logistic-regression

In [1]:

# Jupyter Notebook 환경 설정
from IPython.core.display import display, HTML
display(HTML(
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로지스틱 회귀¶

In [2]:

# 로지스틱 회귀(logistic regression)
# 다중 분류(multi-class classification0)
# Sigmoid 함수
# Softmax 함수

In [3]:

# 이진 분류 문제에서 클래스 확률 예측
# 7가지 생선에 대한 확률

In [4]:

import pandas as pd

In [6]:

fish = pd.read_csv("fish.csv")

In [7]:

fish.head()

Out[7]:

	Species	Weight	Length	Diagonal	Height	Width
0	Bream	242.0	25.4	30.0	11.5200	4.0200
1	Bream	290.0	26.3	31.2	12.4800	4.3056
2	Bream	340.0	26.5	31.1	12.3778	4.6961
3	Bream	363.0	29.0	33.5	12.7300	4.4555
4	Bream	430.0	29.0	34.0	12.4440	5.1340

In [8]:

print(pd.unique(fish['Species']))

['Bream' 'Roach' 'Whitefish' 'Parkki' 'Perch' 'Pike' 'Smelt']

In [12]:

fish_input = fish[['Weight', 'Length', 'Diagonal', 'Height', 'Width']].to_numpy()

In [13]:

print(fish_input[:5])

[[242.      25.4     30.      11.52     4.02  ]
 [290.      26.3     31.2     12.48     4.3056]
 [340.      26.5     31.1     12.3778   4.6961]
 [363.      29.      33.5     12.73     4.4555]
 [430.      29.      34.      12.444    5.134 ]]

In [11]:

fish_target = fish['Species'].to_numpy()

In [14]:

from sklearn.model_selection import train_test_split

In [15]:

train_input, test_input, train_target, test_target = train_test_split(fish_input, fish_target, random_state=42)

In [16]:

from sklearn.preprocessing import StandardScaler
ss = StandardScaler()
ss.fit(train_input)
train_scaled = ss.transform(train_input)
test_scaled = ss.transform(test_input)

In [17]:

from sklearn.neighbors import KNeighborsClassifier

In [18]:

kn = KNeighborsClassifier(n_neighbors=3)
kn.fit(train_scaled, train_target)
print(kn.score(train_scaled, train_target))
print(kn.score(test_scaled, test_target))

0.8907563025210085
0.85

In [19]:

print(kn.classes_)

['Bream' 'Parkki' 'Perch' 'Pike' 'Roach' 'Smelt' 'Whitefish']

In [22]:

print(kn.predict(test_scaled[:5]))

['Perch' 'Smelt' 'Pike' 'Perch' 'Perch']

In [23]:

import numpy as np

proba = kn.predict_proba(test_scaled[:5])  # 클래스 별 확률값을 리턴
print(np.round(proba, decimals=4))

[[0.     0.     1.     0.     0.     0.     0.    ]
 [0.     0.     0.     0.     0.     1.     0.    ]
 [0.     0.     0.     1.     0.     0.     0.    ]
 [0.     0.     0.6667 0.     0.3333 0.     0.    ]
 [0.     0.     0.6667 0.     0.3333 0.     0.    ]]

In [24]:

distances, indexes = kn.kneighbors(test_scaled[3:4])
print(train_target[indexes])

[['Roach' 'Perch' 'Perch']]

In [25]:

# 로지스틱 회귀: 분류 모델
# z = a * (Weight) + b * (Length) + c * (Diagonal) + d * (Height) + e * (Width) + f
# a, b, c, d, e : 계수
# 다중 회귀 선형 방정식과 동일

In [28]:

import numpy as np
import matplotlib.pyplot as plt

In [29]:

z = np.arange(-5, 5, 0.1)
phi = 1 / (1+np.exp(-z))

In [32]:

plt.plot(z, phi)
plt.xlabel('z')
plt.ylabel('phi')
plt.show()

In [33]:

char_array = np.array(['A', 'B','C','D','F'])
print(char_array[[True, False, True, False, False]])

['A' 'C']

In [34]:

bream_smelt_indexes = (train_target == 'Bream') | (train_target == 'Smelt')
train_bream_smelt = train_scaled[bream_smelt_indexes]
target_bream_smelt = train_target[bream_smelt_indexes]

In [35]:

print(train_bream_smelt)

[[ 0.91965782  0.60943175  0.81041221  1.85194896  1.00075672]
 [-1.0858536  -1.68646987 -1.70848587 -1.70159849 -2.0044758 ]
 [ 0.63818253  0.56257661  0.73223951  1.64473401  0.50705737]
 [ 0.30041219  0.23459067  0.42823457  1.36042157  0.22329758]
 [ 0.9027693   0.70314202  0.88858491  1.89027545  0.85537174]
 [-1.0824759  -1.61150165 -1.62162731 -1.7000674  -1.92815631]
 [ 0.10337949  0.04717013  0.23714575  0.88445197  0.41799764]
 [ 1.49668216  1.03112796  1.21864741  2.44274986  1.40289707]
 [ 0.23004337  0.23459067  0.42823457  1.3336029   0.39983213]
 [-0.42579405 -0.29018684 -0.11028847  0.65627104 -0.26107519]
 [ 1.28557569  0.70314202  0.89727076  1.98228866  1.06683526]
 [ 0.93373158  0.60943175  0.83646978  1.85150445  0.97832415]
 [ 0.80706771  0.60943175  0.81041221  1.63137406  1.0255057 ]
 [-1.07262426 -1.52716241 -1.55214047 -1.67235972 -1.86207776]
 [ 1.6374198   1.17169337  1.27076255  2.41341232  1.40143407]
 [-1.07966115 -1.63961473 -1.67374245 -1.6462819  -1.87036806]
 [-1.05151362 -1.33037084 -1.39579507 -1.47914678 -1.45146425]
 [ 0.15967454  0.11276732  0.29794674  1.17051775  0.29205828]
 [ 1.56705098  1.17169337  1.32287768  2.16352457  1.17174409]
 [-0.00921063  0.1408804   0.3240043   0.94026245  0.14734384]
 [ 0.15967454  0.1408804   0.33269016  1.26991474  0.24109734]
 [-0.14994827  0.32830094  0.52377898  1.24719543  0.3806913 ]
 [-0.08520896  0.04717013  0.19371647  0.95507939  0.00439718]
 [ 0.86336276  0.42201121  0.62800925  1.5003429   0.45670601]
 [ 0.30041219  0.11276732  0.28057503  1.31303204  0.50608204]
 [-1.07262426 -1.45219419 -1.51739705 -1.62627903 -1.94607798]
 [ 0.82114147  0.51572148  0.68881023  1.76102232  0.5621025 ]
 [-1.07937967 -1.54590446 -1.56951218 -1.64420753 -2.01154694]
 [-1.07937967 -1.62087268 -1.63899902 -1.67413775 -1.93303295]
 [-0.29068592 -0.2058476  -0.0060582   0.89334213 -0.08697896]
 [-1.05095067 -1.26477365 -1.30893652 -1.46447801 -1.56606541]
 [ 0.51151865  0.51572148  0.7148678   1.54738669  0.68347   ]
 [ 0.58188748  0.32830094  0.51509312  1.50439286  0.4404302 ]]

In [36]:

from sklearn.linear_model import LogisticRegression

In [37]:

lr = LogisticRegression()
lr.fit(train_bream_smelt, target_bream_smelt)

Out[37]:

LogisticRegression()

In [38]:

print(lr.predict(train_bream_smelt[:5]))

['Bream' 'Smelt' 'Bream' 'Bream' 'Bream']

In [39]:

print(lr.predict_proba(train_bream_smelt[:5]))

[[0.99759855 0.00240145]
 [0.02735183 0.97264817]
 [0.99486072 0.00513928]
 [0.98584202 0.01415798]
 [0.99767269 0.00232731]]

In [40]:

print(lr.classes_)

['Bream' 'Smelt']

In [41]:

print(lr.coef_, lr.intercept_)

[[-0.4037798  -0.57620209 -0.66280298 -1.01290277 -0.73168947]] [-2.16155132]

In [42]:

# z = -0.404 * (weight) - 0.576 * (Length) ,,,,,,, - 2.161
decisions = lr.decision_function(train_bream_smelt[:5])
print(decisions)

[-6.02927744  3.57123907 -5.26568906 -4.24321775 -6.0607117 ]

In [43]:

#scipy
from scipy.special import expit

In [44]:

print(expit(decisions))

[0.00240145 0.97264817 0.00513928 0.01415798 0.00232731]

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