1 匯入numpy包
import numpy as np
2 sigmoid函式
def sigmoid(x):
return 1/(1+np.exp(-x))
demox = np.array([1,2,3])
print(sigmoid(demox))
#報錯
#demox = [1,2,3]
# print(sigmoid(demox))
結果：
[0.73105858 0.88079708 0.95257413]
3 定義邏輯迴歸模型主體
### 定義邏輯迴歸模型主體
def logistic(x, y, w, b):
# 訓練樣本量
num_train = x.shape[0]
# 邏輯迴歸模型輸出
y_hat = sigmoid(np.dot(x,w)+b)
# 交叉熵損失
cost = -1/(num_train)*(np.sum(y*np.log(y_hat)+(1-y)*np.log(1-y_hat)))
# 權值梯度
dW = np.dot(x.T,(y_hat-y))/num_train
# 偏置梯度
db = np.sum(y_hat- y)/num_train
# 壓縮損失陣列維度
cost = np.squeeze(cost)
return y_hat, cost, dW, db
4 初始化函式
def init_parm(dims):
w = np.zeros((dims,1))
b = 0
return w ,b
5 定義邏輯迴歸模型訓練過程
### 定義邏輯迴歸模型訓練過程
def logistic_train(X, y, learning_rate, epochs):
# 初始化模型引數
W, b = init_parm(X.shape[1])
cost_list = []
for i in range(epochs):
# 計算當前次的模型計算結果、損失和引數梯度
a, cost, dW, db = logistic(X, y, W, b)
# 引數更新
W = W -learning_rate * dW
b = b -learning_rate * db
if i % 100 == 0:
cost_list.append(cost)
if i % 100 == 0:
print('epoch %d cost %f' % (i, cost))
params = {
'W': W,
'b': b
}
grads = {
'dW': dW,
'db': db
}
return cost_list, params, grads
6 定義預測函式
def predict(X,params):
y_pred = sigmoid(np.dot(X,params['W'])+params['b'])
y_preds = [1 if y_pred[i]>0.5 else 0 for i in range(len(y_pred))]
return y_preds
7 生成資料
# 匯入matplotlib繪相簿
import matplotlib.pyplot as plt
# 匯入生成分類資料函式
from sklearn.datasets import make_classification
# 生成100*2的模擬二分類資料集
x ,label = make_classification(
n_samples=100,# 樣本個數
n_classes=2,# 樣本類別
n_features=2,#特徵個數
n_redundant=0,#冗餘特徵個數（有效特徵的隨機組合）
n_informative=2,#有效特徵，有價值特徵
n_repeated=0, # 重複特徵個數（有效特徵和冗餘特徵的隨機組合）
n_clusters_per_class=2 ,# 簇的個數
random_state=1,
)
print("x.shape =",x.shape)
print("label.shape = ",label.shape)
print("np.unique(label) =",np.unique(label))
print(set(label))
# 設定隨機數種子
rng = np.random.RandomState(2)
# 對生成的特徵資料新增一組均勻分佈噪聲https://blog.csdn.net/vicdd/article/details/52667709
x += 2*rng.uniform(size=x.shape)
# 標籤類別數
unique_label = set(label)
# 根據標籤類別數設定顏色
print(np.linspace(0,1,len(unique_label)))
colors = plt.cm.Spectral(np.linspace(0,1,len(unique_label)))
print(colors)
# 繪製模擬資料的散點圖
for k,col in zip(unique_label , colors):
x_k=x[label==k]
plt.plot(x_k[:,0],x_k[:,1],'o',markerfacecolor=col,markeredgecolor="k",
markersize=14)
plt.title('Simulated binary data set')
plt.show();
結果：
x.shape = (100, 2)
label.shape = (100,)
np.unique(label) = [0 1]
{0, 1}
[0. 1.]
[[0.61960784 0.00392157 0.25882353 1. ]
[0.36862745 0.30980392 0.63529412 1. ]]
複習
# 複習
mylabel = label.reshape((-1,1))
data = np.concatenate((x,mylabel),axis=1)
print(data.shape)
結果：
(100, 3)
8 劃分資料集
offset = int(x.shape[0]*0.7)
x_train, y_train = x[:offset],label[:offset].reshape((-1,1))
x_test, y_test = x[offset:],label[offset:].reshape((-1,1))
print(x_train.shape)
print(y_train.shape)
print(x_test.shape)
print(y_test.shape)
結果：
(70, 2)
(70, 1)
(30, 2)
(30, 1)
9 訓練
cost_list, params, grads = logistic_train(x_train, y_train, 0.01, 1000)
print(params['b'])
結果：
epoch 0 cost 0.693147
epoch 100 cost 0.568743
epoch 200 cost 0.496925
epoch 300 cost 0.449932
epoch 400 cost 0.416618
epoch 500 cost 0.391660
epoch 600 cost 0.372186
epoch 700 cost 0.356509
epoch 800 cost 0.343574
epoch 900 cost 0.332689
-0.6646648941379839
10 準確率計算
from sklearn.metrics import accuracy_score,classification_report
y_pred = predict(x_test,params)
print("y_pred = ",y_pred)
print(y_pred)
print(y_test.shape)
print(accuracy_score(y_pred,y_test)) #不需要都是1維的，貌似會自動squeeze()
print(classification_report(y_test,y_pred))
結果：
y_pred = [0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0]
[0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0]
(30, 1)
0.9333333333333333
precision recall f1-score support
0 0.92 0.92 0.92 12
1 0.94 0.94 0.94 18
accuracy 0.93 30
macro avg 0.93 0.93 0.93 30
weighted avg 0.93 0.93 0.93 30
11 繪製邏輯迴歸決策邊界
### 繪製邏輯迴歸決策邊界
def plot_logistic(X_train, y_train, params):
# 訓練樣本量
n = X_train.shape[0]
xcord1,ycord1,xcord2,ycord2 = [],[],[],[]
# 獲取兩類座標點並存入列表
for i in range(n):
if y_train[i] == 1:
xcord1.append(X_train[i][0])
ycord1.append(X_train[i][1])
else:
xcord2.append(X_train[i][0])
ycord2.append(X_train[i][1])
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(xcord1,ycord1,s = 30,c = 'red')
ax.scatter(xcord2,ycord2,s = 30,c = 'green')
# 取值範圍
x =np.arange(-1.5,3,0.1)
# 決策邊界公式
y = (-params['b'] - params['W'][0] * x) / params['W'][1]
# 繪圖
ax.plot(x, y)
plt.xlabel('X1')
plt.ylabel('X2')
plt.show()
plot_logistic(x_train, y_train, params)
結果：
11 sklearn實現
from sklearn.linear_model import LogisticRegression
clf = LogisticRegression(random_state=0).fit(x_train,y_train)
y_pred = clf.predict(x_test)
print(y_pred)
accuracy_score(y_test,y_pred)
結果：
[0 0 1 1 1 1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0]
0.9333333333333333