机器学习之监督学习--（分类）逻辑回归
注：数据集放在文章末尾
（1）逻辑回归 —— 梯度下降法
import matplotlib.pyplot as plt
import numpy as np
from sklearn.metrics import classification_report
from sklearn import preprocessing
# 数据是否需要标准化
scale = True
# 载入数据
data = np.genfromtxt("LR-testSet.csv", delimiter=",")
x_data = data[:,:-1]
y_data = data[:,-1]
def plot():
x0 = []
x1 = []
y0 = []
y1 = []
# 切分不同类别的数据
for i in range(len(x_data)):
if y_data[i]==0:
x0.append(x_data[i,0])
y0.append(x_data[i,1])
else:
x1.append(x_data[i,0])
y1.append(x_data[i,1])
# 画图
scatter0 = plt.scatter(x0, y0, c='b', marker='o')
scatter1 = plt.scatter(x1, y1, c='r', marker='x')
#画图例
plt.legend(handles=[scatter0,scatter1],labels=['label0','label1'],loc='best')
plot()
plt.show()
输出：
# 数据处理，添加偏置项
x_data = data[:,:-1]
y_data = data[:,-1,np.newaxis]
print(np.mat(x_data).shape)
print(np.mat(y_data).shape)
# 给样本添加偏置项
X_data = np.concatenate((np.ones((100,1)),x_data),axis=1)
print(X_data.shape)
输出：
def sigmoid(x):
return 1.0/(1+np.exp(-x))
def cost(xMat, yMat, ws):
left = np.multiply(yMat, np.log(sigmoid(xMat*ws)))
right = np.multiply(1 - yMat, np.log(1 - sigmoid(xMat*ws)))
return np.sum(left + right) / -(len(xMat))
def gradAscent(xArr, yArr):
if scale == True:
xArr = preprocessing.scale(xArr)
xMat = np.mat(xArr)
yMat = np.mat(yArr)
lr = 0.001
epochs = 10000
costList = []
# 计算数据行列数
# 行代表数据个数，列代表权值个数
m,n = np.shape(xMat)
# 初始化权值
ws = np.mat(np.ones((n,1)))
for i in range(epochs+1):
# xMat和weights矩阵相乘
h = sigmoid(xMat*ws)
# 计算误差
ws_grad = xMat.T*(h - yMat)/m
ws = ws - lr*ws_grad
if i % 50 == 0:
costList.append(cost(xMat,yMat,ws))
return ws,costList
# 训练模型，得到权值和cost值的变化
ws,costList = gradAscent(X_data, y_data)
print(ws)
输出：
if scale == False:
# 画图决策边界
plot()
x_test = [[-4],[3]]
y_test = (-ws[0] - x_test*ws[1])/ws[2]
plt.plot(x_test, y_test, 'k')
plt.show()
# 画图 loss值的变化
x = np.linspace(0,10000,201)
plt.plot(x, costList, c='r')
plt.title('Train')
plt.xlabel('Epochs')
plt.ylabel('Cost')
plt.show()
输出：
# 预测
def predict(x_data, ws):
if scale == True:
x_data = preprocessing.scale(x_data)
xMat = np.mat(x_data)
ws = np.mat(ws)
return [1 if x >= 0.5 else 0 for x in sigmoid(xMat*ws)]
predictions = predict(X_data, ws)
print(classification_report(y_data, predictions))
输出：
（2）逻辑回归 —— sklearn
import matplotlib.pyplot as plt
import numpy as np
from sklearn.metrics import classification_report
from sklearn import preprocessing
from sklearn import linear_model
# 数据是否需要标准化
scale = False
# 载入数据
data = np.genfromtxt("LR-testSet.csv", delimiter=",")
x_data = data[:,:-1]
y_data = data[:,-1]
def plot():
x0 = []
x1 = []
y0 = []
y1 = []
# 切分不同类别的数据
for i in range(len(x_data)):
if y_data[i]==0:
x0.append(x_data[i,0])
y0.append(x_data[i,1])
else:
x1.append(x_data[i,0])
y1.append(x_data[i,1])
# 画图
scatter0 = plt.scatter(x0, y0, c='b', marker='o')
scatter1 = plt.scatter(x1, y1, c='r', marker='x')
#画图例
plt.legend(handles=[scatter0,scatter1],labels=['label0','label1'],loc='best')
plot()
plt.show()
输出：
logistic = linear_model.LogisticRegression()
logistic.fit(x_data, y_data)
if scale == False:
# 画图决策边界
plot()
x_test = np.array([[-4],[3]])
y_test = (-logistic.intercept_ - x_test*logistic.coef_[0][0])/logistic.coef_[0][1]
plt.plot(x_test, y_test, 'k')
plt.show()
输出：
predictions = logistic.predict(x_data)
print(classification_report(y_data, predictions))
输出：
数据集：“LR-testSet.csv”：
-0.017612,14.053064,0
-1.395634,4.662541,1
-0.752157,6.53862,0
-1.322371,7.152853,0
0.423363,11.054677,0
0.406704,7.067335,1
0.667394,12.741452,0
-2.46015,6.866805,1
0.569411,9.548755,0
-0.026632,10.427743,0
0.850433,6.920334,1
1.347183,13.1755,0
1.176813,3.16702,1
-1.781871,9.097953,0
-0.566606,5.749003,1
0.931635,1.589505,1
-0.024205,6.151823,1
-0.036453,2.690988,1
-0.196949,0.444165,1
1.014459,5.754399,1
1.985298,3.230619,1
-1.693453,-0.55754,1
-0.576525,11.778922,0
-0.346811,-1.67873,1
-2.124484,2.672471,1
1.217916,9.597015,0
-0.733928,9.098687,0
-3.642001,-1.618087,1
0.315985,3.523953,1
1.416614,9.619232,0
-0.386323,3.989286,1
0.556921,8.294984,1
1.224863,11.58736,0
-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
-0.364009,4.7473,1
-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
0.074798,11.02365,0
-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
1.821096,10.28399,0
3.01015,8.401766,1
-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,-0.7153,1
1.825662,12.693808,0
0.197445,9.744638,0
0.126117,0.922311,1
-0.679797,1.22053,1
0.677983,2.556666,1
0.761349,10.693862,0
-2.168791,0.143632,1
1.38861,9.341997,0
0.317029,14.739025,0