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R语言学习系列(数据挖掘之决策树算法实现--ID3代码篇)
1、辅助类，用于计算过程和结果存储
/// <summary>
/// 决策树节点.
/// </summary>
public class DecisionTreeNode
{
/// <summary>
/// 类型：分支或叶子
/// </summary>
public string Type { get; set; }
/// <summary>
/// 关键字一般存当前属性因子
/// </summary>
public string Key { get; set; }
/// <summary>
/// 判断值，叶子节点有效.
/// </summary>
public string DecisionValue { get; set; }
/// <summary>
/// 前一个属性因子，可以看作是分支条件.
/// </summary>
public string ParentFactor { get; set; }
/// <summary>
/// 当前节点的样本数量，
/// </summary>
public int CalcCount { get; set; }
/// <summary>
/// 当前节点的样本索引集合.
/// </summary>
public List<int> DataIndexes {get;set;}
/// <summary>
/// 分支节点集合.
/// </summary>
public Dictionary<string, DecisionTreeNode> Children { get; private set; }
/// <summary>
/// 父节点
/// </summary>
public DecisionTreeNode Parent { get; set; }
public DecisionTreeNode()
{
DataIndexes = new List<int>();
Children = new Dictionary<string, DecisionTreeNode>();
}
}
/// <summary>
/// 用于计算过程存放数据.用数组不是很方便，这里采用字典，可以减少循环次数.
/// </summary>
public class CalcNode
{
public string Key { get; set; }
public string Type { get; set; }
public int CalcCount { get; set; }
public List<int> DataIndexes {get;set;}
public Dictionary<string, CalcNode> Children { get; private set; }
public CalcNode()
{
DataIndexes = new List<int>();
Children = new Dictionary<string, CalcNode>();
}
public void AddChildren(string Key,string AType,int AIndex, int Count = 1)
{
if (Children.ContainsKey(Key) == false)
{
Children.Add(Key, new CalcNode());
}
Children[Key].Key = Key;
Children[Key].Type = AType;
Children[Key].CalcCount += Count;
Children[Key].DataIndexes.Add(AIndex);
}
}
2、算法类，注释比较详细，有时间再写一篇原理文章
/// <summary>
/// 决策树算法类，不适合连续性值。
/// </summary>
public class DecisionTreeAlg
{
private string PrefixString = " ";
/// <summary>
/// 构建决策树，决策分类属性约定放在第1列。
/// </summary>
/// <param name="Inputs">行表示属性，列为值，注意列等长</param>
/// <param name="PNode">父节点</param>
/// <param name="PropertyNames">测试属性名称</param>
/// <param name="TestProperties">当前可用测试属性索引</param>
/// <param name="DefaultClassFactor">缺省判别决策分类因子</param>
/// <param name="CallLevel">用来测试输出控制，无实际作用</param>
/// <param name="OutContents">输出内容，为调试用</param>
/// <param name="PropertyFactors">属性因子</param>
public void BuildDecisionTree(int CallLevel, ref string OutContents, string[][] Inputs, DecisionTreeNode PNode, string[] PropertyNames, List<int> TestProperties, string DefaultClassFactor, Dictionary<string, List<string>> PropertyFactors)
{
string thePrefix = PrefixString.Substring(0, CallLevel * 2);
CallLevel++;
//如果没有测试属性，将当前节点设为叶子节点，选择高概率分类，然后返回
if (TestProperties.Count <= 1)
{
PNode.Type = "叶子";
PNode.DecisionValue = DefaultClassFactor;
return;
}
//如果没有学习样本集，将当前节点设为叶子节点，选择高概率分类，然后返回
if (PNode.DataIndexes.Count <= 0)
{
PNode.Type = "叶子";
PNode.DecisionValue = DefaultClassFactor;
return;
}
if (PropertyFactors == null)
{
PropertyFactors = new Dictionary<string, List<string>>();
}
//准备存储遍历时的计数存储结构
Dictionary<string, CalcNode> thePropertyCount = new Dictionary<string, CalcNode>();
foreach (var theProIndex in TestProperties)
{
thePropertyCount.Add(PropertyNames[theProIndex], new CalcNode() { Key = PropertyNames[theProIndex] });
if (PropertyFactors.ContainsKey(PropertyNames[theProIndex]) == false)
{
PropertyFactors.Add(PropertyNames[theProIndex], new List<string>());
}
}
//遍历当前可遍历的数据，进行统计，为计算各属性熵做准备
for (int n = 0; n < PNode.DataIndexes.Count; n++)
{
int theI = PNode.DataIndexes[n];
for (int k = 0; k < TestProperties.Count; k++)
{
int theJ = TestProperties[k];
var thePropertyCalcNode = thePropertyCount[PropertyNames[theJ]];
//对当前属性计数
thePropertyCalcNode.CalcCount++;
//对第j个属性的当前因子计数
thePropertyCalcNode.AddChildren(Inputs[theJ][theI], "测试属性因子", theI, 1);
//对第j个属性的当前因子的主分类因子计数
thePropertyCalcNode.Children[Inputs[theJ][theI]].AddChildren(Inputs[0][theI], "主分类因子", theI, 1);
//统计归纳各属性因子，采用这种方式可以减少循环.
if (PropertyFactors[PropertyNames[theJ]].Contains(Inputs[theJ][theI]) == false)
{
PropertyFactors[PropertyNames[theJ]].Add(Inputs[theJ][theI]);
}
}
}
//计算信息增益量,获取具有最大信息增益属性
string theDefaultClassFactor = DefaultClassFactor;
//初始化最大测试属性熵值.
double theMaxEA = double.MinValue;
//记录具有最大熵值属性的索引位置
int theMaxPropertyIndex = TestProperties[1];
//总信息熵值，其实就是分类属性的熵值.
double theTotalEA = 0.0;
//记录总的样本数，用于估算概率.
double theTotalSimple = 0;
for(int theI=0;theI<TestProperties.Count;theI++)
{
int thePIndex_1 = TestProperties[theI];
if (thePIndex_1 == 0)
{
//主分类熵值计算，计算公式与测试属性有所不同.
CalcNode theCalcNode = thePropertyCount[PropertyNames[thePIndex_1]];
double theCount = theCalcNode.CalcCount;
theTotalSimple = theCount;
double theMaxSubCount = -1;
theTotalEA = 0.0;
//求和(-Pj*log2(Pj))
foreach (var theSubNode in theCalcNode.Children)
{
if (theSubNode.Value.CalcCount > 0)
{
double thePj = theSubNode.Value.CalcCount / theCount;
theTotalEA += 0 - thePj * Math.Log(thePj, 2);
}
if (theMaxSubCount < theSubNode.Value.CalcCount)
{
theMaxSubCount = theSubNode.Value.CalcCount;
theDefaultClassFactor = theSubNode.Key;
}
//测试输出，跟踪计算路径.
OutContents += "\r\n" + thePrefix + theCalcNode.CalcCount + ":: " + PropertyNames[thePIndex_1] + ":: " + theSubNode.Value.Type + " :: " + theSubNode.Key + " :: " + theSubNode.Value.CalcCount;
}
}
else
{
//测试属性熵值计算。
CalcNode theCalcNode = thePropertyCount[PropertyNames[thePIndex_1]];
double theJEA = 0.0;
foreach (var theSubNode_1 in theCalcNode.Children)
{
if (theSubNode_1.Value.CalcCount > 0)
{
double theSjCount = theSubNode_1.Value.CalcCount;
double theSj_1 = theSjCount / theTotalSimple;
double theSj_2 = 0.0;
foreach (var theSubNode_2 in theSubNode_1.Value.Children)
{
if (theSubNode_2.Value.CalcCount > 0)
{
double thePj_1 = Convert.ToDouble(theSubNode_2.Value.CalcCount) / theSjCount;
theSj_2 += 0.0 - thePj_1 * Math.Log(thePj_1, 2);
}
OutContents += "\r\n" + thePrefix + theCalcNode.CalcCount + ":: " + PropertyNames[thePIndex_1] + " :: " + theSubNode_1.Value.Type + " :: " + theSubNode_1.Key + " :: " + theSubNode_1.Value.CalcCount
+ theSubNode_2.Value.Type + " :: " + theSubNode_2.Key + " :: " + theSubNode_2.Value.CalcCount;
}
theJEA += theSj_1 * theSj_2;
}
}
theJEA = theTotalEA - theJEA;
//只记录最大熵值属性信息.
if (theMaxEA < theJEA)
{
theMaxEA = theJEA;
theMaxPropertyIndex = thePIndex_1;
}
}
}
//如果分类因子只有一个，则置当前节点为叶子节点，设置判定为当前分类因子，然后返回
if (thePropertyCount[PropertyNames[0]].Children.Count <= 1)
{
PNode.Type = "叶子";
PNode.DecisionValue = theDefaultClassFactor;
return;
}
//具有多个分类因子，还剩有测试属性，则设当前节点为分支节点，准备分支.
PNode.Type = "分支";
//1选取最大增益信息量测试属性，做分支处理,做处理,注意属性一旦处理，将不在后续节点中再处理
//因此需要在测试属性集合中删除所选测试属性.注意保持分类属性在开始索引处(0).
PNode.Key = PropertyNames[theMaxPropertyIndex];
CalcNode theCalcNode_2 = thePropertyCount[PropertyNames[theMaxPropertyIndex]];
List<string> theFactors = PropertyFactors[PropertyNames[theMaxPropertyIndex]];
List<int> theAvailableTestPs = new List<int>();
for (int i = 0; i < TestProperties.Count; i++)
{
if (theMaxPropertyIndex != TestProperties[i])
{
theAvailableTestPs.Add(TestProperties[i]);
}
}
//对所选测试属性的所有因子进行处理.
foreach (var theFactor_1 in theFactors)
{
//如果当前因子不在计算中，则添加一个叶子节点，判定为高概率分类。
if (theCalcNode_2.Children.ContainsKey(theFactor_1) == false)
{
DecisionTreeNode theNode_1 = new DecisionTreeNode();
theNode_1.ParentFactor = theFactor_1;
theNode_1.CalcCount = 0;
theNode_1.DecisionValue = theDefaultClassFactor;
theNode_1.Parent = PNode;
theNode_1.Key = theFactor_1;
theNode_1.Type = "叶子";
PNode.Children.Add(theFactor_1, theNode_1);
continue;
}
//如果当前因子存在，但不存在样本，则添加一个叶子节点，判定为高概率分类。
if (theCalcNode_2.Children[theFactor_1].CalcCount<=0)
{
DecisionTreeNode theNode_1 = new DecisionTreeNode();
theNode_1.ParentFactor = theFactor_1;
theNode_1.CalcCount = 0;
theNode_1.DecisionValue = theDefaultClassFactor;
theNode_1.Parent = PNode;
theNode_1.Type = "叶子";
theNode_1.Key = theFactor_1;
PNode.Children.Add(theFactor_1, theNode_1);
continue;
}
//如果存在，且有学习样本，则添加一个节点，并以此节点递归处理.
DecisionTreeNode theNode_2 = new DecisionTreeNode();
theNode_2.ParentFactor = theFactor_1;
theNode_2.Parent = PNode;
theNode_2.Key = theFactor_1;
theNode_2.CalcCount = theCalcNode_2.Children[theFactor_1].CalcCount;
theNode_2.DataIndexes.AddRange(theCalcNode_2.Children[theFactor_1].DataIndexes);
PNode.Children.Add(theFactor_1, theNode_2);
BuildDecisionTree(CallLevel, ref OutContents, Inputs, theNode_2, PropertyNames, theAvailableTestPs, theDefaultClassFactor, PropertyFactors);
}
}
}
3、测试代码：
private void button1_Click(object sender, EventArgs e)
{
DecisionTreeAlg theAlg = new DecisionTreeAlg();
string[][] theInputs = new string[4][];
theInputs[0] = new string[] { "no", "yes", "yes", "yes", "yes", "yes", "no", "yes", "yes", "no" };
theInputs[1] = new string[] { "s", "s", "l", "m", "l", "m", "m", "l", "m", "s" };
theInputs[2] = new string[] { "s", "l", "m", "m", "m", "l", "s", "m", "s", "s" };
theInputs[3] = new string[] { "no", "yes", "yes", "yes", "no", "no", "no", "no", "no", "yes" };
string[] thePropertyName = new string[] {"是否真实帐号","日志密度","好友密度","是否真实头像" };
DecisionTreeNode theRootNode = new DecisionTreeNode();
theRootNode.DataIndexes.AddRange(new List<int>() { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 });
List<int> theTestPs = new List<int>() { 0, 1, 2, 3 };
string theOuts = "";
theAlg.BuildDecisionTree(0,ref theOuts, theInputs, theRootNode, thePropertyName, theTestPs, "", null);
this.treeView1.Nodes.Clear();
TreeNode theRoot = new TreeNode();
this.treeView1.Nodes.Add(theRoot);
VisitTree(theRoot, theRootNode);
this.textBox1.Text = theOuts;
}
private void VisitTree(TreeNode PNode, DecisionTreeNode PDNode)
{
PNode.Text = PDNode.Key + "(" + PDNode.Type + ")[判定："+PDNode.DecisionValue +"]";
foreach (var theNode in PDNode.Children.Values)
{
TreeNode theTmpNode = new TreeNode();
PNode.Nodes.Add(theTmpNode);
VisitTree(theTmpNode, theNode);
}
}
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