ModelSelection主要是用于选择合适的列对数据集进行分割，结合上一篇J48的主流程，发现用到的ModelSelection有 C45ModelSelection以及BinC45ModelSelection，先来分析C45ModelSelection。
一、C45ModelSelection
首先作为一个ModelSelection接口，实现的主要方法有两个，分别是selectModel(Instances)和selectionModel(Instances,Instances)。C45ModelSelection的后一个方法如下：
public final ClassifierSplitModel selectModel(Instances train, Instances test) {
return selectModel(train);
}先放出整段代码，然后对该段代码进行分析：
public final ClassifierSplitModel selectModel(Instances data){
double minResult;
double currentResult;
C45Split [] currentModel;
C45Split bestModel = null;
NoSplit noSplitModel = null;
double averageInfoGain = 0;
int validModels = 0;
boolean multiVal = true;
Distribution checkDistribution;
Attribute attribute;
double sumOfWeights;
int i;
try{
// Check if all Instances belong to one class or if not
// enough Instances to split.
checkDistribution = new Distribution(data);
noSplitModel = new NoSplit(checkDistribution);
if (Utils.sm(checkDistribution.total(),2*m_minNoObj) ||
Utils.eq(checkDistribution.total(),
checkDistribution.perClass(checkDistribution.maxClass())))
return noSplitModel;
// Check if all attributes are nominal and have a
// lot of values.
if (m_allData != null) {
Enumeration enu = data.enumerateAttributes();
while (enu.hasMoreElements()) {
attribute = (Attribute) enu.nextElement();
if ((attribute.isNumeric()) ||
(Utils.sm((double)attribute.numValues(),
(0.3*(double)m_allData.numInstances())))){
multiVal = false;
break;
}
}
}
currentModel = new C45Split[data.numAttributes()];
sumOfWeights = data.sumOfWeights();
// For each attribute.
for (i = 0; i < data.numAttributes(); i++){
// Apart from class attribute.
if (i != (data).classIndex()){
// Get models for current attribute.
currentModel[i] = new C45Split(i,m_minNoObj,sumOfWeights);
currentModel[i].buildClassifier(data);
// Check if useful split for current attribute
// exists and check for enumerated attributes with
// a lot of values.
if (currentModel[i].checkModel())
if (m_allData != null) {
if ((data.attribute(i).isNumeric()) ||
(multiVal || Utils.sm((double)data.attribute(i).numValues(),
(0.3*(double)m_allData.numInstances())))){
averageInfoGain = averageInfoGain+currentModel[i].infoGain();
validModels++;
}
} else {
averageInfoGain = averageInfoGain+currentModel[i].infoGain();
validModels++;
}
}else
currentModel[i] = null;
}
// Check if any useful split was found.
if (validModels == 0)
return noSplitModel;
averageInfoGain = averageInfoGain/(double)validModels;
// Find "best" attribute to split on.
minResult = 0;
for (i=0;i<data.numAttributes();i++){
if ((i != (data).classIndex()) &&
(currentModel[i].checkModel()))
// Use 1E-3 here to get a closer approximation to the original
// implementation.
if ((currentModel[i].infoGain() >= (averageInfoGain-1E-3)) &&
Utils.gr(currentModel[i].gainRatio(),minResult)){
bestModel = currentModel[i];
minResult = currentModel[i].gainRatio();
}
}
// Check if useful split was found.
if (Utils.eq(minResult,0))
return noSplitModel;
// Add all Instances with unknown values for the corresponding
// attribute to the distribution for the model, so that
// the complete distribution is stored with the model.
bestModel.distribution().
addInstWithUnknown(data,bestModel.attIndex());
// Set the split point analogue to C45 if attribute numeric.
if (m_allData != null)
bestModel.setSplitPoint(m_allData);
return bestModel;
}catch(Exception e){
e.printStackTrace();
}
return null;
} double minResult;//最小的信息增益率
double currentResult;//当前信息增益率
C45Split [] currentModel;//存放所有未分类属性产生的模型
C45Split bestModel = null;//目前为止的最好模型
NoSplit noSplitModel = null;//代表不用分的模型
double averageInfoGain = 0;//各模型(currentModel)的平均信息增益
int validModels = 0;//是否存在有效模型
boolean multiVal = true;//是否多值
Distribution checkDistribution;//训练数据集的分布
Attribute attribute;//属性列集合
double sumOfWeights;//训练数据集的weight的和
int i;//循环变量第二部分，递归出口。
checkDistribution = new Distribution(data);
noSplitModel = new NoSplit(checkDistribution);
if (Utils.sm(checkDistribution.total(),2*m_minNoObj) ||
Utils.eq(checkDistribution.total(),
checkDistribution.perClass(checkDistribution.maxClass())))
return noSplitModel;第三部分，判断是否是多值：
if (m_allData != null) {
Enumeration enu = data.enumerateAttributes();
while (enu.hasMoreElements()) {
attribute = (Attribute) enu.nextElement();
if ((attribute.isNumeric()) ||
(Utils.sm((double)attribute.numValues(),
(0.3*(double)m_allData.numInstances())))){
multiVal = false;
break;
}
}
} 第四部分，对于每一列属性构造Spliter。
for (i = 0; i < data.numAttributes(); i++){
// Apart from class attribute.
if (i != (data).classIndex()){
// Get models for current attribute.
currentModel[i] = new C45Split(i,m_minNoObj,sumOfWeights);
currentModel[i].buildClassifier(data);
// Check if useful split for current attribute
// exists and check for enumerated attributes with
// a lot of values.
if (currentModel[i].checkModel())
if (m_allData != null) {
if ((data.attribute(i).isNumeric()) ||
(multiVal || Utils.sm((double)data.attribute(i).numValues(),
(0.3*(double)m_allData.numInstances())))){
averageInfoGain = averageInfoGain+currentModel[i].infoGain();
validModels++;
}
} else {
averageInfoGain = averageInfoGain+currentModel[i].infoGain();
validModels++;
}
}else
currentModel[i] = null;
}对于每一列属性，如果不是存放分类的值得话，则构造C45Split对象，在该对象上进行分类，然后算出信息增益，相加到averageInfoGain上。对于C45Split的构造，稍后再看。
第五部分，选出最优模型。
if (validModels == 0)
return noSplitModel;
averageInfoGain = averageInfoGain/(double)validModels;
// Find "best" attribute to split on.
minResult = 0;
for (i=0;i<data.numAttributes();i++){
if ((i != (data).classIndex()) &&
(currentModel[i].checkModel()))
// Use 1E-3 here to get a closer approximation to the original
// implementation.
if ((currentModel[i].infoGain() >= (averageInfoGain-1E-3)) &&
Utils.gr(currentModel[i].gainRatio(),minResult)){
bestModel = currentModel[i];
minResult = currentModel[i].gainRatio();
} 如果存在有效模型，则选出有效模型。注意这个选出最优模型的逻辑，并不是单纯的选出gainRatio最大的，而是在基础上必须还要大于平均信息增益，这也是和传统的c45算法不一样的一点。
从上述过程来看，Weka在实现C45的时候做了一个小的变动，并没有从“还没有使用的”属性列中找出最合理的列最为分割属性，而是在“所有的列”中找出最合理的列作为分割属性，虽然这二者在结果上肯定是等价的（之前是有过的属性不和能有很好的信息增益率），但效率上个人对Weka的做法持保留意见。
二、C45Spliter
在ModelSelection中真正根据属性对训练集进行分割、计算信息增益和信息增益率的是C45Spliter，首先也从其buildClassifier方法入手进行分析。
public void buildClassifier(Instances trainInstances)
throws Exception {
// Initialize the remaining instance variables.
m_numSubsets = 0;
m_splitPoint = Double.MAX_VALUE;
m_infoGain = 0;
m_gainRatio = 0;
// Different treatment for enumerated and numeric
// attributes.
if (trainInstances.attribute(m_attIndex).isNominal()) {
m_complexityIndex = trainInstances.attribute(m_attIndex).numValues();
m_index = m_complexityIndex;
handleEnumeratedAttribute(trainInstances);
}else{
m_complexityIndex = 2;
m_index = 0;
trainInstances.sort(trainInstances.attribute(m_attIndex));
handleNumericAttribute(trainInstances);
}
} 首先来看枚举类型是如何处理的。
private void handleEnumeratedAttribute(Instances trainInstances)
throws Exception {
Instance instance;
m_distribution = new Distribution(m_complexityIndex,
trainInstances.numClasses());
// Only Instances with known values are relevant.
Enumeration enu = trainInstances.enumerateInstances();
while (enu.hasMoreElements()) {
instance = (Instance) enu.nextElement();
if (!instance.isMissing(m_attIndex))
m_distribution.add((int)instance.value(m_attIndex),instance);
}
// Check if minimum number of Instances in at least two
// subsets.
if (m_distribution.check(m_minNoObj)) {
m_numSubsets = m_complexityIndex;
m_infoGain = infoGainCrit.
splitCritValue(m_distribution,m_sumOfWeights);
m_gainRatio =
gainRatioCrit.splitCritValue(m_distribution,m_sumOfWeights,
m_infoGain);
}
}接下来看数值型是如何处理的：
private void handleNumericAttribute(Instances trainInstances)
throws Exception {
int firstMiss;//最后一个有效instance的下标
int next = 1;//下一个instance的index
int last = 0;//当前instance的index
int splitIndex = -1;//分裂点
double currentInfoGain;//当前信息增益
double defaultEnt;//分割之前的信息熵
double minSplit;
Instance instance;
int i;
//首先新建一个分布，数值型默认处理为2维分布，也就可以理解为小于某个值放到一个Bag里，其余的放到另外一个Bag里 m_distribution = new Distribution(2,trainInstances.numClasses());
Enumeration enu = trainInstances.enumerateInstances();
i = 0;<pre name="code" class="cpp">//注意instances传入的时候是排好序的，这个排序保证了missingValue放在最后面，所以读到了missingValue其之后肯定都是miss//ingValue，换言之，firstMiss在循环之后代表了最后一个有效的instance的下标。//minSplit是最后分类好每个Bag里最小的数据的量，也就是0.1*每个类的均值。
minSplit = 0.1*(m_distribution.total())/
((double)trainInstances.numClasses());
if (Utils.smOrEq(minSplit,m_minNoObj))
minSplit = m_minNoObj;
else
if (Utils.gr(minSplit,25))
minSplit = 25;
//如果有效数据总量不到2*minSplit，换言之无论怎么分均不能保证2个bag里的数量大于minSplit，就直接返回。
if (Utils.sm((double)firstMiss,2*minSplit))
return;
//defaultEnt代表旧的信息熵，也就是对该属性进行分类之前，Indexclass对应的信息熵。
defaultEnt = infoGainCrit.oldEnt(m_distribution);
while (next < firstMiss) {
if (trainInstances.instance(next-1).value(m_attIndex)+1e-5 <
trainInstances.instance(next).value(m_attIndex)) {
<pre name="code" class="cpp">//Instances里的记录是升序排列的，加上这个条件默认把值相差很小的Instance就当做同一个instance处理了//last代表当前，next代表下一个，默认next=1,last=0，所以shiftRange可以理解成把当前记录从bag1移动到bag0中<span style="font-family: Arial, Helvetica, sans-serif;">//注意一开始初始化时候所有的都是在bag1里面的。 </span> if (Utils.gr(currentInfoGain,m_infoGain)) {
m_infoGain = currentInfoGain;//如果信息增益比当前最大的要大，则替换当前最大的值，并记录splitIndex
splitIndex = next-1;
}
m_index++;
}
last = next;
}
next++;
}
if (m_index == 0)
return; //执行到这里说明没找到一个合适的分裂点，直接返回。
// 计算最佳信息增益
m_infoGain = m_infoGain-(Utils.log2(m_index)/m_sumOfWeights);
if (Utils.smOrEq(m_infoGain,0))
return; //如果信息增益是0也说明没找到合适的分裂点，直接返回。
//剩下的就是根据分裂点进行属性的划分。
m_numSubsets = 2;
m_splitPoint =
(trainInstances.instance(splitIndex+1).value(m_attIndex)+
trainInstances.instance(splitIndex).value(m_attIndex))/2;
// In case we have a numerical precision problem we need to choose the
// smaller value
if (m_splitPoint == trainInstances.instance(splitIndex + 1).value(m_attIndex)) {
m_splitPoint = trainInstances.instance(splitIndex).value(m_attIndex);
}
// Restore distributioN for best split.
m_distribution = new Distribution(2,trainInstances.numClasses());
m_distribution.addRange(0,trainInstances,0,splitIndex+1);
m_distribution.addRange(1,trainInstances,splitIndex+1,firstMiss);
// Compute modified gain ratio for best split.
m_gainRatio = gainRatioCrit.
splitCritValue(m_distribution,m_sumOfWeights,
m_infoGain);
}三、BinC45ModelSelection
该函数只负责生成二元分类树的模型，selectModel方法和C45ModelSelection几乎一样，不在多说，不同点在于其使用BinC45Spliter而不是C45Spliter。
四、BinC45Spliter
handleNumericAttribute对于数值类型的属性处理和C45Spliter完全一样。下面只分析一下handleEnumeratedAttribute。
private void handleEnumeratedAttribute(Instances trainInstances)
throws Exception {
Distribution newDistribution,secondDistribution;
int numAttValues;
double currIG,currGR;
Instance instance;
int i;
numAttValues = trainInstances.attribute(m_attIndex).numValues();
newDistribution = new Distribution(numAttValues,
trainInstances.numClasses());
// Only Instances with known values are relevant.
Enumeration enu = trainInstances.enumerateInstances();
while (enu.hasMoreElements()) {
instance = (Instance) enu.nextElement();
if (!instance.isMissing(m_attIndex))
newDistribution.add((int)instance.value(m_attIndex),instance);
}
m_distribution = newDistribution;
// For all values
for (i = 0; i < numAttValues; i++){
if (Utils.grOrEq(newDistribution.perBag(i),m_minNoObj)){
secondDistribution = new Distribution(newDistribution,i);
// Check if minimum number of Instances in the two
// subsets.
if (secondDistribution.check(m_minNoObj)){
m_numSubsets = 2;
currIG = m_infoGainCrit.splitCritValue(secondDistribution,
m_sumOfWeights);
currGR = m_gainRatioCrit.splitCritValue(secondDistribution,
m_sumOfWeights,
currIG);
if ((i == 0) || Utils.gr(currGR,m_gainRatio)){
m_gainRatio = currGR;
m_infoGain = currIG;
m_splitPoint = (double)i;
m_distribution = secondDistribution;
}
}
}
}secondDistribution = new Distribution(newDistribution,i);换句话说，离散值分类的二元化处理就是选出其中一列当做一个branch，其余的当做另外一个branch。虽然从结构上来讲这肯定不是最优的选择，但简单易用就够了。
到这里基本分析完了J48的两个ModelSelection，下一篇文章将对classifierInstance过程进行分析，并给出一个简单的总结。
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