diff --git a/LogisticRegression/data1.npy b/LogisticRegression/data1.npy new file mode 100644 index 0000000..a95550d Binary files /dev/null and b/LogisticRegression/data1.npy differ diff --git a/LogisticRegression/data1.txt b/LogisticRegression/data1.txt new file mode 100644 index 0000000..3a5f952 --- /dev/null +++ b/LogisticRegression/data1.txt @@ -0,0 +1,100 @@ +34.62365962451697,78.0246928153624,0 +30.28671076822607,43.89499752400101,0 +35.84740876993872,72.90219802708364,0 +60.18259938620976,86.30855209546826,1 +79.0327360507101,75.3443764369103,1 +45.08327747668339,56.3163717815305,0 +61.10666453684766,96.51142588489624,1 +75.02474556738889,46.55401354116538,1 +76.09878670226257,87.42056971926803,1 +84.43281996120035,43.53339331072109,1 +95.86155507093572,38.22527805795094,0 +75.01365838958247,30.60326323428011,0 +82.30705337399482,76.48196330235604,1 +69.36458875970939,97.71869196188608,1 +39.53833914367223,76.03681085115882,0 +53.9710521485623,89.20735013750205,1 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+90.44855097096364,87.50879176484702,1 +55.48216114069585,35.57070347228866,0 +74.49269241843041,84.84513684930135,1 +89.84580670720979,45.35828361091658,1 +83.48916274498238,48.38028579728175,1 +42.2617008099817,87.10385094025457,1 +99.31500880510394,68.77540947206617,1 +55.34001756003703,64.9319380069486,1 +74.77589300092767,89.52981289513276,1 diff --git a/LogisticRegression/data2.txt b/LogisticRegression/data2.txt new file mode 100644 index 0000000..a888992 --- /dev/null +++ b/LogisticRegression/data2.txt @@ -0,0 +1,118 @@ +0.051267,0.69956,1 +-0.092742,0.68494,1 +-0.21371,0.69225,1 +-0.375,0.50219,1 +-0.51325,0.46564,1 +-0.52477,0.2098,1 +-0.39804,0.034357,1 +-0.30588,-0.19225,1 +0.016705,-0.40424,1 +0.13191,-0.51389,1 +0.38537,-0.56506,1 +0.52938,-0.5212,1 +0.63882,-0.24342,1 +0.73675,-0.18494,1 +0.54666,0.48757,1 +0.322,0.5826,1 +0.16647,0.53874,1 +-0.046659,0.81652,1 +-0.17339,0.69956,1 +-0.47869,0.63377,1 +-0.60541,0.59722,1 +-0.62846,0.33406,1 +-0.59389,0.005117,1 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b/LogisticRegression/logisticRegression.py new file mode 100644 index 0000000..a117580 --- /dev/null +++ b/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() + +