線性迴歸python及調用sklearn實現

最小二乘法的理解

線性迴歸的原理

import numpy as np
import matplotlib.pyplot as plt
data = np.genfromtxt("data.csv",delimiter=",")
x_data  = data[:,0]
y_data  = data[:,1]
print(x_data.shape)
print(y_data.shape)
plt.scatter(x_data,y_data)
plt.xlabel('this is x')
plt.ylabel('this is y')
plt.title('this is a demo')
plt.show()

最小二乘法及梯度下降實現：

#learning rate 
lr = 0.0001

#截距
b = 0  
#斜率
k = 0  
#最大迭代次數
epochs  = 50  

#最小二乘法
def compute_error(b,k,x_data,y_data):
    totalError =  0
    for i in range(0,len(x_data)):
        totalError += (y_data[i]-(k*x_data[i]+b))**2
    return totalError/float(len(x_data))/2.0

#梯度下降
def gradient_descent_runner(x_data,y_data,b,k,lr,epochs):
    m = float(len(x_data))
    for i in range(epochs):
        b_grad = 0
        k_grad = 0
        for j in range(0,len(x_data)):
            b_grad += (1/m)*(((k*x_data[i])+b)-y_data[j])
            k_grad += (1/m) * x_data[j] * (((k * x_data[j]) + b) - y_data[j])
        b = b-(lr*b_grad)
        k = k-(lr*k_grad)
    return b,k

開啓訓練

print("Starting b = {0}, k = {1}, error = {2}".format(b, k, compute_error(b, k, x_data, y_data)))
print("Running...")
b, k = gradient_descent_runner(x_data, y_data, b, k, lr, epochs)
print("After {0} iterations b = {1}, k = {2}, error = {3}".format(epochs, b, k, compute_error(b, k, x_data, y_data)))

#畫圖
plt.plot(x_data, y_data, 'b.')
plt.plot(x_data, k*x_data + b, 'r')
plt.show()

用sklearn實現使一元線性迴歸

from sklearn.linear_model import LinearRegression
x_data2 = data[:,0,np.newaxis]
y_data2 = data[:,1,np.newaxis]
# 創建並擬合模型
model = LinearRegression()
model.fit(x_data2, y_data2)
# 畫圖
plt.plot(x_data2, y_data2, 'b.')
plt.plot(x_data2, model.predict(x_data2), 'r')
plt.show()

多元線性迴歸sklearn實現

#!/usr/bin/env python
# coding: utf-8

import numpy as np
from numpy import genfromtxt
from sklearn import linear_model
import matplotlib.pyplot as plt  
from mpl_toolkits.mplot3d import Axes3D  

# 讀入數據 
data = genfromtxt(r"Delivery.csv",delimiter=',')
print(data)


# 切分數據
x_data = data[:,:-1]
y_data = data[:,-1]
print(x_data)
print(y_data)


# 創建模型
model = linear_model.LinearRegression()
model.fit(x_data, y_data)

# 係數
print("coefficients:",model.coef_)

# 截距
print("intercept:",model.intercept_)

# 測試
x_test = [[102,4]]
predict = model.predict(x_test)
print("predict:",predict)

ax = plt.figure().add_subplot(111, projection = '3d') 
ax.scatter(x_data[:,0], x_data[:,1], y_data, c = 'r', marker = 'o', s = 100) #點爲紅色三角形  
x0 = x_data[:,0]
x1 = x_data[:,1]
# 生成網格矩陣
x0, x1 = np.meshgrid(x0, x1)
#特徵值                      特徵0                特徵1
z = model.intercept_ + x0*model.coef_[0] + x1*model.coef_[1]
# 畫3D圖
ax.plot_surface(x0, x1, z)
#設置座標軸  
ax.set_xlabel('Miles')  
ax.set_ylabel('Num of Deliveries')  
ax.set_zlabel('Time')  
  
#顯示圖像  
plt.show()  

代碼鏈接