import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
from sklearn.linear_model import LinearRegression
# 一元二次
# f(x) = w1*x**2 + w2*x + b
# 二元一次
# f(x1,x2) = w1*x1 + w2*x2 + b
X = np.linspace(0,10,num = 500).reshape(-1,1)
X = np.concatenate([X**2,X],axis = 1)
X
w = np.random.randint(1,10,size = 2)
b = np.random.randint(-5,5,size = 1)
# 矩阵乘法
y = X.dot(w) + b
plt.plot(X[:,1],y,color = 'r')
plt.title('w1:%d.w2:%d.b:%d'%(w[0],w[1],b[0]))
Text(0.5, 1.0, 'w1:2.w2:5.b:3')
[外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-cLwuuLIQ-1574861729760)(output_2_1.png)]
使用sklearn自带的算法,预测
lr = LinearRegression()
lr.fit(X,y)
print(lr.coef_,lr.intercept_)
plt.scatter(X[:,1],y,marker = '*')
x = np.linspace(-2,12,100)
plt.plot(x,2*x**2 + 5*x + 3,color = 'green')
[2. 5.] 2.9999999999999716
[<matplotlib.lines.Line2D at 0x1dad7f59a20>]
[外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-ACS4T6yL-1574861729762)(output_4_2.png)]
自己手写的线性回归,拟合多属性,多元方程
# epoch 训练的次数,梯度下降训练多少
def gradient_descent(X,y,lr,epoch,w,b):
# 一批量多少,长度
batch = len(X)
for i in range(epoch):
# d_loss:是损失的梯度
d_loss = 0
# 梯度,斜率梯度
dw = [0 for _ in range(len(w))]
# 截距梯度
db = 0
for j in range(batch):
y_ = 0 #预测的值 预测方程 y_ = f(x) = w1*x1 + w2*x2 + b
for n in range(len(w)):
y_ += X[j][n]*w[n]
y_ += b
# (y - y_)**2 -----> 2*(y-y_)*(-1)
# (y_- y)**2 -----> 2*(y_ - y)*(1)
d_loss = -(y[j] - y_)
for n in range(len(w)):
dw[n] += X[j][n]*d_loss/float(batch)
db += 1*d_loss/float(batch)
# 更新一下系数和截距,梯度下降
for n in range(len(w)):
w[n] -= dw[n]*lr[n]
b -= db*lr[0]
return w,b
lr = [0.0001,0.0001]
w = np.random.randn(2)
b = np.random.randn(1)[0]
w_,b_ = gradient_descent(X,y,lr,5000,w,b)
print(w_,b_)
[2.27453115 2.68026281] 3.926330551786382
plt.scatter(X[:,1],y,marker = '*')
x = np.linspace(-2,12,100)
f = lambda x:w_[0]*x**2 + w_[1]*x + b_
plt.plot(x,f(x),color = 'green')
[<matplotlib.lines.Line2D at 0x1dad7f28c50>]
[外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-zJAETMva-1574861729763)(output_8_1.png)]