03-1 K-최근접 이웃 회귀
농어 데이터 준비 : 링크 텍스트
import numpy as np
perch_length = np.array([8.4, 13.7, 15.0, 16.2, 17.4, 18.0, 18.7, 19.0, 19.6, 20.0, 21.0,
21.0, 21.0, 21.3, 22.0, 22.0, 22.0, 22.0, 22.0, 22.5, 22.5, 22.7,
23.0, 23.5, 24.0, 24.0, 24.6, 25.0, 25.6, 26.5, 27.3, 27.5, 27.5,
27.5, 28.0, 28.7, 30.0, 32.8, 34.5, 35.0, 36.5, 36.0, 37.0, 37.0,
39.0, 39.0, 39.0, 40.0, 40.0, 40.0, 40.0, 42.0, 43.0, 43.0, 43.5,
44.0])
perch_weight = np.array([5.9, 32.0, 40.0, 51.5, 70.0, 100.0, 78.0, 80.0, 85.0, 85.0, 110.0,
115.0, 125.0, 130.0, 120.0, 120.0, 130.0, 135.0, 110.0, 130.0,
150.0, 145.0, 150.0, 170.0, 225.0, 145.0, 188.0, 180.0, 197.0,
218.0, 300.0, 260.0, 265.0, 250.0, 250.0, 300.0, 320.0, 514.0,
556.0, 840.0, 685.0, 700.0, 700.0, 690.0, 900.0, 650.0, 820.0,
850.0, 900.0, 1015.0, 820.0, 1100.0, 1000.0, 1100.0, 1000.0,
1000.0])
위 데이터 산점도
import matplotlib.pyplot as plt
plt.scatter(perch_length, perch_weight)
plt.xlabel('length')
plt.ylabel('weight')
plt.show()
길이에 따라 무게도 증가하는 특성을 띄고있음
훈련세트와 테스트세트 분리
from sklearn.model_selection import train_test_split
train_input, test_input, train_target, test_target = train_test_split(perch_length,perch_weight,random_state=42)
print('train_input : ',train_input,',',train_input.shape)
print('test_input : ',test_input,',',test_input.shape)
print('train_target : ',train_target,',',train_target.shape)
print('test_target : ',test_target,',',test_target.shape)
train_input : [19.6 22. 18.7 17.4 36. 25. 40. 39. 43. 22. 20. 22. 24. 27.5
43. 40. 24. 21. 27.5 40. 32.8 26.5 36.5 13.7 22.7 15. 37. 35.
28.7 23.5 39. 21. 23. 22. 44. 22.5 19. 37. 22. 25.6 42. 34.5] , (42,)
test_input : [ 8.4 18. 27.5 21.3 22.5 40. 30. 24.6 39. 21. 43.5 16.2 28. 27.3] , (14,)
train_target : [ 85. 135. 78. 70. 700. 180. 850. 820. 1000. 120. 85. 130.
225. 260. 1100. 900. 145. 115. 265. 1015. 514. 218. 685. 32.
145. 40. 690. 840. 300. 170. 650. 110. 150. 110. 1000. 150.
80. 700. 120. 197. 1100. 556.] , (42,)
test_target : [ 5.9 100. 250. 130. 130. 820. 320. 188. 900. 125.
1000. 51.5 250. 300. ] , (14,)
# =========== numpy 연습 =========== #
test_array = np.array([1,2,3,4])
# 형태 확인
print(test_array.shape) # (4,)배열
test_array2 = test_array.reshape(2,2) # (2,2)배열로 변환
print(test_array2.shape) #(2,2)배열
print(test_array2)
test_array3 = test_array.reshape(1,4)
print(test_array3.shape)
print(test_array3)
(4,)
(2, 2)
[[1 2]
[3 4]]
(1, 4)
[[1 2 3 4]]
train_input = train_input.reshape(-1,1)
test_input = test_input.reshape(-1,1)
print(train_input,'\n')
print(test_input,'\n')
print(train_input.shape, test_input.shape)
[[19.6]
[22. ]
[18.7]
[17.4]
[36. ]
[25. ]
[40. ]
[39. ]
[43. ]
[22. ]
[20. ]
[22. ]
[24. ]
[27.5]
[43. ]
[40. ]
[24. ]
[21. ]
[27.5]
[40. ]
[32.8]
[26.5]
[36.5]
[13.7]
[22.7]
[15. ]
[37. ]
[35. ]
[28.7]
[23.5]
[39. ]
[21. ]
[23. ]
[22. ]
[44. ]
[22.5]
[19. ]
[37. ]
[22. ]
[25.6]
[42. ]
[34.5]]
[[ 8.4]
[18. ]
[27.5]
[21.3]
[22.5]
[40. ]
[30. ]
[24.6]
[39. ]
[21. ]
[43.5]
[16.2]
[28. ]
[27.3]]
(42, 1) (14, 1)
결정계수(R^)
from sklearn.neighbors import KNeighborsRegressor
knr = KNeighborsRegressor()
knr.fit(train_input, train_target)
print(knr.score(test_input, test_target))
0.992809406101064
타깃과 예측의 절댓값 오차의 평균
from sklearn.metrics import mean_absolute_error
# 테스트 세트에 대한 에측을 만듭니다.
test_prediction = knr.predict(test_input)
# x테스트 세트에 대한 평균 절댓값 오차를 계산
mae = mean_absolute_error(test_target, test_prediction)
print('MAE : ',mae)
print('R^ : ', knr.score(train_input,train_target))
MAE : 19.157142857142862
R^ : 0.9698823289099254
# neighobrs 갯수 3
knr.n_neighbors = 3
# 모델 훈련
knr.fit(train_input,train_target)
print('R^ : ', knr.score(train_input,train_target))
R^ : 0.9804899950518966
print(knr.score(test_input,test_target))
0.9746459963987609
03-2 선형회귀
import numpy as np
perch_length = np.array([8.4, 13.7, 15.0, 16.2, 17.4, 18.0, 18.7, 19.0, 19.6, 20.0, 21.0,
21.0, 21.0, 21.3, 22.0, 22.0, 22.0, 22.0, 22.0, 22.5, 22.5, 22.7,
23.0, 23.5, 24.0, 24.0, 24.6, 25.0, 25.6, 26.5, 27.3, 27.5, 27.5,
27.5, 28.0, 28.7, 30.0, 32.8, 34.5, 35.0, 36.5, 36.0, 37.0, 37.0,
39.0, 39.0, 39.0, 40.0, 40.0, 40.0, 40.0, 42.0, 43.0, 43.0, 43.5,
44.0])
perch_weight = np.array([5.9, 32.0, 40.0, 51.5, 70.0, 100.0, 78.0, 80.0, 85.0, 85.0, 110.0,
115.0, 125.0, 130.0, 120.0, 120.0, 130.0, 135.0, 110.0, 130.0,
150.0, 145.0, 150.0, 170.0, 225.0, 145.0, 188.0, 180.0, 197.0,
218.0, 300.0, 260.0, 265.0, 250.0, 250.0, 300.0, 320.0, 514.0,
556.0, 840.0, 685.0, 700.0, 700.0, 690.0, 900.0, 650.0, 820.0,
850.0, 900.0, 1015.0, 820.0, 1100.0, 1000.0, 1100.0, 1000.0,
1000.0])
from sklearn.model_selection import train_test_split
train_input, test_input, train_target, test_target = train_test_split(perch_length,perch_weight,random_state=42)
train_input = train_input.reshape(-1,1)
test_input = test_input.reshape(-1,1)
from sklearn.neighbors import KNeighborsRegressor
knr = KNeighborsRegressor(n_neighbors=3)
knr.fit(train_input, train_target)
print(knr.predict([[50]]))
[1033.33333333]
import matplotlib.pyplot as plt
# 50cm 농어의 이웃 구하기
distances, indexes = knr.kneighbors([[50]])
# 훈련 세트의 산점도
plt.scatter(train_input, train_target)
# 훈련 세트 중에서 이웃 샘플만 다시 그리기
plt.scatter(train_input[indexes], train_target[indexes], marker='D')
#50cm 농어 데이터
plt.scatter(50, 1033, marker='^')
plt.xlabel('length')
plt.ylabel('weight')
plt.show()
print(np.mean(train_target[indexes]))
print(knr.predict([[100]]))
1033.3333333333333
[1033.33333333]
# 100cm 농어의 이웃 구하기
distances, indexes = knr.kneighbors([[100]])
# 훈련 세트의 산점도
plt.scatter(train_input, train_target)
# 훈련 세트 중에서 이웃 샘플만 다시 그리기
plt.scatter(train_input[indexes], train_target[indexes], marker='D')
#50cm 농어 데이터
plt.scatter(100, 1033, marker='^')
plt.xlabel('length')
plt.ylabel('weight')
plt.show()
from sklearn.linear_model import LinearRegression
lr = LinearRegression()
#선형 회귀 모델 훈련
lr.fit(train_input, train_target)
#50cm 농어 무게 예측
print(lr.predict([[50]]))
print('기울기 x : ',lr.coef_, ' y절편',lr.intercept_)
[1241.83860323]
기울기 x : [39.01714496] y절편 -709.0186449535474
학습한 직선 그리기
# 훈련 세트의 산점도
plt.scatter(train_input, train_target)
# 15 - 50 1차 방정식
plt.plot([15,50], [15*lr.coef_+lr.intercept_, 50*lr.coef_+lr.intercept_])
# 50cm 농어 데이터
plt.scatter(50, 1241, marker='^')
plt.xlabel('length')
plt.ylabel('weight')
plt.show()
다항회귀
# 데이터셋에 있는 모든 요소 제곱 **2
train_poly = np.column_stack((train_input ** 2, train_input))
test_poly = np.column_stack((test_input ** 2, test_input))
# 데이터셋 크기 확인
print(train_poly.shape, test_poly.shape)
print(train_poly,'\n',test_poly)
(42, 2) (14, 2)
[[ 384.16 19.6 ]
[ 484. 22. ]
[ 349.69 18.7 ]
[ 302.76 17.4 ]
[1296. 36. ]
[ 625. 25. ]
[1600. 40. ]
[1521. 39. ]
[1849. 43. ]
[ 484. 22. ]
[ 400. 20. ]
[ 484. 22. ]
[ 576. 24. ]
[ 756.25 27.5 ]
[1849. 43. ]
[1600. 40. ]
[ 576. 24. ]
[ 441. 21. ]
[ 756.25 27.5 ]
[1600. 40. ]
[1075.84 32.8 ]
[ 702.25 26.5 ]
[1332.25 36.5 ]
[ 187.69 13.7 ]
[ 515.29 22.7 ]
[ 225. 15. ]
[1369. 37. ]
[1225. 35. ]
[ 823.69 28.7 ]
[ 552.25 23.5 ]
[1521. 39. ]
[ 441. 21. ]
[ 529. 23. ]
[ 484. 22. ]
[1936. 44. ]
[ 506.25 22.5 ]
[ 361. 19. ]
[1369. 37. ]
[ 484. 22. ]
[ 655.36 25.6 ]
[1764. 42. ]
[1190.25 34.5 ]]
[[ 70.56 8.4 ]
[ 324. 18. ]
[ 756.25 27.5 ]
[ 453.69 21.3 ]
[ 506.25 22.5 ]
[1600. 40. ]
[ 900. 30. ]
[ 605.16 24.6 ]
[1521. 39. ]
[ 441. 21. ]
[1892.25 43.5 ]
[ 262.44 16.2 ]
[ 784. 28. ]
[ 745.29 27.3 ]]
모델 다시 훈련
lr = LinearRegression()
lr.fit(train_poly, train_target)
print(lr.predict([[50**2, 50]])) # 다항회귀에서 예측하기 위해 똑같이 제곱해준다.
print('x기울기 : ',lr.coef_, ' y절편 : ',lr.intercept_)
# 다항회귀식
print('무게 = ',lr.coef_[0],'* X^ ',lr.coef_[1],' * X +',lr.intercept_)
[1573.98423528]
x기울기 : [ 1.01433211 -21.55792498] y절편 : 116.05021078278264
무게 = 1.0143321093767304 * X^ -21.557924978837356 * X + 116.05021078278264
point = np.arange(15,50)
# 산점도 그리기
plt.scatter(train_input, train_target)
# 그래프 그리기 : 다항회귀(2차원 그래프)
plt.plot(point, 1.01*point**2 - 21.6*point + 116.05)
# 50cm 농어 데이터
plt.scatter([50],[1574], marker='^')
plt.show
print(lr.score(train_poly, train_target))
print(lr.score(test_poly, test_target))
0.9706807451768623
0.9775935108325121
03-3 특성 공학과 규제
다중회귀
# 데이터 준비
import pandas as pd
df = pd.read_csv('https://bit.ly/perch_csv_data')
perch_full = df.to_numpy()
print(perch_full)
[[ 8.4 2.11 1.41]
[13.7 3.53 2. ]
[15. 3.82 2.43]
[16.2 4.59 2.63]
[17.4 4.59 2.94]
[18. 5.22 3.32]
[18.7 5.2 3.12]
[19. 5.64 3.05]
[19.6 5.14 3.04]
[20. 5.08 2.77]
[21. 5.69 3.56]
[21. 5.92 3.31]
[21. 5.69 3.67]
[21.3 6.38 3.53]
[22. 6.11 3.41]
[22. 5.64 3.52]
[22. 6.11 3.52]
[22. 5.88 3.52]
[22. 5.52 4. ]
[22.5 5.86 3.62]
[22.5 6.79 3.62]
[22.7 5.95 3.63]
[23. 5.22 3.63]
[23.5 6.28 3.72]
[24. 7.29 3.72]
[24. 6.38 3.82]
[24.6 6.73 4.17]
[25. 6.44 3.68]
[25.6 6.56 4.24]
[26.5 7.17 4.14]
[27.3 8.32 5.14]
[27.5 7.17 4.34]
[27.5 7.05 4.34]
[27.5 7.28 4.57]
[28. 7.82 4.2 ]
[28.7 7.59 4.64]
[30. 7.62 4.77]
[32.8 10.03 6.02]
[34.5 10.26 6.39]
[35. 11.49 7.8 ]
[36.5 10.88 6.86]
[36. 10.61 6.74]
[37. 10.84 6.26]
[37. 10.57 6.37]
[39. 11.14 7.49]
[39. 11.14 6. ]
[39. 12.43 7.35]
[40. 11.93 7.11]
[40. 11.73 7.22]
[40. 12.38 7.46]
[40. 11.14 6.63]
[42. 12.8 6.87]
[43. 11.93 7.28]
[43. 12.51 7.42]
[43.5 12.6 8.14]
[44. 12.49 7.6 ]]
import numpy as np
perch_weight = np.array([5.9, 32.0, 40.0, 51.5, 70.0, 100.0, 78.0, 80.0, 85.0, 85.0, 110.0,
115.0, 125.0, 130.0, 120.0, 120.0, 130.0, 135.0, 110.0, 130.0,
150.0, 145.0, 150.0, 170.0, 225.0, 145.0, 188.0, 180.0, 197.0,
218.0, 300.0, 260.0, 265.0, 250.0, 250.0, 300.0, 320.0, 514.0,
556.0, 840.0, 685.0, 700.0, 700.0, 690.0, 900.0, 650.0, 820.0,
850.0, 900.0, 1015.0, 820.0, 1100.0, 1000.0, 1100.0, 1000.0,
1000.0])
from sklearn.model_selection import train_test_split
train_input, test_input, train_target, test_target = train_test_split(perch_full,perch_weight,random_state=42)
from sklearn.preprocessing import PolynomialFeatures
poly = PolynomialFeatures(include_bias=False)
poly.fit([[2,3]])
print(poly.transform([[2,3]]))
[[2. 3. 4. 6. 9.]]
poly = PolynomialFeatures(include_bias=False)
poly.fit(train_input)
train_poly = poly.transform(train_input)
print(train_poly.shape)
poly.get_feature_names()
test_poly = poly.transform(test_input)
(42, 9)
from sklearn.linear_model import LinearRegression
lr = LinearRegression()
lr.fit(train_poly, train_target)
print(lr.score(train_poly, train_target))
print(lr.score(test_poly, test_target))
0.9903183436982124
0.9714559911594218
특성(Features)의 개수를 늘려보면?
poly = PolynomialFeatures(degree=5, include_bias=False)
poly.fit(train_input)
train_poly = poly.transform(train_input)
test_poly = poly.transform(test_input)
print(train_poly.shape)
(42, 55)
선형회귀 결과 학습데이터 : 점수 높음 테스트데이터:낮은 점수
과대적합 발생 < 이를 해결하기 위하여
lr.fit(train_poly, train_target)
print(lr.score(train_poly, train_target))
print(lr.score(test_poly, test_target))
0.9999999999997731
-144.404886087405
규제
from sklearn.preprocessing import StandardScaler
ss = StandardScaler()
ss.fit(train_poly)
train_scaled = ss.transform(train_poly)
test_scaled = ss.transform(test_poly)
릿지 회귀
from sklearn.linear_model import Ridge
ridge = Ridge()
ridge.fit(train_scaled, train_target)
print(ridge.score(train_scaled, train_target))
print(ridge.score(test_scaled, test_target))
0.9896101671037343
0.9790693977615389
import matplotlib.pyplot as plt
train_score = []
test_score = []
alpha_list = [0.001,0.01,0.1,1,10,100]
for alpha in alpha_list:
# 릿지 모델 생성
ridge = Ridge(alpha=alpha)
# 릿지 모델 훈련
ridge.fit(train_scaled, train_target)
# 훈련 점수와 테스트 점수 저장
train_score.append(ridge.score(train_scaled, train_target))
test_score.append(ridge.score(test_scaled, test_target))
적절한 alpha값 찾기 = 두 그래프간 간격이 가장 짧은 alpha값
plt.plot(np.log10(alpha_list), train_score)
plt.plot(np.log10(alpha_list), test_score)
plt.xlabel('alpha')
plt.ylabel('R^2')
plt.show()
ridge = Ridge(alpha=0.1)
ridge.fit(train_scaled, train_target)
print(ridge.score(train_scaled, train_target))
print(ridge.score(test_scaled, test_target))
0.9903815817570372
0.9827976465386934
라쏘회귀
from sklearn.linear_model import Lasso
lasso = Lasso()
lasso.fit(train_scaled, train_target)
print(lasso.score(train_scaled, train_target))
print(lasso.score(test_scaled, test_target))
0.989789897208096
0.9800593698421884
x축을 log스케일로 변환하여 그래프 그리기 적절한 alpha값 분석
import matplotlib.pyplot as plt
train_score = []
test_score = []
alpha_list = [0.001,0.01,0.1,1,10,100]
for alpha in alpha_list:
# 릿지 모델 생성
lasso = Lasso(alpha=alpha)
# 릿지 모델 훈련
lasso.fit(train_scaled, train_target)
# 훈련 점수와 테스트 점수 저장
train_score.append(lasso.score(train_scaled, train_target))
test_score.append(lasso.score(test_scaled, test_target))
plt.plot(np.log10(alpha_list), train_score)
plt.plot(np.log10(alpha_list), test_score)
plt.xlabel('alpha')
plt.ylabel('R^2')
plt.show()
C:\Python\Python37\lib\site-packages\sklearn\linear_model\_coordinate_descent.py:532: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 23364.075969939804, tolerance: 518.2793833333334
positive)
C:\Python\Python37\lib\site-packages\sklearn\linear_model\_coordinate_descent.py:532: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 20251.975097475428, tolerance: 518.2793833333334
positive)
C:\Python\Python37\lib\site-packages\sklearn\linear_model\_coordinate_descent.py:532: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 806.237092633397, tolerance: 518.2793833333334
positive)
lasso = Lasso(alpha=10)
lasso.fit(train_scaled, train_target)
print(lasso.score(train_scaled, train_target))
print(lasso.score(test_scaled, test_target))
print(np.sum(lasso.coef_ == 0))
0.9888067471131867
0.9824470598706695
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