1.逻辑回归假设函数

2.成本函数

3.参数学习(梯度下降)

4.Python代码实现

```from sklearn.datasets import load_iris
import matplotlib.pyplot as plt
import numpy as np
data = iris.data
target = iris.target
#print data[:10]
#print target[10:]
X = data[0:100,[0,2]]
y = target[0:100]
print X[:5]
print y[-5:]
label = np.array(y)
index_0 = np.where(label==0)
plt.scatter(X[index_0,0],X[index_0,1], marker='x',color = 'b',label = '0',s = 15)
index_1 =np.where(label==1)
plt.scatter(X[index_1,0],X[index_1,1], marker='o',color = 'r',label = '1',s = 15)
plt.xlabel('X1')
plt.ylabel('X2')
plt.legend(loc = 'upper left')
plt.show()```

```import numpy as np
class logistic(object):
def __init__(self):
self.W = None
def train(self,X,y,learn_rate = 0.01,num_iters = 5000):
num_train,num_feature = X.shape
#init the weight
self.W = 0.001*np.random.randn(num_feature,1).reshape((-1,1))
loss = []
for i in range(num_iters):
error,dW = self.compute_loss(X,y)
self.W += -learn_rate*dW
loss.append(error)
if i%200==0:
print 'i=%d,error=%f' %(i,error)
return loss
def compute_loss(self,X,y):
num_train = X.shape[0]
h = self.output(X)
loss = -np.sum((y*np.log(h) + (1-y)*np.log((1-h))))
loss = loss / num_train
dW = X.T.dot((h-y)) / num_train
return loss,dW
def output(self,X):
g = np.dot(X,self.W)
return self.sigmod(g)
def sigmod(self,X):
return 1/(1+np.exp(-X))
def predict(self,X_test):
h = self.output(X_test)
y_pred = np.where(h>=0.5,1,0)
return y_pred```

``` import matplotlib.pyplot as plt
y = y.reshape((-1,1))
one = np.ones((X.shape[0],1))
X_train = np.hstack((one,X))
classify = logistic()
loss = classify.train(X_train,y)
print classify.W
plt.plot(loss)
plt.xlabel('Iteration number')
plt.ylabel('Loss value')
plt.show()```

``` label = np.array(y)
index_0 = np.where(label==0)
plt.scatter(X[index_0,0],X[index_0,1], marker='x',color = 'b',label = '0',s = 15)
index_1 =np.where(label==1)
plt.scatter(X[index_1,0],X[index_1,1], marker='o',color = 'r',label = '1',s = 15)
#show the decision boundary
x1 = np.arange(4,7.5,0.5)
x2 = (- classify.W[0] - classify.W[1]*x1) / classify.W[2]
plt.plot(x1,x2,color = 'black')
plt.xlabel('X1')
plt.ylabel('X2')
plt.legend(loc = 'upper left')
plt.show()```

ps:可以看出，最后学习得到的决策边界（分类边界）成功的隔开了两个类别。当然，分类问题还有多分类问题（一对多），还有就是对于非线性分类问题，详情请参见分享的资料。