import numpy as np
class DecisionTree:
"""决策树使用方法：
- 生成实例： clf = DecisionTrees(). 参数mode可选，ID3或C4.5，默认C4.5
- 训练，调用fit方法： clf.fit(X,y). X,y均为np.ndarray类型
- 预测，调用predict方法： clf.predict(X). X为np.ndarray类型
- 可视化决策树，调用showTree方法
"""
def __init__(self,mode='C4.5'):
self._tree = None
if mode == 'C4.5' or mode == 'ID3':
self._mode = mode
else:
raise Exception('mode should be C4.5 or ID3')
def _calcEntropy(self,y):
"""
函数功能：计算熵
参数y：数据集的标签
"""
num = y.shape[0]
#统计y中不同label值的个数，并用字典labelCounts存储
labelCounts = {}
for label in y:
if label not in labelCounts.keys(): labelCounts[label] = 0
labelCounts[label] += 1
#计算熵
entropy = 0.0
for key in labelCounts:
prob = float(labelCounts[key])/num
entropy -= prob * np.log2(prob)
return entropy
def _splitDataSet(self,X,y,index,value):
"""
函数功能：返回数据集中特征下标为index，特征值等于value的子数据集
"""
ret = []
featVec = X[:,index]
X = X[:,[i for i in range(X.shape[1]) if i!=index]]
for i in range(len(featVec)):
if featVec[i]==value:
ret.append(i)
return X[ret,:],y[ret]
def _chooseBestFeatureToSplit_ID3(self,X,y):
"""ID3
函数功能：对输入的数据集，选择最佳分割特征
参数dataSet：数据集，最后一列为label
主要变量说明：
numFeatures：特征个数
oldEntropy：原始数据集的熵
newEntropy：按某个特征分割数据集后的熵
infoGain：信息增益
bestInfoGain：记录最大的信息增益
bestFeatureIndex：信息增益最大时，所选择的分割特征的下标
"""
numFeatures = X.shape[1]
oldEntropy = self._calcEntropy(y)
bestInfoGain = 0.0
bestFeatureIndex = -1
for i in range(numFeatures):
featList = X[:,i]
uniqueVals = set(featList)
newEntropy = 0.0
for value in uniqueVals:
sub_X,sub_y = self._splitDataSet(X,y,i,value)
prob = len(sub_y)/float(len(y))
newEntropy += prob * self._calcEntropy(sub_y)
#计算信息增益，根据信息增益选择最佳分割特征
infoGain = oldEntropy - newEntropy
if (infoGain > bestInfoGain):
bestInfoGain = infoGain
bestFeatureIndex = i
return bestFeatureIndex
def _chooseBestFeatureToSplit_C45(self,X,y):
"""C4.5
ID3算法计算的是信息增益，C4.5算法计算的是信息增益比
"""
numFeatures = X.shape[1]
oldEntropy = self._calcEntropy(y)
bestGainRatio = 0.0
bestFeatureIndex = -1
#对每个特征都计算一下gainRatio=infoGain/splitInformation
for i in range(numFeatures):
featList = X[:,i]
uniqueVals = set(featList)
newEntropy = 0.0
splitInformation = 0.0
#对第i个特征的各个value，得到各个子数据集，计算各个子数据集的熵，
#进一步地可以计算得到根据第i个特征分割原始数据集后的熵newEntropy
for value in uniqueVals:
sub_X,sub_y = self._splitDataSet(X,y,i,value)
prob = len(sub_y)/float(len(y))
newEntropy += prob * self._calcEntropy(sub_y)
splitInformation -= prob * np.log2(prob)
#计算信息增益比，根据信息增益比选择最佳分割特征
if splitInformation==0.0:
pass
else:
infoGain = oldEntropy - newEntropy
gainRatio = infoGain/splitInformation
if(gainRatio > bestGainRatio):
bestGainRatio = gainRatio
bestFeatureIndex = i
return bestFeatureIndex
def _majorityCnt(self,labelList):
"""
函数功能：返回labelList中出现次数最多的label
"""
labelCount={}
for vote in labelList:
if vote not in labelCount.keys(): labelCount[vote] = 0
labelCount[vote] += 1
sortedClassCount = sorted(labelCount.iteritems(),key=lambda x:x[1], reverse=True)
return sortedClassCount[0][0]
def _createTree(self,X,y,featureIndex):
"""建立决策树
featureIndex，类型是元组，它记录了X中的特征在原始数据中对应的下标。
"""
labelList = list(y)
#所有label都相同的话，则停止分割，返回该label
if labelList.count(labelList[0]) == len(labelList):
return labelList[0]
#没有特征可分割时，停止分割，返回出现次数最多的label
if len(featureIndex) == 0:
return self._majorityCnt(labelList)
#可以继续分割的话，确定最佳分割特征
if self._mode == 'C4.5':
bestFeatIndex = self._chooseBestFeatureToSplit_C45(X,y)
elif self._mode == 'ID3':
bestFeatIndex = self._chooseBestFeatureToSplit_ID3(X,y)
bestFeatStr = featureIndex[bestFeatIndex]
featureIndex = list(featureIndex)
featureIndex.remove(bestFeatStr)
featureIndex = tuple(featureIndex)
#用字典存储决策树。最佳分割特征作为key，而对应的键值仍然是一棵树
myTree = {bestFeatStr:{}}
featValues = X[:,bestFeatIndex]
uniqueVals = set(featValues)
for value in uniqueVals:
#对每个value递归地创建树
sub_X,sub_y = self._splitDataSet(X,y, bestFeatIndex, value)
myTree[bestFeatStr][value] = self._createTree(sub_X,sub_y,featureIndex)
return myTree
def fit(self,X,y):
#类型检查
if isinstance(X,np.ndarray) and isinstance(y,np.ndarray):
pass
else:
try:
X = np.array(X)
y = np.array(y)
except:
raise TypeError("numpy.ndarray required for X,y")
featureIndex = tuple(['x'+str(i) for i in range(X.shape[1])])
self._tree = self._createTree(X,y,featureIndex)
return self #allow chaining: clf.fit().predict()
def predict(self,X):
if self._tree==None:
raise NotFittedError("Estimator not fitted, call `fit` first")
if isinstance(X,np.ndarray):
pass
else:
try:
X = np.array(X)
except:
raise TypeError("numpy.ndarray required for X")
def _classify(tree,sample):
"""
用训练好的决策树对输入数据分类
决策树的构建是一个递归的过程，用决策树分类也是一个递归的过程
_classify()一次只能对一个样本(sample)分类
To Do: 多个sample的预测怎样并行化？
"""
featIndex = tree.keys()[0]
secondDict = tree[featIndex]
key = sample[int(featIndex[1:])]
valueOfkey = secondDict[key]
if isinstance(valueOfkey, dict):
label = _classify(valueOfkey,sample)
else: label = valueOfkey
return label
if len(X.shape)==1:
return _classify(self._tree,X)
else:
results = []
for i in range(X.shape[0]):
results.append(_classify(self._tree,X[i]))
return np.array(results)
def show(self):
if self._tree==None:
raise NotFittedError("Estimator not fitted, call `fit` first")
#plot the tree using matplotlib
import treePlotter
treePlotter.createPlot(self._tree)
class NotFittedError(Exception):
"""
Exception class to raise if estimator is used before fitting
"""
pass
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