Decision Tree Model
- Select the best features and feature values data set into
- Create a decision tree based on the results obtained above
- Pruning test data (not the default data branch of the tree is cut)
- The input prediction
Model Tree
import numpy as np
def loadDataSet(fileName): #general function to parse tab -delimited floats
dataMat = [] #assume last column is target value
with open(fileName) as fr:
for line in fr.readlines():
curLine = line.strip().split('\t')
# fltLine = map(float, curLine) #map all elements to float()
fltLine = [float(i) for i in curLine]
dataMat.append(fltLine)
# dataMat = [map(float,line.strip().split('\t')) for line in fr.readlines()]
return np.mat(dataMat)
# dataSet为矩阵，feature 为特征索引，value为值
def binSplitDataSet(dataSet, feature, value):
mat0 = dataSet[np.nonzero(dataSet[:,feature] > value)[0],:]
mat1 = dataSet[np.nonzero(dataSet[:,feature] <= value)[0],:]
return np.mat(mat0),np.mat(mat1)
def regLeaf(dataSet):#returns the value used for each leaf
return np.mean(dataSet[:,-1])
def regErr(dataSet): # 输出的平方误差和
return np.var(dataSet[:,-1]) * np.shape(dataSet)[0]
# ops[0]误差下降值，小于此值不再切分
# ops[1] 切分的最小样本数，小于此值不再切分
def chooseBestSplit(dataSet, leafType=regLeaf, errType=regErr, ops=(1,4)):
tolS = ops[0]; tolN = ops[1]
#if all the target variables are the same value: quit and return value
# print(set(dataSet[:,-1].T.tolist()[0]))
if len(set(dataSet[:,-1].T.tolist()[0])) == 1: #exit cond 1
# if len(set(dataSet[:, -1])) == 1: # exit cond 1
return None, leafType(dataSet) # 返回None,输出值
m,n = np.shape(dataSet)
#the choice of the best feature is driven by Reduction in RSS error from mean
S = errType(dataSet)
bestS = np.inf; bestIndex = 0; bestValue = 0
for featIndex in range(n-1):
for splitVal in set(dataSet[:,featIndex].T.tolist()[0]):
mat0, mat1 = binSplitDataSet(dataSet, featIndex, splitVal)
if (np.shape(mat0)[0] < tolN) or (np.shape(mat1)[0] < tolN):
continue # 结束本次循环，小于最小切分样本数，不再切分
newS = errType(mat0) + errType(mat1)
if newS < bestS:
bestIndex = featIndex
bestValue = splitVal
bestS = newS
#if the decrease (S-bestS) is less than a threshold don't do the split
if (S - bestS) < tolS: # 切分前的和切分后的误差小于给定值，不再切分
return None, leafType(dataSet) #exit cond 2
# mat0, mat1 = binSplitDataSet(dataSet, bestIndex, bestValue) # ?按照最优特征和值切分
# if (np.shape(mat0)[0] < tolN) or (np.shape(mat1)[0] < tolN): #exit cond 3
# return None, leafType(dataSet)
return bestIndex,bestValue#returns the best feature to split on
#and the value used for that split
def createTree(dataSet, leafType=regLeaf, errType=regErr, ops=(1,4)):#assume dataSet is NumPy Mat so we can array filtering
feat, val = chooseBestSplit(dataSet, leafType, errType, ops)#choose the best split
if feat == None: return val #if the splitting hit a stop condition return val
retTree = {}
retTree['spInd'] = feat
retTree['spVal'] = val
lSet, rSet = binSplitDataSet(dataSet, feat, val)
retTree['left'] = createTree(lSet, leafType, errType, ops)
retTree['right'] = createTree(rSet, leafType, errType, ops)
return retTree
def isTree(obj):
return (type(obj).__name__ == 'dict')
def getMean(tree):
if isTree(tree['right']): tree['right'] = getMean(tree['right'])
if isTree(tree['left']): tree['left'] = getMean(tree['left'])
return (tree['left'] + tree['right']) / 2.0
def prune(tree, testData):
if np.shape(testData)[0] == 0: return getMean(
tree) # if we have no test data collapse the tree
if (isTree(tree['right']) or isTree(
tree['left'])): # if the branches are not trees try to prune them
lSet, rSet = binSplitDataSet(testData, tree['spInd'], tree['spVal'])
if isTree(tree['left']): tree['left'] = prune(tree['left'], lSet)
if isTree(tree['right']): tree['right'] = prune(tree['right'], rSet)
# if they are now both leafs, see if we can merge them
if not isTree(tree['left']) and not isTree(tree['right']):
lSet, rSet = binSplitDataSet(testData, tree['spInd'], tree['spVal'])
errorNoMerge = sum(np.power(lSet[:, -1] - tree['left'], 2)) + \
sum(np.power(rSet[:, -1] - tree['right'], 2))
treeMean = (tree['left'] + tree['right']) / 2.0
errorMerge = sum(np.power(testData[:, -1] - treeMean, 2))
if errorMerge < errorNoMerge:
print("merging")
return treeMean
else:
return tree
else:
return tree
# 模型树代码--未测试
def linearSolve(dataSet): #helper function used in two places
m,n = np.shape(dataSet)
X = np.mat(np.ones((m,n))); Y = np.mat(np.ones((m,1)))#create a copy of
# data with 1
# in 0th postion
X[:,1:n] = dataSet[:,0:n-1]; Y = dataSet[:,-1]#and strip out Y
xTx = X.T*X
if np.linalg.det(xTx) == 0.0:
raise NameError('This matrix is singular, cannot do inverse,\n\
try increasing the second value of ops')
ws = xTx.I * (X.T * Y)
return ws,X,Y
def regTreeEval(model, inDat):
return float(model)
def modelTreeEval(model, inDat):
n = np.shape(inDat)[1]
X = np.mat(np.ones((1, n + 1)))
X[:, 1:n + 1] = inDat
return float(X * model)
def treeForeCast(tree, inData, modelEval=regTreeEval):
if not isTree(tree): return modelEval(tree, inData)
if inData[tree['spInd']] > tree['spVal']:
if isTree(tree['left']):
return treeForeCast(tree['left'], inData, modelEval)
else:
return modelEval(tree['left'], inData)
else:
if isTree(tree['right']):
return treeForeCast(tree['right'], inData, modelEval)
else:
return modelEval(tree['right'], inData)
def createForeCast(tree, testData, modelEval=regTreeEval):
m = len(testData)
yHat = np.mat(np.zeros((m, 1)))
for i in range(m):
yHat[i, 0] = treeForeCast(tree, np.mat(testData[i]), modelEval)
return yHat
if __name__ == '__main__':
# mat0, mat1 = binSplitDataSet(np.mat(np.eye(4)),1,0.5) # 二分测试
dataMat = loadDataSet('ex00.txt') # 构建数测试
myTree = createTree(dataMat)
print(myTree)
dataMat2 = loadDataSet('ex0.txt')
myTree2 = createTree(dataMat2)
print(myTree2)
dataMat31 = loadDataSet('ex2.txt') # 剪枝测试
dataMat32 = loadDataSet('ex2test.txt')
myTree31 = createTree(dataMat31)
retTree = prune(myTree31, dataMat32)
print(myTree31)
print(retTree)
