线性回归（非矩阵实现）

Posted 2022-01-18 liualex1109

1 import numpy as np
2 import pandas as pd

#读取数据
points = np.genfromtxt(‘data.csv‘,dtype=np.double,delimiter=",")
print(points)

[[ 32.50234527  31.70700585]
 [ 53.42680403  68.77759598]
 [ 61.53035803  62.5623823 ]
 [ 47.47563963  71.54663223]
 [ 59.81320787  87.23092513]
 [ 55.14218841  78.21151827]
 [ 52.21179669  79.64197305]
 [ 39.29956669  59.17148932]
 [ 48.10504169  75.3312423 ]
 [ 52.55001444  71.30087989]
 [ 45.41973014  55.16567715]
 [ 54.35163488  82.47884676]
 [ 44.1640495   62.00892325]
 [ 58.16847072  75.39287043]
 [ 56.72720806  81.43619216]
 [ 48.95588857  60.72360244]
 [ 44.68719623  82.89250373]
 [ 60.29732685  97.37989686]
 [ 45.61864377  48.84715332]
 [ 38.81681754  56.87721319]
 [ 66.18981661  83.87856466]
 [ 65.41605175 118.5912173 ]
 [ 47.48120861  57.25181946]
 [ 41.57564262  51.39174408]
 [ 51.84518691  75.38065167]
 [ 59.37082201  74.76556403]
 [ 57.31000344  95.45505292]
 [ 63.61556125  95.22936602]
 [ 46.73761941  79.05240617]
 [ 50.55676015  83.43207142]
 [ 52.22399609  63.35879032]
 [ 35.56783005  41.4128853 ]
 [ 42.43647694  76.61734128]
 [ 58.16454011  96.76956643]
 [ 57.50444762  74.08413012]
 [ 45.44053073  66.58814441]
 [ 61.89622268  77.76848242]
 [ 33.09383174  50.71958891]
 [ 36.43600951  62.12457082]
 [ 37.67565486  60.81024665]
 [ 44.55560838  52.68298337]
 [ 43.31828263  58.56982472]
 [ 50.07314563  82.90598149]
 [ 43.87061265  61.4247098 ]
 [ 62.99748075 115.2441528 ]
 [ 32.66904376  45.57058882]
 [ 40.16689901  54.0840548 ]
 [ 53.57507753  87.99445276]
 [ 33.86421497  52.72549438]
 [ 64.70713867  93.57611869]
 [ 38.11982403  80.16627545]
 [ 44.50253806  65.10171157]
 [ 40.59953838  65.56230126]
 [ 41.72067636  65.28088692]
 [ 51.08863468  73.43464155]
 [ 55.0780959   71.13972786]
 [ 41.37772653  79.10282968]
 [ 62.49469743  86.52053844]
 [ 49.20388754  84.74269781]
 [ 41.10268519  59.35885025]
 [ 41.18201611  61.68403752]
 [ 50.18638949  69.84760416]
 [ 52.37844622  86.09829121]
 [ 50.13548549  59.10883927]
 [ 33.64470601  69.89968164]
 [ 39.55790122  44.86249071]
 [ 56.13038882  85.49806778]
 [ 57.36205213  95.53668685]
 [ 60.26921439  70.25193442]
 [ 35.67809389  52.72173496]
 [ 31.588117    50.39267014]
 [ 53.66093226  63.64239878]
 [ 46.68222865  72.24725107]
 [ 43.10782022  57.81251298]
 [ 70.34607562 104.25710159]
 [ 44.49285588  86.64202032]
 [ 57.5045333   91.486778  ]
 [ 36.93007661  55.23166089]
 [ 55.80573336  79.55043668]
 [ 38.95476907  44.84712424]
 [ 56.9012147   80.20752314]
 [ 56.86890066  83.14274979]
 [ 34.3331247   55.72348926]
 [ 59.04974121  77.63418251]
 [ 57.78822399  99.05141484]
 [ 54.28232871  79.12064627]
 [ 51.0887199   69.58889785]
 [ 50.28283635  69.51050331]
 [ 44.21174175  73.68756432]
 [ 38.00548801  61.36690454]
 [ 32.94047994  67.17065577]
 [ 53.69163957  85.66820315]
 [ 68.76573427 114.85387123]
 [ 46.2309665   90.12357207]
 [ 68.31936082  97.91982104]
 [ 50.03017434  81.53699078]
 [ 49.23976534  72.11183247]
 [ 50.03957594  85.23200734]
 [ 48.14985889  66.22495789]
 [ 25.12848465  53.45439421]]

#定义损失函数 loss = ∑(y-*(wx-b))² / m
def get_loss_function_sum(w,b,points):
    totalError=0
    m = len(points)
    for i in range(m):
        x = points[i,0]
        y = points[i,1]
        totalError += (y - (w * x - b)) ** 2
    return totalError / m

#梯度下降 dw = ∑(y-(wx-b))*x / m, db = ∑(y-(wx-b)) / m
def gradient_descent(w_current,b_current,points,learning_rate):
    dw = 0
    db = 0
    m = len(points)
    for i in range(m):
        x = points[i,0]
        y = points[i,1]
        dw += -(2 / m) * x * (y - (w_current * x - b_current))
        db += -(2 / m) * (y - (w_current * x - b_current))
    w = w_current - (learning_rate * dw )
    b = b_current - (learning_rate * db )
    return w,b

def runner(w_start,b_start,points,learning_rate,itera_num):
    w = w_start
    b = b_start
    for i in range(itera_num):
        w,b = gradient_descent(w,b,points,learning_rate)
    return w,b

#注：learning rate要足够小
w,b = runner(0,0,points,0.0001,10000)
print("totalError:" + str(get_loss_function_sum(w,b,points)))

totalError:113.08177442339228

from matplotlib import pyplot as plt

points = np.array(points)
x = points[:,0]
y = points[:,1]
f = w * x + b
plt.title("data")
plt.xlabel("x")
plt.ylabel("y")
plt.scatter(x,y)#数据集
plt.plot(x,f)#拟合曲线
plt.show()