已知：流感训练数据集，预定义两个类别；
求：用ID3算法建立流感的属性描述决策树
流感训练数据集
|
No. |
头痛 |
肌肉痛 |
体温 |
患流感 |
|
1 |
是(1) |
是(1) |
正常(0) |
否(0) |
|
2 |
是(1) |
是(1) |
高(1) |
是(1) |
|
3 |
是(1) |
是(1) |
很高(2) |
是(1) |
|
4 |
否(0) |
是(1) |
正常(0) |
否(0) |
|
5 |
否(0) |
否(0) |
高(1) |
否(0) |
|
6 |
否(0) |
是(1) |
很高(2) |
是(1) |
|
7 |
是(1) |
否(0) |
高(1) |
是(1) |
原理分析：
在决策树的每一个非叶子结点划分之前，先计算每一个属性所带来的信息增益，选择最大信息增益的属性来划分，因为信息增益越大，区分样本的能力就越强，越具有代表性其中。
信息熵计算：
信息增益：
计算的结果（草稿上的字丑别喷）：
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*************************************************************************************************************
************************实现*********************************************
package ID3Tree;
import java.util.Comparator;;
@SuppressWarnings("rawtypes")
public class Comparisons implements Comparator
{
public int compare(Object a, Object b) throws ClassCastException{
String str1 = (String)a;
String str2 = (String)b;
return str1.compareTo(str2);
}
}
package ID3Tree;
public class Entropy {
//信息熵
public static double getEntropy(int x, int total)
{
if (x == 0)
{
return 0;
}
double x_pi = getShang(x,total);
return -(x_pi*Logs(x_pi));
}
public static double Logs(double y)
{
return Math.log(y) / Math.log(2);
}
public static double getShang(int x, int total)
{
return x * Double.parseDouble("1.0") / total;
}
}
package ID3Tree;
public class TreeNode {
//父节点
TreeNode parent;
//指向父节点的属性
String parentAttribute;
String nodeName;
String[] attributes;
TreeNode[] childNodes;
}
package ID3Tree;
import java.util.*; public class UtilID3 {
TreeNode root;
private boolean[] flag;
//训练集
private Object[] trainArrays;
//节点索引
private int nodeIndex;
public static void main(String[] args)
{
//初始化训练集数组
Object[] arrays = new Object[]{
new String[]{"是","是","正常","否"},
new String[]{"是","是","高","是"},
new String[]{"是","是","很高","是"},
new String[]{"否","是","正常","否"},
new String[]{"否","否","高","否"},
new String[]{"否","是","很高","是"},
new String[]{"是","否","高","是"}};
UtilID3 ID3Tree = new UtilID3();
ID3Tree.create(arrays, 3);
} //创建
public void create(Object[] arrays, int index)
{
this.trainArrays = arrays;
initial(arrays, index);
createDTree(arrays);
printDTree(root);
} //初始化
public void initial(Object[] dataArray, int index)
{
this.nodeIndex = index; //数据初始化
this.flag = new boolean[((String[])dataArray[0]).length];
for (int i = 0; i<this.flag.length; i++)
{
if (i == index)
{
this.flag[i] = true;
}
else
{
this.flag[i] = false;
}
}
} //创建决策树
public void createDTree(Object[] arrays)
{
Object[] ob = getMaxGain(arrays);
if (this.root == null)
{
this.root = new TreeNode();
root.parent = null;
root.parentAttribute = null;
root.attributes = getAttributes(((Integer)ob[1]).intValue());
root.nodeName = getNodeName(((Integer)ob[1]).intValue());
root.childNodes = new TreeNode[root.attributes.length];
insert(arrays, root);
}
} //插入决策树
public void insert(Object[] arrays, TreeNode parentNode)
{
String[] attributes = parentNode.attributes;
for (int i = 0; i < attributes.length; i++)
{
Object[] Arrays = pickUpAndCreateArray(arrays, attributes[i],getNodeIndex(parentNode.nodeName));
Object[] info = getMaxGain(Arrays);
double gain = ((Double)info[0]).doubleValue();
if (gain != 0)
{
int index = ((Integer)info[1]).intValue();
TreeNode currentNode = new TreeNode();
currentNode.parent = parentNode;
currentNode.parentAttribute = attributes[i];
currentNode.attributes = getAttributes(index);
currentNode.nodeName = getNodeName(index);
currentNode.childNodes = new TreeNode[currentNode.attributes.length];
parentNode.childNodes[i] = currentNode;
insert(Arrays, currentNode);
}
else
{
TreeNode leafNode = new TreeNode();
leafNode.parent = parentNode;
leafNode.parentAttribute = attributes[i];
leafNode.attributes = new String[0];
leafNode.nodeName = getLeafNodeName(Arrays);
leafNode.childNodes = new TreeNode[0];
parentNode.childNodes[i] = leafNode;
}
}
} //输出
public void printDTree(TreeNode node)
{
System.out.println(node.nodeName);
TreeNode[] childs = node.childNodes;
for (int i = 0; i < childs.length; i++)
{
if (childs[i] != null)
{
System.out.println("如果："+childs[i].parentAttribute);
printDTree(childs[i]);
}
}
} //剪取数组
public Object[] pickUpAndCreateArray(Object[] arrays, String attribute, int index)
{
List<String[]> list = new ArrayList<String[]>();
for (int i = 0; i < arrays.length; i++)
{
String[] strs = (String[])arrays[i];
if (strs[index].equals(attribute))
{
list.add(strs);
}
}
return list.toArray();
} //取得节点名
public String getNodeName(int index)
{
String[] strs = new String[]{"头痛","肌肉痛","体温","患流感"};
for (int i = 0; i < strs.length; i++)
{
if (i == index)
{
return strs[i];
}
}
return null;
} //取得叶子节点名
public String getLeafNodeName(Object[] arrays)
{
if (arrays != null && arrays.length > 0)
{
String[] strs = (String[])arrays[0];
return strs[nodeIndex];
}
return null;
} //取得节点索引
public int getNodeIndex(String name)
{
String[] strs = new String[]{"头痛","肌肉痛","体温","患流感"};
for (int i = 0; i < strs.length; i++)
{
if (name.equals(strs[i]))
{
return i;
}
}
return -1;
} //得到最大信息增益
public Object[] getMaxGain(Object[] arrays)
{
Object[] result = new Object[2];
double gain = 0;
int index = -1;
for (int i = 0; i<this.flag.length; i++)
{
if (!this.flag[i])
{
double value = gain(arrays, i);
if (gain < value)
{
gain = value;
index = i;
}
}
}
result[0] = gain;
result[1] = index;
if (index != -1)
{
this.flag[index] = true;
}
return result;
} //取得属性数组
public String[] getAttributes(int index)
{
@SuppressWarnings("unchecked")
TreeSet<String> set = new TreeSet<String>(new Comparisons());
for (int i = 0; i<this.trainArrays.length; i++)
{
String[] strs = (String[])this.trainArrays[i];
set.add(strs[index]);
}
String[] result = new String[set.size()];
return set.toArray(result); } //计算信息增益
public double gain(Object[] arrays, int index)
{
String[] playBalls = getAttributes(this.nodeIndex);
int[] counts = new int[playBalls.length];
for (int i = 0; i<counts.length; i++)
{
counts[i] = 0;
} for (int i = 0; i<arrays.length; i++)
{
String[] strs = (String[])arrays[i];
for (int j = 0; j<playBalls.length; j++)
{
if (strs[this.nodeIndex].equals(playBalls[j]))
{
counts[j]++;
}
}
} double entropyS = 0;
for (int i = 0;i <counts.length; i++)
{
entropyS = entropyS + Entropy.getEntropy(counts[i], arrays.length);
} String[] attributes = getAttributes(index);
double total = 0;
for (int i = 0; i<attributes.length; i++)
{
total = total + entropy(arrays, index, attributes[i], arrays.length);
}
return entropyS - total;
} public double entropy(Object[] arrays, int index, String attribute, int totals)
{
String[] playBalls = getAttributes(this.nodeIndex);
int[] counts = new int[playBalls.length];
for (int i = 0; i < counts.length; i++)
{
counts[i] = 0;
} for (int i = 0; i < arrays.length; i++)
{
String[] strs = (String[])arrays[i];
if (strs[index].equals(attribute))
{
for (int k = 0; k<playBalls.length; k++)
{
if (strs[this.nodeIndex].equals(playBalls[k]))
{
counts[k]++;
}
}
}
} int total = 0;
double entropy = 0;
for (int i = 0; i < counts.length; i++)
{
total = total +counts[i];
} for (int i = 0; i < counts.length; i++)
{
entropy = entropy + Entropy.getEntropy(counts[i], total);
}
return Entropy.getShang(total, totals)*entropy;
}
}