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Logistic Regression
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‎LogisticRegression/data1.npy‎

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‎LogisticRegression/data1.txt‎

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‎LogisticRegression/data2.txt‎

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‎LogisticRegression/logisticRegression.py‎

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#-*- coding: utf-8 -*-
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import numpy as np
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import matplotlib.pyplot as plt
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from scipy import optimize
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from matplotlib.font_manager import FontProperties
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font = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=14) # 解决windows环境下画图汉字乱码问题
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def LogisticRegression():
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data = loadtxtAndcsv_data("data2.txt", ",", np.float64)
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X = data[:,0:-1]
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y = data[:,-1]
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plot_data(X,y) # 作图
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X = mapFeature(X[:,0],X[:,1]) #映射为多项式
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initial_theta = np.zeros((X.shape[1],1))#初始化theta
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initial_lambda = 0.1 #初始化正则化系数，一般取0.01,0.1,1.....
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J = costFunction(initial_theta,X,y,initial_lambda) #计算一下给定初始化的theta和lambda求出的代价J
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print J #输出一下计算的值，应该为0.693147
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# result = optimize.fmin(costFunction, initial_theta, args=(X,y,initial_lambda)) #直接使用最小化的方法，效果不好
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'''调用scipy中的优化算法fmin_bfgs（拟牛顿法Broyden-Fletcher-Goldfarb-Shanno）
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- costFunction是自己实现的一个求代价的函数，
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- initial_theta表示初始化的值,
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- fprime指定costFunction的梯度
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- args是其余测参数，以元组的形式传入，最后会将最小化costFunction的theta返回
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'''
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result = optimize.fmin_bfgs(costFunction, initial_theta, fprime=gradient, args=(X,y,initial_lambda))
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p = predict(X, result) #预测
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print u'在训练集上的准确度为%f%%'%np.mean(np.float64(p==y)*100) # 与真实值比较，p==y返回True，转化为float
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X = data[:,0:-1]
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y = data[:,-1]
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plotDecisionBoundary(result,X,y) #画决策边界
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# 加载txt和csv文件
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def loadtxtAndcsv_data(fileName,split,dataType):
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return np.loadtxt(fileName,delimiter=split,dtype=dataType)
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# 加载npy文件
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def loadnpy_data(fileName):
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return np.load(fileName)
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# 显示二维图形
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def plot_data(X,y):
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pos = np.where(y==1) #找到y==1的坐标位置
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neg = np.where(y==0) #找到y==0的坐标位置
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#作图
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plt.figure(figsize=(15,12))
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plt.plot(X[pos,0],X[pos,1],'ro') # red o
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plt.plot(X[neg,0],X[neg,1],'bo') # blue o
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plt.title(u"两个类别散点图",fontproperties=font)
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plt.show()
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# 映射为多项式
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def mapFeature(X1,X2):
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degree = 3; # 映射的最高次方
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out = np.ones((X1.shape[0],1)) # 映射后的结果数组（取代X）
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'''
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这里以degree=2为例，映射为1,x1,x2,x1^2,x1,x2,x2^2
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'''
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for i in np.arange(1,degree+1):
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for j in range(i+1):
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temp = X1**(i-j)*(X2**j) #矩阵直接乘相当于matlab中的点乘.*
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out = np.hstack((out, temp.reshape(-1,1)))
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return out
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# 代价函数
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def costFunction(initial_theta,X,y,inital_lambda):
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m = len(y)
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J = 0
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h = sigmoid(np.dot(X,initial_theta)) # 计算h(z)
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theta1 = initial_theta.copy() # 因为正则化j=1从1开始，不包含0，所以赋值一份，前theta(0)值为0
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theta1[0] = 0
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temp = np.dot(np.transpose(theta1),theta1)
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J = (-np.dot(np.transpose(y),np.log(h))-np.dot(np.transpose(1-y),np.log(1-h))+temp*inital_lambda/2)/m # 正则化的代价方程
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return J
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# 计算梯度
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def gradient(initial_theta,X,y,inital_lambda):
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m = len(y)
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grad = np.zeros((initial_theta.shape[0]))
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h = sigmoid(np.dot(X,initial_theta))# 计算h(z)
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theta1 = initial_theta.copy()
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theta1[0] = 0
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grad = np.dot(np.transpose(X),h-y)/m+inital_lambda/m*theta1 #正则化的梯度
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return grad
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# S型函数
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def sigmoid(z):
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h = np.zeros((len(z),1)) # 初始化，与z的长度一置
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h = 1.0/(1+np.exp(-z))
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return h
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#画决策边界
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def plotDecisionBoundary(theta,X,y):
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pos = np.where(y==1) #找到y==1的坐标位置
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neg = np.where(y==0) #找到y==0的坐标位置
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#作图
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plt.figure(figsize=(15,12))
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plt.plot(X[pos,0],X[pos,1],'ro') # red o
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plt.plot(X[neg,0],X[neg,1],'bo') # blue o
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plt.title(u"决策边界",fontproperties=font)
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#u = np.linspace(30,100,100)
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#v = np.linspace(30,100,100)
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u = np.linspace(-1,1.5,50) #根据具体的数据，这里需要调整
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v = np.linspace(-1,1.5,50)
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z = np.zeros((len(u),len(v)))
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for i in range(len(u)):
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for j in range(len(v)):
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z[i,j] = np.dot(mapFeature(u[i].reshape(1,-1),v[j].reshape(1,-1)),theta) # 计算对应的值，需要map
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z = np.transpose(z)
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plt.contour(u,v,z,[0,0.01],linewidth=2.0) # 画等高线，范围在[0,0.01]，即近似为决策边界
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#plt.legend()
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plt.show()
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# 预测
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def predict(X,theta):
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m = X.shape[0]
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p = np.zeros((m,1))
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p = sigmoid(np.dot(X,theta)) # 预测的结果，是个概率值
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for i in range(m):
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if p[i] > 0.5: #概率大于0.5预测为1，否则预测为0
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p[i] = 1
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else:
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p[i] = 0
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return p
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# 测试逻辑回归函数
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def testLogisticRegression():
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LogisticRegression()
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if __name__ == "__main__":
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testLogisticRegression()
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