提升树(BoostingTree)原理与实现

作者：金良（[email protected]） csdn博客： http://blog.csdn.net/u012176591

类Classifier将多个基本分类器组合成一个强分类器

import numpy as np
class Classifier:
    def __init__(self):
        self.__stumps = []
        self.aa = self.__stumps
        self.__hasmakemodel = False

        self.__posuniq = np.nan
        self.__valuelist = np.nan
    def add(self,pos,val1,val2):
        self.__hasmakemodel = False
        exceptlabel = False
        try:
            np.sum(np.array([pos,val1,val2])+1)       
        except:
            exceptlabel = True
        if exceptlabel == False:
            stump = self.__stump(pos,val1,val2)
            self.__stumps.append(stump)
        else:
            print 'Input parameter is INVALID.\n\t Try again please.'

    def __stump(self,pos,val1,val2):
        return {'pos':pos,'val':(val1,val2)}
    def __makemodel(self):

        self.__posuniq = list(set([stump['pos'] for stump in self.__stumps]))
        self.__posuniq.sort()
        self.__valuelist = np.zeros(len(self.__posuniq)+1)

        for stump in stumps:
            idx = self.__posuniq.index(stump['pos'])
            self.__valuelist[:idx+1] += stump['val'][0]
            self.__valuelist[idx+1:] += stump['val'][1] 
        self.__hasmakemodel = True
    def predict(self,x):
        if self.__hasmakemodel == False:
            self.__makemodel()            
        for idx in range(len(self.__posuniq)+1):
            try:
                if x <  self.__posuniq[idx]:
                    break
            except:
                pass  
        y = self.__valuelist[idx]   
        return y
if __name__ == "__main__":
    classifier = Classifier()
    classifier.add(6.5,6.24,8.91)
    classifier.add(3.5,-0.52,0.22)
    classifier.add(6.5,0.15,-0.22)
    classifier.add(4.5,-0.16,0.11)
    classifier.add(6.5,0.07,-0.11)
    classifier.add(2.5,-0.15,0.04)

    predictlist = np.array([classifier.predict(i+1) for i in range(10)])
    valuelist = np.array([5.56,5.70,5.91,6.40,6.80,7.05,8.90,8.70,9.00,9.05])
    loss = np.sum(np.power(predictlist - valuelist,2))
    print '平方误差：',str(loss)     

类BoostingTree是主体，它有一个Classifier对象成员

import numpy as np
import copy
class BoostingTree:
    def __init__(self,data,iters=6):
        self.__data = copy.deepcopy(data)

        #将一个Classifier对象作为成员
        self.__classifier = Classifier()
        self.__division = [(self.__data['x'][idx]+self.__data['x'][idx+1])/2.0 for idx in range(self.__data['x'].shape[0]-1)]
        self.__iters = iters
        self.__hasmakemodel = False

    def __makemodel(self):
        residuallist = self.__data['y']

        for it in range(self.__iters):
            performancelist = []
            predictlist = np.zeros(residuallist.shape[0])
            for idx,x in enumerate(self.__division): 

                meanleft = np.mean(residuallist[:idx+1]) #左侧的均值
                predictlist[:idx+1] = meanleft
                meanright = np.mean(residuallist[idx+1:]) #右侧的均值
                predictlist[idx+1:] = meanright
                loss = np.sum(np.power(residuallist - predictlist,2)) #平方误差
                performancelist.append([loss,x,meanleft,meanright])

            #xidx是最优的分界点序号
            xidx = np.argmin([performance[0] for performance in performancelist]) 

            #下面两行求残差
            residuallist[:xidx+1] -= performancelist[xidx][2]
            residuallist[xidx+1:] -= performancelist[xidx][3]

            #添加新的弱分类器
            self.__classifier.add(performancelist[xidx][1],performancelist[xidx][2],performancelist[xidx][3])
        self.__hasmakemodel = True
    def predict(self,x):

        if self.__hasmakemodel == False:
            self.__makemodel()
        try: #当x不是单个数字元素时
            x[0]
            size = np.shape(x)[0]
            y = [0]*size
            for i in range(size):
                y[i] = self.__classifier.predict(x[i])
            return y
        except:
            return self.__classifier.predict(x)   

对BoostingTree进行测试：

data = {'x':np.array([1,2,3,4,5,6,7,8,9,10]),
        'y':np.array([5.56,5.70,5.91,6.40,6.80,7.05,8.90,8.70,9.00,9.05])}
boostingtree = BoostingTree(data)
predictlist = boostingtree.predict(np.array([1,2,3,4,5,6,7,8,9,10]))
valuelist = np.array([5.56,5.70,5.91,6.40,6.80,7.05,8.90,8.70,9.00,9.05])
loss = np.sum(np.power(predictlist - valuelist,2))
print '平方误差：',str(loss)  

平方误差： 0.1703

可视化

代码：

trainx = np.array([1,2,3,4,5,6,7,8,9,10])
trainy = boostingtree.predict(trainx)
testx = np.linspace(0,11,400)
testy = boostingtree.predict(x)
plt.plot(trainx,trainy,'r.',marker = u'o',label=u'训练集')
plt.plot(testx,testy,'b',label=u'测试集')

plt.legend(prop={'family':'SimHei','size':15})

plt.title(u'BoostingTree效果图',{'fontname':'STFangsong','fontsize':18})
plt.xlabel(u'X轴',{'fontname':'STFangsong','fontsize':18})
plt.ylabel(u'Y轴',{'fontname':'STFangsong','fontsize':18})