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李航《统计学习方法》第八章——用Python+Cpp实现AdaBoost算法（MNIST数据集）

2016-11-17 09:31 453 查看

AdaBoost算法

这里先贴上书上的算法

算法

细节处理

我们使用的弱分类器是例8.1的阈值分类器，但阈值分类器只能分类单一维度的特征，而通常情况下我们的特征都是多维的，这时就需要我们使用一些trick。

假设特征有n维，我们针对每一维特征求一个分类器，选取这些分类器中分类误差率最低的分类器作为本轮的分类器，将其特征坐标与分类器一起存入G(x)中。

当分类时，获取当前分类器Gm(x)及其特征坐标i，选取测试数据X的第i个特征X[i],放入分类器中分类，即Gm(X[i])。

如此一来，就能解决阈值分类器在多维特征下的情况了！

数据集

数据集和感知器那个博文用的是同样的数据集。

数据地址：https://github.com/WenDesi/lihang_book_algorithm/blob/master/data/train_binary.csv

特征

将整个图作为特征，但需要先经过二值化处理

代码

因为纯python的代码运行速度有些慢，所以我又写了一个版本，将计算阈值分类器那段写成了C++版本，编译成dll，加快运行速度。

纯python

代码已放到Github上，这边也贴出来

# encoding=utf-8
# @Author: wendesi
# @Date:   15-11-16
# @Email:  wendesi@foxmail.com
# @Last modified by:   wendesi
# @Last modified time: 17-11-16

import cv2
import time
import math
import logging
import numpy as np
import pandas as pd

from sklearn.cross_validation import train_test_split
from sklearn.metrics import accuracy_score

sign_time_count = 0

class Sign(object):
'''
阈值分类器

有两种方向，
1）x<v y=1
2) x>v y=1
v 是阈值轴

因为是针对已经二值化后的MNIST数据集，所以v的取值只有3个 {0,1,2}
'''

def __init__(self,features,labels,w):
self.X = features               # 训练数据特征
self.Y = labels                 # 训练数据的标签
self.N = len(labels)            # 训练数据大小

self.w = w                      # 训练数据权值分布

self.indexes = [0,1,2]          # 阈值轴可选范围

def _train_less_than_(self):
'''
寻找(x<v y=1)情况下的最优v
'''

index = -1
error_score = 1000000

for i in self.indexes:
score = 0
for j in xrange(self.N):
val = -1
if self.X[j]<i:
val = 1

if val*self.Y[j]<0:
score += self.w[j]

if score < error_score:
index = i
error_score = score

return index,error_score

def _train_more_than_(self):
'''
寻找(x>v y=1)情况下的最优v
'''

index = -1
error_score = 1000000

for i in self.indexes:
score = 0
for j in xrange(self.N):
val = 1
if self.X[j]<i:
val = -1

if val*self.Y[j]<0:
score += self.w[j]

if score < error_score:
index = i
error_score = score

return index,error_score

def train(self):
global sign_time_count
time1 = time.time()
less_index,less_score = self._train_less_than_()
more_index,more_score = self._train_more_than_()
time2 = time.time()
sign_time_count += time2-time1

if less_score < more_score:
self.is_less = True
self.index = less_index
return less_score

else:
self.is_less = False
self.index = more_index
return more_score

def predict(self,feature):
if self.is_less>0:
if feature<self.index:
return 1.0
else:
return -1.0
else:
if feature<self.index:
return -1.0
else:
return 1.0

class AdaBoost(object):

def __init__(self):
pass

def _init_parameters_(self,features,labels):
self.X = features                           # 训练集特征
self.Y = labels                             # 训练集标签

self.n = len(features[0])                   # 特征维度
self.N = len(features)                      # 训练集大小
self.M = 10                                 # 分类器数目

self.w = [1.0/self.N]*self.N                # 训练集的权值分布
self.alpha = []                             # 分类器系数  公式8.2
self.classifier = []                        # (维度，分类器)，针对当前维度的分类器

def _w_(self,index,classifier,i):
'''
公式8.4不算Zm
'''

return self.w[i]*math.exp(-self.alpha[-1]*self.Y[i]*classifier.predict(self.X[i][index]))

def _Z_(self,index,classifier):
'''
公式8.5
'''

Z = 0

for i in xrange(self.N):
Z += self._w_(index,classifier,i)

return Z

def train(self,features,labels):

self._init_parameters_(features,labels)

for times in xrange(self.M):
logging.debug('iterater %d' % times)

time1 = time.time()
map_time = 0

best_classifier = (100000,None,None)        #(误差率,针对的特征，分类器)
for i in xrange(self.n):
map_time -= time.time()
features = map(lambda x:x[i],self.X)
map_time += time.time()
classifier = Sign(features,self.Y,self.w)
error_score = classifier.train()

if error_score < best_classifier[0]:
best_classifier = (error_score,i,classifier)

em = best_classifier[0]

# 分析用，之后删除 开始
print 'em is %s, index is %d' % (str(em),best_classifier[1])
time2 = time.time()
global sign_time_count
print '总运行时间:%s, 那两段关键代码运行时间:%s, map的时间是:%s' % (str(time2-time1),str(sign_time_count),str(map_time))
sign_time_count = 0
# 分析用，之后删除  结束

if em==0:
self.alpha.append(100)
else:
self.alpha.append(0.5*math.log((1-em)/em))

self.classifier.append(best_classifier[1:])

Z = self._Z_(best_classifier[1],best_classifier[2])

# 计算训练集权值分布 8.4
for i in xrange(self.N):
self.w[i] = self._w_(best_classifier[1],best_classifier[2],i)/Z

def _predict_(self,feature):

result = 0.0
for i in xrange(self.M):
index = self.classifier[i][0]
classifier = self.classifier[i][1]

result += self.alpha[i]*classifier.predict(feature[index])

if result>0:
return 1
return -1

def predict(self,features):
results = []

for feature in features:
results.append(self._predict_(feature))

return results

# 二值化
def binaryzation(img):
cv_img = img.astype(np.uint8)
cv2.threshold(cv_img,50,1,cv2.cv.CV_THRESH_BINARY_INV,cv_img)
return cv_img

def binaryzation_features(trainset):
features = []

for img in trainset:
img = np.reshape(img,(28,28))
cv_img = img.astype(np.uint8)

img_b = binaryzation(cv_img)
# hog_feature = np.transpose(hog_feature)
features.append(img_b)

features = np.array(features)
features = np.reshape(features,(-1,784))

return features

if __name__ == '__main__':
logger = logging.getLogger()
logger.setLevel(logging.DEBUG)

print 'Start read data'

time_1 = time.time()

raw_data = pd.read_csv('../data/train_binary.csv',header=0)
data = raw_data.values

imgs = data[0::,1::]
labels = data[::,0]

# 选取 2/3 数据作为训练集， 1/3 数据作为测试集
features = binaryzation_features(imgs)
train_features, test_features, train_labels, test_labels = train_test_split(features, labels, test_size=0.5, random_state=0)

time_2 = time.time()
print 'read data cost ',time_2 - time_1,' second','\n'

print 'Start training'
train_labels = map(lambda x:2*x-1,train_labels)
ada = AdaBoost()
ada.train(train_features, train_labels)

time_3 = time.time()
print 'training cost ',time_3 - time_2,' second','\n'

print 'Start predicting'
test_predict = ada.predict(test_features)
time_4 = time.time()
print 'predicting cost ',time_4 - time_3,' second','\n'

test_labels = map(lambda x:2*x-1,test_labels)
score = accuracy_score(test_labels,test_predict)
print "The accruacy socre is ", score

python+cpp

因为大体思路同纯python版，所以懒得写注释了

adaboost_cpp.py Github

# encoding=utf-8
# @Author: wendesi
# @Date:   15-11-16
# @Email:  wendesi@foxmail.com
# @Last modified by:   wendesi
# @Last modified time: 15-11-16

import cv2
import time
import math
import ctypes
import logging
import numpy as np
import pandas as pd

from sklearn.cross_validation import train_test_split
from sklearn.metrics import accuracy_score

sign_time_count = 0

class Sign(object):
def __init__(self,is_less,index):
self.is_less = is_less
self.index = index

def predict(self,feature):
if self.is_less>0:
if feature<self.index:
return 1.0
else:
return -1.0
else:
if feature<self.index:
return -1.0
else:
return 1.0

class AdaBoost(object):

def __init__(self):
ll = ctypes.cdll.LoadLibrary
self.lib = ll("Sign/x64/Release/Sign.dll")

def rebuild_X(self,X):
length = self.n*self.N
self.X_matrix = (ctypes.c_int * length)()

for i in xrange(self.n):
for j in xrange(self.N):
self.X_matrix[i*self.N+j] = X[j][i]

def rebuild_Y(self,Y):
self.C_Y = (ctypes.c_int * self.N)()
for i in xrange(self.N):
self.C_Y[i] = Y[i]

def _init_parameters_(self,features,labels):
self.Y = labels

self.n = len(features[0])
self.N = len(features)
self.M = 100                            # 分类器数目

self.w = [1.0/self.N]*self.N
self.alpha = []
self.classifier = []

self.rebuild_X(features)
self.rebuild_Y(labels)

def _w_(self,index,classifier,i):
feature = self.X_matrix[index*self.N+i]
return self.w[i]*math.exp(-self.alpha[-1]*self.Y[i]*classifier.predict(feature))

def _Z_(self,index,classifier):
Z = 0

for i in xrange(self.N):
Z += self._w_(index,classifier,i)

return Z

def build_c_w(self):
C_w = (ctypes.c_double * self.N)()
for i in xrange(self.N):
C_w[i] = ctypes.c_double(self.w[i])
return C_w

def train(self,features,labels):

self._init_parameters_(features,labels)

for times in xrange(self.M):
logging.debug('iterater %d' % times)

C_w = self.build_c_w()
min_error = ctypes.c_double(100000)
is_less = ctypes.c_int(-1)
feature_index = ctypes.c_int(-1)

index = self.lib.find_min_error(self.X_matrix,self.n,self.N,self.C_Y,C_w,ctypes.byref(min_error),ctypes.byref(is_less),ctypes.byref(feature_index))

em = min_error.value
best_classifier = (em,feature_index.value,Sign(is_less.value,index))        #(误差率,针对的特征,分类器)
print 'em is %s, index is %s' % (str(em),str(feature_index.value))

if em==0:
self.alpha.append(100)
else:
self.alpha.append(0.5*math.log((1-em)/em))

self.classifier.append(best_classifier[1:])

Z = self._Z_(best_classifier[1],best_classifier[2])

for i in xrange(self.N):
self.w[i] = self._w_(best_classifier[1],best_classifier[2],i)/Z

def _predict_(self,feature):

result = 0.0
for i in xrange(self.M):
index = self.classifier[i][0]
classifier = self.classifier[i][1]

result += self.alpha[i]*classifier.predict(feature[index])

if result>0:
return 1
return -1

def predict(self,features):
results = []

for feature in features:
results.append(self._predict_(feature))

return results

# 二值化
def binaryzation(img):
cv_img = img.astype(np.uint8)
cv2.threshold(cv_img,50,1,cv2.cv.CV_THRESH_BINARY_INV,cv_img)
return cv_img

def binaryzation_features(trainset):
features = []

for img in trainset:
img = np.reshape(img,(28,28))
cv_img = img.astype(np.uint8)

img_b = binaryzation(cv_img)
# hog_feature = np.transpose(hog_feature)
features.append(img_b)

features = np.array(features)
features = np.reshape(features,(-1,784))

return features

if __name__ == '__main__':
logger = logging.getLogger()
logger.setLevel(logging.DEBUG)

print 'Start read data'

time_1 = time.time()

raw_data = pd.read_csv('../data/train_binary.csv',header=0)
data = raw_data.values

imgs = data[0::,1::]
labels = data[::,0]

# 选取 2/3 数据作为训练集， 1/3 数据作为测试集
features = binaryzation_features(imgs)
train_features, test_features, train_labels, test_labels = train_test_split(features, labels, test_size=0.33, random_state=23323)

time_2 = time.time()
print 'read data cost ',time_2 - time_1,' second','\n'

print 'Start training'
train_labels = map(lambda x:2*x-1,train_labels)
ada = AdaBoost()
ada.train(train_features, train_labels)

time_3 = time.time()
print 'training cost ',time_3 - time_2,' second','\n'

print 'Start predicting'
test_predict = ada.predict(test_features)
time_4 = time.time()
print 'predicting cost ',time_4 - time_3,' second','\n'

test_labels = map(lambda x:2*x-1,test_labels)
score = accuracy_score(test_labels,test_predict)
print "The accruacy socre is ", score

sign.h Github

#pragma once

extern "C" __declspec(dllexport) int find_min_error(int* X,int rows,int cols,int* y,double* w,double& min_error,int& is_less,int& feature_index);

sign.cpp Github

#include <iostream>
using namespace std;
#include "sign.h"

int find_min_error(int* X,int rows,int cols,int* y,double* w,double& min_error,int& is_less,int& feature_index)
{
int index = -1;

for(int row=0;row<rows;row++)
{
for(int i=0;i<3;i++)
{
double score = 0;

for(int j=0;j<cols;j++)
{
int val = -1;
if(X[row*cols+j]<i)
{
val = 1;
}

if(val*y[j]<0)
score += w[j];

}

if(score < min_error)
{
index = i;
is_less = 1;
min_error = score;
feature_index = row;
}
}
}

for(int row=0;row<rows;row++)
{
for(int i=0;i<3;i++)
{
double score = 0;

for(int j=0;j<cols;j++)
{
int val = 1;
if(X[row*cols+j]<i)
{
val = -1;
}

if(val*y[j]<0)
score += w[j];

}

if(score < min_error)
{
index = i;
is_less = 0;
min_error = score;
feature_index = row;
}
}
}

return index;
}

运行结果

结果还是不错的嘛！

让我比较惊讶的是Python和C++运算速度差真的很大，网上说是大约30倍。但我这测试大约是200倍左右，可能也和这数据量大有些关系。

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标签： python 统计学李航数据算法

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