[딥러닝] 다항회귀

다항회귀

 

선형회귀 모델을 다항회귀로 변환

 

 * linear_reg10.py

import numpy as np
import matplotlib.pyplot as plt

x = np.array([1,2,3,4,5])
y = np.array([4,2,1,3,7])
plt.scatter(x, y) # 산포도
plt.show()

선형회귀 모델

from sklearn.linear_model import LinearRegression
x = x[:, np.newaxis] # 입력을 matrix로 주어야함으로 차원 확대
print(x)
'''
[[1]
 [2]
 [3]
 [4]
 [5]]
'''
model = LinearRegression().fit(x, y) # 선형회귀 모델
y_pred = model.predict(x) # 예측값
print(y_pred)
# [2.  2.7 3.4 4.1 4.8]

plt.scatter(x, y) # 산포도
plt.plot(x, y_pred, c='red') # 추세선 그래프
plt.show()

 

다항식 특징을 추가

# 비선형인 경우 다항식 특징을 추가해서 작업한다.
from sklearn.preprocessing import PolynomialFeatures
poly = PolynomialFeatures(degree=3, include_bias = False) # degree : 열 개수, include_bias : 편향
print(poly)
x2 = poly.fit_transform(x) # 특징 행렬 생성
print(x2)
'''
[[  1.   1.   1.]
 [  2.   4.   8.]
 [  3.   9.  27.]
 [  4.  16.  64.]
 [  5.  25. 125.]]
  ----제곱------>
'''

model2 = LinearRegression().fit(x2, y) # 선형회귀 모델
y_pred2 = model2.predict(x2) # 예측값
print(y_pred2)
# [4.04285714 1.82857143 1.25714286 2.82857143 7.04285714]

plt.scatter(x, y) # 산포도
plt.plot(x, y_pred2, c='red') # 추세선 그래프
plt.show()

---

선형회귀 모델을 다항회귀로 변환

 : 다항식 추가. 특징행렬 생성.

 

 * linear_reg11.py

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
from sklearn.metrics._regression import mean_squared_error, r2_score

x = np.array([258, 270, 294, 320, 342, 368, 396, 446, 480, 586])[:, np.newaxis]
print(x)
'''
[[258]
 [270]
 [294]
 [320]
 [342]
 [368]
 [396]
 [446]
 [480]
 [586]] 
'''
y = np.array([236, 234, 253, 298, 314, 342, 360, 368, 391, 390])

# 비교목적으로 일반회귀 모델 클래스와 다항식 모델 클래스
lr = LinearRegression()
pr = LinearRegression()
polyf = PolynomialFeatures(degree=2) # 특징 행렬 생성
x_quad = polyf.fit_transform(x)
print(x_quad)
'''
[[1.00000e+00 2.58000e+02 6.65640e+04]
 [1.00000e+00 2.70000e+02 7.29000e+04]
 [1.00000e+00 2.94000e+02 8.64360e+04]
'''
lr.fit(x, y)
x_fit = np.arange(250, 600, 10)[:, np.newaxis]
print(x_fit)
'''
[[250]
 [260]
 [270]
 [280]
 [290]
'''

y_lin_fit = lr.predict(x_fit)
print(y_lin_fit)
# [250.63869122 256.03244588 261.42620055 ...

pr.fit(x_quad, y)
y_quad_fit = pr.predict(polyf.fit_transform(x_fit))
print(y_quad_fit)
# [215.50100168 228.03388862 240.11490613 ...

# 시각화
plt.scatter(x, y, label='train points')
plt.plot(x_fit, y_lin_fit, label='linear fit', linestyle='--', c='red')
plt.plot(x_fit, y_quad_fit, label='quadratic fit', linestyle='-', c='blue')
plt.legend()
plt.show()
print()

# MSE(평균 제곱오차)와 R2(결정계수) 확인
y_lin_pred = lr.predict(x)
print('y_lin_pred :\n', y_lin_pred)
'''
 [254.95369495 261.42620055 274.37121174 288.39497387 300.26123414
 314.28499627 329.38750933 356.35628266 374.69504852 431.86884797]
'''
y_quad_pred = pr.predict(x_quad)
print('y_quad_pred :\n', y_quad_pred)
'''
 [225.56346079 240.11490613 267.26572086 293.74195218 313.75904653
 334.59594733 353.61955374 378.77882554 389.43443486 389.12615204]
'''

print('train MSE 비교 : 선형모델은 %.3f, 다항모델은 %.3f'%(mean_squared_error(y, y_lin_pred), mean_squared_error(y, y_quad_pred)))
# train MSE 비교 : 선형모델은 570.885, 다항모델은 58.294

print('train 결정계수 비교 : 선형모델은 %.3f, 다항모델은 %.3f'%(r2_score(y, y_lin_pred), r2_score(y, y_quad_pred)))
# train 결정계수 비교 : 선형모델은 0.831, 다항모델은 0.983