mirror of
https://github.com/apachecn/ailearning.git
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ApacheCN
1
.gitignore
vendored
1
.gitignore
vendored
@@ -88,4 +88,3 @@ ENV/
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# Rope project settings
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.ropeproject
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.vscode
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.idea
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@@ -1,11 +1,36 @@
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# 1) 逻辑回归基础
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# 5) 逻辑回归基础
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* 逻辑回归(Logistic Regression)
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* 1.1 分类问题
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* 1.2 假说表示
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* 1.3 判定边界
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* 1.4 代价函数
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* 1.5 简化的成本函数和梯度下降
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* 1.6 高级优化
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* 1.7 多类分类：一个对所有
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* 5.1 分类问题
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* 在分类问题中，尝试预测的是结果是否属于某一个类（例如正确或错误）。
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* 分类问题的例子有：
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* 判断一封电子邮件是否是垃圾邮件；
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* 判断一次金融交易是否是欺诈等等。
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* 从二元的分类问题开始讨论:
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将因变量(dependant variable)可能属于的两个类分别称为负向类（negative class）和正向类（positive class），则因变量
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y属于{0，1}
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注：其中 0 表示负向类，1 表示正向类。
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* 5.2 假说表示
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* 5.3 判定边界
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* 在逻辑回归中，我们预测：
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当 hθ 大于等于 0.5 时，预测 y=1
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当 hθ 小于 0.5 时，预测 y=0
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* 根据上面绘制出的 S 形函数图像，我们知道当
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z=0时 ，g(z)=0.5
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z>0时 ，g(z)>0.5
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z<0时 ，g(z)<0.5
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又z=θ的T次方与X的积，即：
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z大于等于0时，预测：y=1
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z小于0时，预测：y=0
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* 现在假设我们有一个模型：Hθ(x)=g(θ0+θ1*x1+θ2*x2)
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并且参数θ是向量[-3 1 1]。则当-3+x1+x2大于等于0，即x1+x2大于等于3时，模型将预测y=1。
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我们可以绘制直线x1+x2=3，这条线便是我们模型的分界线，将预测为1的区域和预测为0的区域分隔开。
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* 假使我们的数据呈现这样的分布情况，怎样的模型才能适合呢？
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因为需要用曲线才能分隔 y=0 的区域和 y=1 的区域，我们需要二次方特征： 假设参数是Hθ(x)=g(θ0+θ1*x1+θ2*x2+θ3*(x1^2)+θ4*(x2^2)+θ4*(x2^2))
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是[-1 0 0 1 1]，则我们得到的判定边界恰好是圆点在原点且半径为 1 的圆形。可以用非常复杂的模型来适应非常复杂形状的判定边界。
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* 5.4 代价函数
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* 5.5 简化的成本函数和梯度下降
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* 5.6 高级优化
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* 5.7 多类分类：一个对所有
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@@ -6,6 +6,12 @@ from sklearn import tree
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from sklearn.metrics import precision_recall_curve
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from sklearn.metrics import classification_report
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from sklearn.cross_validation import train_test_split
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"""
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需要安装依赖模块：
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pip install scikit_learn-0.18-cp27-cp27m-win_amd64.whl
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非常完整的网址：
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http://www.lfd.uci.edu/~gohlke/pythonlibs/#numpy
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"""
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def createDataSet():
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103
src/python/05.Logistic/core/logRegression01.py
Normal file
103
src/python/05.Logistic/core/logRegression01.py
Normal file
@@ -0,0 +1,103 @@
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#!/usr/bin/env python
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# encoding: utf-8
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from numpy import *
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import matplotlib.pyplot as plt
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import time
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'''
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1、需要安装模块：pip install matplotlib-1.5.0-cp27-none-win_amd64.whl
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由于直接安装会出现问题，所以建议下载whl包进行安装，下载网址：
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https://pypi.python.org/pypi/matplotlib/1.5.0
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2、可以看见画出的图像
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'''
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"""
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@version:
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@author: yangjf
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@license: ApacheCN
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@contact: highfei2011@126.com
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@site: https://github.com/apachecn/MachineLearning
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@software: PyCharm
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@file: logRegression01.py
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@time: 2017/3/3 22:03
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@test result: ok
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"""
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# sigmoid函数
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def sigmoid(inX):
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return 1.0 / (1 + exp(-inX))
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def trainLogRegres(train_x, train_y, opts):
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# 计算训练时间
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startTime = time.time()
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numSamples, numFeatures = shape(train_x)
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alpha = opts['alpha']; maxIter = opts['maxIter']
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weights = ones((numFeatures, 1))
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# 通过梯度下降算法优化
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for k in range(maxIter):
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if opts['optimizeType'] == 'gradDescent': # 梯度下降算法
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output = sigmoid(train_x * weights)
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error = train_y - output
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weights = weights + alpha * train_x.transpose() * error
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elif opts['optimizeType'] == 'stocGradDescent': # 随机梯度下降
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for i in range(numSamples):
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output = sigmoid(train_x[i, :] * weights)
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error = train_y[i, 0] - output
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weights = weights + alpha * train_x[i, :].transpose() * error
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elif opts['optimizeType'] == 'smoothStocGradDescent': # 光滑随机梯度下降
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# 随机选择样本以优化以减少周期波动
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dataIndex = range(numSamples)
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for i in range(numSamples):
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alpha = 4.0 / (1.0 + k + i) + 0.01
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randIndex = int(random.uniform(0, len(dataIndex)))
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output = sigmoid(train_x[randIndex, :] * weights)
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error = train_y[randIndex, 0] - output
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weights = weights + alpha * train_x[randIndex, :].transpose() * error
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del(dataIndex[randIndex]) # 在一次交互期间，删除优化的样品
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else:
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raise NameError('Not support optimize method type!')
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print 'Congratulations, training complete! Took %fs!' % (time.time() - startTime)
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return weights
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#测试给定测试集的训练Logistic回归模型
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def testLogRegres(weights, test_x, test_y):
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numSamples, numFeatures = shape(test_x)
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matchCount = 0
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for i in xrange(numSamples):
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predict = sigmoid(test_x[i, :] * weights)[0, 0] > 0.5
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if predict == bool(test_y[i, 0]):
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matchCount += 1
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accuracy = float(matchCount) / numSamples
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return accuracy
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# 显示你的训练逻辑回归模型只有2-D数据可用
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def showLogRegres(weights, train_x, train_y):
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# 注意：train_x和train_y是垫数据类型
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numSamples, numFeatures = shape(train_x)
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if numFeatures != 3:
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print "抱歉! 我不能绘制，因为你的数据的维度不是2！"
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return 1
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# 画出所有抽样数据
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for i in xrange(numSamples):
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if int(train_y[i, 0]) == 0:
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plt.plot(train_x[i, 1], train_x[i, 2], 'or')
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elif int(train_y[i, 0]) == 1:
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plt.plot(train_x[i, 1], train_x[i, 2], 'ob')
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# 画图操作
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min_x = min(train_x[:, 1])[0, 0]
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max_x = max(train_x[:, 1])[0, 0]
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weights = weights.getA() # 将mat转换为数组
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y_min_x = float(-weights[0] - weights[1] * min_x) / weights[2]
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y_max_x = float(-weights[0] - weights[1] * max_x) / weights[2]
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plt.plot([min_x, max_x], [y_min_x, y_max_x], '-g')
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plt.xlabel('X1'); plt.ylabel('X2')
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#显示图像
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plt.show()
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54
src/python/05.Logistic/core/test_logRegression.py
Normal file
54
src/python/05.Logistic/core/test_logRegression.py
Normal file
@@ -0,0 +1,54 @@
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#!/usr/bin/env python
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# encoding: utf-8
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import os
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import sys
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sys.path.append("C:\Python27")
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from numpy import *
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from logRegression01 import *
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"""
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@version:
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@author: yangjf
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@license: ApacheCN
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@contact: highfei2011@126.com
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@site: https://github.com/apachecn/MachineLearning
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@software: PyCharm
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@file: test_logRegression.py
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@time: 2017/3/3 22:09
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@test result: ok
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"""
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def loadData():
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train_x = []
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train_y = []
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# 获取当前文件所在路径
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project_dir = os.getcwdu()
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# 截取字符串至项目名：Test\
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project_dir = project_dir[:project_dir.find("MachineLearning\\") + 15]
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print project_dir
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fileIn = open("%s/testData/Logistic_testdata.txt" % project_dir)
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for line in fileIn.readlines():
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lineArr = line.strip().split()
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train_x.append([1.0, float(lineArr[0]), float(lineArr[1])])
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train_y.append(float(lineArr[2]))
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return mat(train_x), mat(train_y).transpose()
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##第一步: 加载数据
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print "step 1: load data..."
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train_x, train_y = loadData()
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test_x = train_x; test_y = train_y
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##第二步: 训练数据...
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print "step 2: training..."
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opts = {'alpha': 0.01, 'maxIter': 20, 'optimizeType': 'smoothStocGradDescent'}
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optimalWeights = trainLogRegres(train_x, train_y, opts)
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##第三步: 测试
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print "step 3: testing..."
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accuracy = testLogRegres(optimalWeights, test_x, test_y)
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##第四步: 显示结果
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print "step 4: show the result..."
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print 'The classify accuracy is: %.3f%%' % (accuracy * 100)
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showLogRegres(optimalWeights, train_x, train_y)
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@@ -117,7 +117,7 @@ def plotBestFit(dataArr, labelMat, weights):
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def main():
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project_dir = os.path.dirname(os.path.dirname(os.getcwd()))
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# 1.收集并准备数据
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dataMat, labelMat = loadDataSet("%s/resources/testSet.txt" % project_dir)
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dataMat, labelMat = loadDataSet("%s/testData/Logistic_testdata.txt" % project_dir)
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# print dataMat, '---\n', labelMat
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# 2.训练模型， f(x)=a1*x1+b2*x2+..+nn*xn中 (a1,b2, .., nn).T的矩阵值
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@@ -73,7 +73,7 @@ def apriori(dataSet, minSupport = 0.5):
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def main():
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# project_dir = os.path.dirname(os.path.dirname(os.getcwd()))
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# 1.收集并准备数据
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# dataMat, labelMat = loadDataSet("%s/resources/testSet.txt" % project_dir)
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# dataMat, labelMat = loadDataSet("%s/resources/Logistic_testdata.txt" % project_dir)
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# 1. 加载数据
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100
testData/Logistic_testdata.txt
Normal file
100
testData/Logistic_testdata.txt
Normal file
@@ -0,0 +1,100 @@
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-0.017612 14.053064 0
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-1.395634 4.662541 1
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-0.752157 6.538620 0
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-1.322371 7.152853 0
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0.423363 11.054677 0
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0.406704 7.067335 1
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0.667394 12.741452 0
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-2.460150 6.866805 1
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0.569411 9.548755 0
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-0.026632 10.427743 0
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0.850433 6.920334 1
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1.347183 13.175500 0
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1.176813 3.167020 1
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-1.781871 9.097953 0
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-0.566606 5.749003 1
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0.931635 1.589505 1
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-0.024205 6.151823 1
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-0.036453 2.690988 1
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-0.196949 0.444165 1
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1.014459 5.754399 1
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1.985298 3.230619 1
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-1.693453 -0.557540 1
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-0.576525 11.778922 0
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||||
-0.346811 -1.678730 1
|
||||
-2.124484 2.672471 1
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||||
1.217916 9.597015 0
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||||
-0.733928 9.098687 0
|
||||
-3.642001 -1.618087 1
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0.315985 3.523953 1
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||||
1.416614 9.619232 0
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||||
-0.386323 3.989286 1
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||||
0.556921 8.294984 1
|
||||
1.224863 11.587360 0
|
||||
-1.347803 -2.406051 1
|
||||
1.196604 4.951851 1
|
||||
0.275221 9.543647 0
|
||||
0.470575 9.332488 0
|
||||
-1.889567 9.542662 0
|
||||
-1.527893 12.150579 0
|
||||
-1.185247 11.309318 0
|
||||
-0.445678 3.297303 1
|
||||
1.042222 6.105155 1
|
||||
-0.618787 10.320986 0
|
||||
1.152083 0.548467 1
|
||||
0.828534 2.676045 1
|
||||
-1.237728 10.549033 0
|
||||
-0.683565 -2.166125 1
|
||||
0.229456 5.921938 1
|
||||
-0.959885 11.555336 0
|
||||
0.492911 10.993324 0
|
||||
0.184992 8.721488 0
|
||||
-0.355715 10.325976 0
|
||||
-0.397822 8.058397 0
|
||||
0.824839 13.730343 0
|
||||
1.507278 5.027866 1
|
||||
0.099671 6.835839 1
|
||||
-0.344008 10.717485 0
|
||||
1.785928 7.718645 1
|
||||
-0.918801 11.560217 0
|
||||
-0.364009 4.747300 1
|
||||
-0.841722 4.119083 1
|
||||
0.490426 1.960539 1
|
||||
-0.007194 9.075792 0
|
||||
0.356107 12.447863 0
|
||||
0.342578 12.281162 0
|
||||
-0.810823 -1.466018 1
|
||||
2.530777 6.476801 1
|
||||
1.296683 11.607559 0
|
||||
0.475487 12.040035 0
|
||||
-0.783277 11.009725 0
|
||||
0.074798 11.023650 0
|
||||
-1.337472 0.468339 1
|
||||
-0.102781 13.763651 0
|
||||
-0.147324 2.874846 1
|
||||
0.518389 9.887035 0
|
||||
1.015399 7.571882 0
|
||||
-1.658086 -0.027255 1
|
||||
1.319944 2.171228 1
|
||||
2.056216 5.019981 1
|
||||
-0.851633 4.375691 1
|
||||
-1.510047 6.061992 0
|
||||
-1.076637 -3.181888 1
|
||||
1.821096 10.283990 0
|
||||
3.010150 8.401766 1
|
||||
-1.099458 1.688274 1
|
||||
-0.834872 -1.733869 1
|
||||
-0.846637 3.849075 1
|
||||
1.400102 12.628781 0
|
||||
1.752842 5.468166 1
|
||||
0.078557 0.059736 1
|
||||
0.089392 -0.715300 1
|
||||
1.825662 12.693808 0
|
||||
0.197445 9.744638 0
|
||||
0.126117 0.922311 1
|
||||
-0.679797 1.220530 1
|
||||
0.677983 2.556666 1
|
||||
0.761349 10.693862 0
|
||||
-2.168791 0.143632 1
|
||||
1.388610 9.341997 0
|
||||
0.317029 14.739025 0
|
||||
Reference in New Issue
Block a user