001: /*
002: * This program is free software; you can redistribute it and/or modify
003: * it under the terms of the GNU General Public License as published by
004: * the Free Software Foundation; either version 2 of the License, or
005: * (at your option) any later version.
006: *
007: * This program is distributed in the hope that it will be useful,
008: * but WITHOUT ANY WARRANTY; without even the implied warranty of
009: * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
010: * GNU General Public License for more details.
011: *
012: * You should have received a copy of the GNU General Public License
013: * along with this program; if not, write to the Free Software
014: * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
015: */
016:
017: /*
018: * Id3.java
019: * Copyright (C) 1999 University of Waikato, Hamilton, New Zealand
020: *
021: */
022:
023: package weka.classifiers.trees;
024:
025: import weka.classifiers.Classifier;
026: import weka.core.Attribute;
027: import weka.core.Capabilities;
028: import weka.core.Instance;
029: import weka.core.Instances;
030: import weka.core.NoSupportForMissingValuesException;
031: import weka.core.TechnicalInformation;
032: import weka.core.TechnicalInformationHandler;
033: import weka.core.Utils;
034: import weka.core.Capabilities.Capability;
035: import weka.core.TechnicalInformation.Field;
036: import weka.core.TechnicalInformation.Type;
037:
038: import java.util.Enumeration;
039:
040: /**
041: <!-- globalinfo-start -->
042: * Class for constructing an unpruned decision tree based on the ID3 algorithm. Can only deal with nominal attributes. No missing values allowed. Empty leaves may result in unclassified instances. For more information see: <br/>
043: * <br/>
044: * R. Quinlan (1986). Induction of decision trees. Machine Learning. 1(1):81-106.
045: * <p/>
046: <!-- globalinfo-end -->
047: *
048: <!-- technical-bibtex-start -->
049: * BibTeX:
050: * <pre>
051: * @article{Quinlan1986,
052: * author = {R. Quinlan},
053: * journal = {Machine Learning},
054: * number = {1},
055: * pages = {81-106},
056: * title = {Induction of decision trees},
057: * volume = {1},
058: * year = {1986}
059: * }
060: * </pre>
061: * <p/>
062: <!-- technical-bibtex-end -->
063: *
064: <!-- options-start -->
065: * Valid options are: <p/>
066: *
067: * <pre> -D
068: * If set, classifier is run in debug mode and
069: * may output additional info to the console</pre>
070: *
071: <!-- options-end -->
072: *
073: * @author Eibe Frank (eibe@cs.waikato.ac.nz)
074: * @version $Revision: 1.20 $
075: */
076: public class Id3 extends Classifier implements
077: TechnicalInformationHandler {
078:
079: /** for serialization */
080: static final long serialVersionUID = -2693678647096322561L;
081:
082: /** The node's successors. */
083: private Id3[] m_Successors;
084:
085: /** Attribute used for splitting. */
086: private Attribute m_Attribute;
087:
088: /** Class value if node is leaf. */
089: private double m_ClassValue;
090:
091: /** Class distribution if node is leaf. */
092: private double[] m_Distribution;
093:
094: /** Class attribute of dataset. */
095: private Attribute m_ClassAttribute;
096:
097: /**
098: * Returns a string describing the classifier.
099: * @return a description suitable for the GUI.
100: */
101: public String globalInfo() {
102:
103: return "Class for constructing an unpruned decision tree based on the ID3 "
104: + "algorithm. Can only deal with nominal attributes. No missing values "
105: + "allowed. Empty leaves may result in unclassified instances. For more "
106: + "information see: \n\n"
107: + getTechnicalInformation().toString();
108: }
109:
110: /**
111: * Returns an instance of a TechnicalInformation object, containing
112: * detailed information about the technical background of this class,
113: * e.g., paper reference or book this class is based on.
114: *
115: * @return the technical information about this class
116: */
117: public TechnicalInformation getTechnicalInformation() {
118: TechnicalInformation result;
119:
120: result = new TechnicalInformation(Type.ARTICLE);
121: result.setValue(Field.AUTHOR, "R. Quinlan");
122: result.setValue(Field.YEAR, "1986");
123: result.setValue(Field.TITLE, "Induction of decision trees");
124: result.setValue(Field.JOURNAL, "Machine Learning");
125: result.setValue(Field.VOLUME, "1");
126: result.setValue(Field.NUMBER, "1");
127: result.setValue(Field.PAGES, "81-106");
128:
129: return result;
130: }
131:
132: /**
133: * Returns default capabilities of the classifier.
134: *
135: * @return the capabilities of this classifier
136: */
137: public Capabilities getCapabilities() {
138: Capabilities result = super .getCapabilities();
139:
140: // attributes
141: result.enable(Capability.NOMINAL_ATTRIBUTES);
142:
143: // class
144: result.enable(Capability.NOMINAL_CLASS);
145: result.enable(Capability.MISSING_CLASS_VALUES);
146:
147: // instances
148: result.setMinimumNumberInstances(0);
149:
150: return result;
151: }
152:
153: /**
154: * Builds Id3 decision tree classifier.
155: *
156: * @param data the training data
157: * @exception Exception if classifier can't be built successfully
158: */
159: public void buildClassifier(Instances data) throws Exception {
160:
161: // can classifier handle the data?
162: getCapabilities().testWithFail(data);
163:
164: // remove instances with missing class
165: data = new Instances(data);
166: data.deleteWithMissingClass();
167:
168: makeTree(data);
169: }
170:
171: /**
172: * Method for building an Id3 tree.
173: *
174: * @param data the training data
175: * @exception Exception if decision tree can't be built successfully
176: */
177: private void makeTree(Instances data) throws Exception {
178:
179: // Check if no instances have reached this node.
180: if (data.numInstances() == 0) {
181: m_Attribute = null;
182: m_ClassValue = Instance.missingValue();
183: m_Distribution = new double[data.numClasses()];
184: return;
185: }
186:
187: // Compute attribute with maximum information gain.
188: double[] infoGains = new double[data.numAttributes()];
189: Enumeration attEnum = data.enumerateAttributes();
190: while (attEnum.hasMoreElements()) {
191: Attribute att = (Attribute) attEnum.nextElement();
192: infoGains[att.index()] = computeInfoGain(data, att);
193: }
194: m_Attribute = data.attribute(Utils.maxIndex(infoGains));
195:
196: // Make leaf if information gain is zero.
197: // Otherwise create successors.
198: if (Utils.eq(infoGains[m_Attribute.index()], 0)) {
199: m_Attribute = null;
200: m_Distribution = new double[data.numClasses()];
201: Enumeration instEnum = data.enumerateInstances();
202: while (instEnum.hasMoreElements()) {
203: Instance inst = (Instance) instEnum.nextElement();
204: m_Distribution[(int) inst.classValue()]++;
205: }
206: Utils.normalize(m_Distribution);
207: m_ClassValue = Utils.maxIndex(m_Distribution);
208: m_ClassAttribute = data.classAttribute();
209: } else {
210: Instances[] splitData = splitData(data, m_Attribute);
211: m_Successors = new Id3[m_Attribute.numValues()];
212: for (int j = 0; j < m_Attribute.numValues(); j++) {
213: m_Successors[j] = new Id3();
214: m_Successors[j].makeTree(splitData[j]);
215: }
216: }
217: }
218:
219: /**
220: * Classifies a given test instance using the decision tree.
221: *
222: * @param instance the instance to be classified
223: * @return the classification
224: * @throws NoSupportForMissingValuesException if instance has missing values
225: */
226: public double classifyInstance(Instance instance)
227: throws NoSupportForMissingValuesException {
228:
229: if (instance.hasMissingValue()) {
230: throw new NoSupportForMissingValuesException(
231: "Id3: no missing values, " + "please.");
232: }
233: if (m_Attribute == null) {
234: return m_ClassValue;
235: } else {
236: return m_Successors[(int) instance.value(m_Attribute)]
237: .classifyInstance(instance);
238: }
239: }
240:
241: /**
242: * Computes class distribution for instance using decision tree.
243: *
244: * @param instance the instance for which distribution is to be computed
245: * @return the class distribution for the given instance
246: * @throws NoSupportForMissingValuesException if instance has missing values
247: */
248: public double[] distributionForInstance(Instance instance)
249: throws NoSupportForMissingValuesException {
250:
251: if (instance.hasMissingValue()) {
252: throw new NoSupportForMissingValuesException(
253: "Id3: no missing values, " + "please.");
254: }
255: if (m_Attribute == null) {
256: return m_Distribution;
257: } else {
258: return m_Successors[(int) instance.value(m_Attribute)]
259: .distributionForInstance(instance);
260: }
261: }
262:
263: /**
264: * Prints the decision tree using the private toString method from below.
265: *
266: * @return a textual description of the classifier
267: */
268: public String toString() {
269:
270: if ((m_Distribution == null) && (m_Successors == null)) {
271: return "Id3: No model built yet.";
272: }
273: return "Id3\n\n" + toString(0);
274: }
275:
276: /**
277: * Computes information gain for an attribute.
278: *
279: * @param data the data for which info gain is to be computed
280: * @param att the attribute
281: * @return the information gain for the given attribute and data
282: * @throws Exception if computation fails
283: */
284: private double computeInfoGain(Instances data, Attribute att)
285: throws Exception {
286:
287: double infoGain = computeEntropy(data);
288: Instances[] splitData = splitData(data, att);
289: for (int j = 0; j < att.numValues(); j++) {
290: if (splitData[j].numInstances() > 0) {
291: infoGain -= ((double) splitData[j].numInstances() / (double) data
292: .numInstances())
293: * computeEntropy(splitData[j]);
294: }
295: }
296: return infoGain;
297: }
298:
299: /**
300: * Computes the entropy of a dataset.
301: *
302: * @param data the data for which entropy is to be computed
303: * @return the entropy of the data's class distribution
304: * @throws Exception if computation fails
305: */
306: private double computeEntropy(Instances data) throws Exception {
307:
308: double[] classCounts = new double[data.numClasses()];
309: Enumeration instEnum = data.enumerateInstances();
310: while (instEnum.hasMoreElements()) {
311: Instance inst = (Instance) instEnum.nextElement();
312: classCounts[(int) inst.classValue()]++;
313: }
314: double entropy = 0;
315: for (int j = 0; j < data.numClasses(); j++) {
316: if (classCounts[j] > 0) {
317: entropy -= classCounts[j] * Utils.log2(classCounts[j]);
318: }
319: }
320: entropy /= (double) data.numInstances();
321: return entropy + Utils.log2(data.numInstances());
322: }
323:
324: /**
325: * Splits a dataset according to the values of a nominal attribute.
326: *
327: * @param data the data which is to be split
328: * @param att the attribute to be used for splitting
329: * @return the sets of instances produced by the split
330: */
331: private Instances[] splitData(Instances data, Attribute att) {
332:
333: Instances[] splitData = new Instances[att.numValues()];
334: for (int j = 0; j < att.numValues(); j++) {
335: splitData[j] = new Instances(data, data.numInstances());
336: }
337: Enumeration instEnum = data.enumerateInstances();
338: while (instEnum.hasMoreElements()) {
339: Instance inst = (Instance) instEnum.nextElement();
340: splitData[(int) inst.value(att)].add(inst);
341: }
342: for (int i = 0; i < splitData.length; i++) {
343: splitData[i].compactify();
344: }
345: return splitData;
346: }
347:
348: /**
349: * Outputs a tree at a certain level.
350: *
351: * @param level the level at which the tree is to be printed
352: * @return the tree as string at the given level
353: */
354: private String toString(int level) {
355:
356: StringBuffer text = new StringBuffer();
357:
358: if (m_Attribute == null) {
359: if (Instance.isMissingValue(m_ClassValue)) {
360: text.append(": null");
361: } else {
362: text.append(": "
363: + m_ClassAttribute.value((int) m_ClassValue));
364: }
365: } else {
366: for (int j = 0; j < m_Attribute.numValues(); j++) {
367: text.append("\n");
368: for (int i = 0; i < level; i++) {
369: text.append("| ");
370: }
371: text.append(m_Attribute.name() + " = "
372: + m_Attribute.value(j));
373: text.append(m_Successors[j].toString(level + 1));
374: }
375: }
376: return text.toString();
377: }
378:
379: /**
380: * Main method.
381: *
382: * @param args the options for the classifier
383: */
384: public static void main(String[] args) {
385: runClassifier(new Id3(), args);
386: }
387: }
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