "\n");
text.append("Inverted Covariance Matrix:\n");
double min = -m_L[0][0];
double max = -m_L[0][0];
for (int i = 0; i < m_NumTrain; i++)
for (int j = 0; j <= i; j++) {
if (-m_L[i][j] < min)
min = -m_L[i][j];
else if (-m_L[i][j] > max)
max = -m_L[i][j];
}
text.append(" Lowest Value = " + min + "\n");
text.append(" Highest Value = " + max + "\n");
text.append("Inverted Covariance Matrix * Target-value Vector:\n");
min = m_t.get(0, 0);
max = m_t.get(0, 0);
for (int i = 0; i < m_NumTrain; i++) {
if (m_t.get(i, 0) < min)
min = m_t.get(i, 0);
else if (m_t.get(i, 0) > max)
max = m_t.get(i, 0);
}
text.append(" Lowest Value = " + min + "\n");
text.append(" Highest Value = " + max + "\n \n");
} catch (Exception e) {
return "Can't print the classifier.";
}
return text.toString();
}
/**
* Main method for testing this class.
*
* @param argv
* the commandline parameters
*/
public static void main(String[] argv) {
runClassifier(new GaussianProcesses(), argv);
}
}