[置顶] 《统计学习方法》 逻辑斯谛回归(logistic regression) Python实现

今天看了一下《统计学习方法》里的逻辑斯谛回归，结合下《机器学习实战》里面的代码，很精炼。公式如下：

P(Y=1|x)=exp(w⋅x+b)1+exp(w⋅x+b)
P(Y=0|x)=1−P(Y=1|x)=11+exp(w⋅x+b)

先看下我加载数据的函数。

def loadDataSet(self, fileName = 'testSet.txt'):   #加载数据
        dataMat = []
        labelMat = []
        fr = open(fileName)
for line in fr.readlines(): #遍历文件
            lineArr = line.strip().split()
            dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])]) #数据集
            labelMat.append(int(lineArr[-1]))   #类别标签
return dataMat, labelMat

其中dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])])这句代码使将输入向量做了一个扩充，将1放在输入向量的末尾，变成 x=(x(1),x(2),x(3)⋯,x(n),1) ，然后将权值向量写成 w=(w(1),w(2),w(3)⋯,w(n),b) ，这样可以方便计算。
接下来看sigmoid函数，它的值域是[0, 1]。对应的就是刚才上面的第一个公式。如果写成扩充向量的形式的话，就是 P(Y=1|x)=exp(w⋅x)1+exp(w⋅x) 这个公式了（要同除以 exp(w⋅x) ）。

def sigmoid(self, inX):
return 1.0 / (1 + np.exp(-inX))

最后就是我们的训练的函数了。

def train(self, dataSet, labels):   #训练
        dataMat = np.mat(dataSet)   #将数据集转成矩阵的形式
        labelMat = np.mat(labels).transpose()#将类别集合转成矩阵的形式
        m, n = np.shape(dataSet)    #行列
        alpha = 0.01
        maxIter = 500
        weights = np.ones((n, 1))
for i in range(maxIter):    #迭代
            h = self.sigmoid(dataMat * weights)
            error = h - labelMat    #预测值和标签值所形成的误差
            weights = weights -  alpha * dataMat.transpose() * error    #权重的更新
return weights

这里使用了梯度下降算法来进行训练。
最后我们运行一下。

    logistic = Logistic()
    dataSet, labels = logistic.loadDataSet()
    weights = logistic.gradDescent(dataSet, labels)
    print weights

下面我贴出所有代码。

# --*-- coding:utf-8 --*--
import numpy as np

class Logistic:
def loadDataSet(self, fileName = 'testSet.txt'):   #加载数据
        dataMat = []
        labelMat = []
        fr = open(fileName)
for line in fr.readlines(): #遍历文件
            lineArr = line.strip().split()
            dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])]) #数据集
            labelMat.append(int(lineArr[-1]))   #类别标签
return dataMat, labelMat

def sigmoid(self, inX):
return 1.0 / (1 + np.exp(-inX))

def train(self, dataSet, labels):   #训练
        dataMat = np.mat(dataSet)   #将数据集转成矩阵的形式
        labelMat = np.mat(labels).transpose()#将类别集合转成矩阵的形式
        m, n = np.shape(dataSet)    #行列
        alpha = 0.01
        maxIter = 500
        weights = np.ones((n, 1))
for i in range(maxIter):    #迭代
            h = self.sigmoid(dataMat * weights)
            error = h - labelMat    #预测值和标签值所形成的误差
            weights = weights -  alpha * dataMat.transpose() * error    #权重的更新
return weights

if __name__ == '__main__':
    logistic = Logistic()
    dataSet, labels = logistic.loadDataSet()
    weights = logistic.train(dataSet, labels)
print weights

以及训练样本testSet.txt。

-0.017612 14.053064 0
-1.395634 4.662541 1
-0.752157 6.538620 0
-1.322371 7.152853 0
0.423363    11.054677   0
0.406704    7.067335    1
0.667394    12.741452   0
-2.460150 6.866805 1
0.569411    9.548755    0
-0.026632 10.427743 0
0.850433    6.920334    1
1.347183    13.175500   0
1.176813    3.167020    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 -0.557540 1
-0.576525 11.778922 0
-0.346811 -1.678730 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    11.587360   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