Logistic Regression

LogisticRegression/data1.txt

@@ -0,0 +1,100 @@
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LogisticRegression/data2.txt

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LogisticRegression/logisticRegression.py

@@ -0,0 +1,153 @@
+#-*- coding: utf-8 -*-
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy import optimize
+from matplotlib.font_manager import FontProperties
+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
+
+
+def LogisticRegression():
+    data = loadtxtAndcsv_data("data2.txt", ",", np.float64) 
+    X = data[:,0:-1]
+    y = data[:,-1]
+
+    plot_data(X,y)  # 作图
+
+    X = mapFeature(X[:,0],X[:,1])           #映射为多项式
+    initial_theta = np.zeros((X.shape[1],1))#初始化theta
+    initial_lambda = 0.1                    #初始化正则化系数，一般取0.01,0.1,1.....
+
+    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
+
+    print J  #输出一下计算的值，应该为0.693147
+    # 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
+    '''调用scipy中的优化算法fmin_bfgs（拟牛顿法Broyden-Fletcher-Goldfarb-Shanno）
+    - costFunction是自己实现的一个求代价的函数，
+    - initial_theta表示初始化的值,
+    - fprime指定costFunction的梯度
+    - 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 
+    '''
+    result = optimize.fmin_bfgs(costFunction, initial_theta, fprime=gradient, args=(X,y,initial_lambda))    
+    p = predict(X, result)   #预测
+    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   
+
+    X = data[:,0:-1]
+    y = data[:,-1]    
+    plotDecisionBoundary(result,X,y)    #画决策边界  
+
+
+
+# 加载txt和csv文件
+def loadtxtAndcsv_data(fileName,split,dataType):
+    return np.loadtxt(fileName,delimiter=split,dtype=dataType)
+
+# 加载npy文件
+def loadnpy_data(fileName):
+    return np.load(fileName)
+
+# 显示二维图形
+def plot_data(X,y):
+    pos = np.where(y==1)    #找到y==1的坐标位置
+    neg = np.where(y==0)    #找到y==0的坐标位置
+    #作图
+    plt.figure(figsize=(15,12))
+    plt.plot(X[pos,0],X[pos,1],'ro')        # red o
+    plt.plot(X[neg,0],X[neg,1],'bo')        # blue o
+    plt.title(u"两个类别散点图",fontproperties=font)
+    plt.show()
+
+# 映射为多项式 
+def mapFeature(X1,X2):
+    degree = 3;                     # 映射的最高次方
+    out = np.ones((X1.shape[0],1))  # 映射后的结果数组（取代X）
+    '''
+    这里以degree=2为例，映射为1,x1,x2,x1^2,x1,x2,x2^2
+    '''
+    for i in np.arange(1,degree+1): 
+        for j in range(i+1):
+            temp = X1**(i-j)*(X2**j)    #矩阵直接乘相当于matlab中的点乘.*
+            out = np.hstack((out, temp.reshape(-1,1)))
+    return out
+
+# 代价函数
+def costFunction(initial_theta,X,y,inital_lambda):
+    m = len(y)
+    J = 0
+
+    h = sigmoid(np.dot(X,initial_theta))    # 计算h(z)
+    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 
+    theta1[0] = 0   
+
+    temp = np.dot(np.transpose(theta1),theta1)
+    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
+    return J
+
+# 计算梯度
+def gradient(initial_theta,X,y,inital_lambda):
+    m = len(y)
+    grad = np.zeros((initial_theta.shape[0]))
+
+    h = sigmoid(np.dot(X,initial_theta))# 计算h(z)
+    theta1 = initial_theta.copy()
+    theta1[0] = 0
+
+    grad = np.dot(np.transpose(X),h-y)/m+inital_lambda/m*theta1 #正则化的梯度
+    return grad    
+
+# S型函数    
+def sigmoid(z):
+    h = np.zeros((len(z),1))    # 初始化，与z的长度一置
+
+    h = 1.0/(1+np.exp(-z))
+    return h
+
+
+#画决策边界
+def plotDecisionBoundary(theta,X,y):
+    pos = np.where(y==1)    #找到y==1的坐标位置
+    neg = np.where(y==0)    #找到y==0的坐标位置
+    #作图
+    plt.figure(figsize=(15,12))
+    plt.plot(X[pos,0],X[pos,1],'ro')        # red o
+    plt.plot(X[neg,0],X[neg,1],'bo')        # blue o
+    plt.title(u"决策边界",fontproperties=font)
+
+    #u = np.linspace(30,100,100)
+    #v = np.linspace(30,100,100)
+
+    u = np.linspace(-1,1.5,50)  #根据具体的数据，这里需要调整
+    v = np.linspace(-1,1.5,50)
+
+    z = np.zeros((len(u),len(v)))
+    for i in range(len(u)):
+        for j in range(len(v)):
+            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
+
+    z = np.transpose(z)
+    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
+    #plt.legend()
+    plt.show()
+
+# 预测
+def predict(X,theta):
+    m = X.shape[0]
+    p = np.zeros((m,1))
+    p = sigmoid(np.dot(X,theta))    # 预测的结果，是个概率值
+
+    for i in range(m):
+        if p[i] > 0.5:  #概率大于0.5预测为1，否则预测为0
+            p[i] = 1
+        else:
+            p[i] = 0
+    return p
+
+
+# 测试逻辑回归函数
+def testLogisticRegression():
+    LogisticRegression()
+
+
+if __name__ == "__main__":
+    testLogisticRegression()
+
+