机器学习—降维-特征选择6-5（LDA方法）
使用LDA对糖尿病数据集降维
主要步骤流程：
- 1. 导入包
- 2. 导入数据集
- 3. 数据预处理
- 3.1 检测缺失值
- 3.2 生成自变量和因变量
- 3.3 拆分训练集和测试集
- 3.4 特征缩放
- 4. 使用 LDA 降维
- 4.1 使用 LDA 降维
- 4.2 验证 X_train_lda 的由来
- 5. 构建逻辑回归模型
- 5.1 使用原始数据构建逻辑回归模型
- 5.2 使用降维后数据构建逻辑回归模型
- 6. 可视化LDA降维效果
1. 导入包
In [2]:
# 导入包
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
2. 导入数据集
In [3]:
# 导入数据集
dataset = pd.read_csv('pima-indians-diabetes.csv')
dataset
Out[3]:
3. 数据预处理
3.1 检测缺失值
In [4]:
# 检测缺失值
null_df = dataset.isnull().sum()
null_df
Out[4]:
3.2 生成自变量和因变量
In [5]:
# 生成自变量和因变量
X = dataset.iloc[:,0:8].values
y = dataset.iloc[:,8].values
3.3 拆分训练集和测试集
In [6]:
# 拆分训练集和测试集
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y,
test_size = 0.2, random_state = 2)
3.4 特征缩放
In [7]:
# 特征缩放
from sklearn.preprocessing import StandardScaler
sc_X = StandardScaler()
X_train = sc_X.fit_transform(X_train)
X_test = sc_X.transform(X_test)
4. 使用 LDA 降维
4.1 使用 LDA 降维
In [8]:
# 使用 LDA 生成新的自变量
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA
lda = LDA(n_components = None)
X_train_lda = lda.fit_transform(X_train, y_train)
print(X_train_lda)
[[-7.09580575e-01]
[-1.25232619e+00]
[-7.59813997e-01]
[ 2.24487957e+00]
[-1.83472235e+00]
[ 1.72713900e+00]
[-7.01671717e-01]
[-3.75717668e+00]
[-4.42372899e-02]
[-1.44707200e+00]
[-3.64381132e-01]
[-1.22559889e+00]
[-4.34165087e-01]
[ 2.62545954e+00]
[ 5.29809659e-02]
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[ 1.32496639e+00]
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[ 6.01506952e-01]
[ 8.09658116e-02]
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[ 1.87812923e+00]
[ 3.34056050e-01]
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[ 2.78128145e-01]
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[ 9.24997670e-01]
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[ 1.13819241e+00]
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[ 1.85632789e+00]
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[ 5.82635695e-01]
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[ 2.50713959e+00]
[ 2.31244994e-01]
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[ 1.65566514e+00]
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[ 1.14036484e+00]
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[ 7.58411586e-01]
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[-1.13254653e+00]
[-1.38245096e+00]
[ 1.27808119e+00]
[-1.27616927e+00]
[ 1.87341790e-01]
[-8.75253440e-01]
[ 1.36278834e+00]
[-2.56058432e-01]
[ 3.19885136e-01]
[-1.76746338e+00]
[ 6.75854994e-02]
[-8.54493505e-01]
[-1.79006175e+00]
[-3.79361869e-01]
[-3.16685196e-02]
[ 4.17079705e-01]
[ 1.89624404e+00]
[-4.18415837e+00]
[-2.05042882e+00]
[ 1.11891988e-01]
[-8.26401841e-01]
[ 3.89660783e-02]
[ 4.18491480e-01]
[-9.90051172e-01]
[-2.99557217e-01]]
In [9]:
X_train_lda.shape
Out[9]:
如果 n_components 的值是None，那么其值被设置为 min(n_classes - 1, n_features)，即 min(1,8) = 1
In [10]:
X_test_lda = lda.transform(X_test)
X_test_lda
Out[10]:
array([[-1.60467539],
[-0.54969838],
[-1.12206744],
[-0.2307614 ],
[ 0.91932074],
[-0.9453779 ],
[-1.37419031],
[ 0.42135617],
[-1.61099597],
[ 0.82831279],
[ 0.17838866],
[ 0.29813002],
[ 1.31341755],
[-0.53776713],
[-2.27658875],
[ 1.73281941],
[ 1.97332988],
[-1.88303933],
[-0.209353 ],
[ 2.17460238],
[ 2.75433054],
[ 1.74832377],
[-0.90042382],
[ 0.30119646],
[-1.10762802],
[-1.39660502],
[ 0.95576581],
[ 0.27749218],
[-0.54955422],
[-0.12667065],
[-0.21771912],
[ 0.35106332],
[-2.62136525],
[-0.31951318],
[ 0.1690599 ],
[ 2.98109784],
[ 0.04147731],
[ 1.59721976],
[-0.06088512],
[-1.51278178],
[-0.5315911 ],
[-1.2186132 ],
[ 0.383099 ],
[-0.52068249],
[-1.95545784],
[-1.70670076],
[-0.25108479],
[ 0.35668893],
[-1.05845692],
[ 0.27414828],
[ 4.20063483],
[-0.9429675 ],
[ 0.23691857],
[ 1.47044517],
[ 0.18558897],
[ 0.46446228],
[ 2.72573226],
[ 0.34777019],
[ 0.18384959],
[-1.64900368],
[ 0.1935939 ],
[ 2.11142097],
[ 1.97084855],
[ 2.14582855],
[ 0.02640709],
[-1.07955765],
[ 2.79750127],
[-0.38484886],
[-0.15820474],
[ 0.08456496],
[-1.02076631],
[-1.24202773],
[ 0.47700638],
[-1.10356392],
[-1.13650064],
[ 0.62166903],
[ 0.1552929 ],
[-1.24288166],
[-0.32134212],
[-0.27604553],
[-1.60876309],
[-0.37116888],
[-1.42618373],
[-0.33389981],
[ 1.17440042],
[-0.04360507],
[-1.05621687],
[-0.98830673],
[-0.46398678],
[ 0.86559721],
[-0.89685648],
[-0.1900513 ],
[-0.47231441],
[-1.63402045],
[-0.58684382],
[ 1.26580498],
[-0.00456354],
[ 0.79176022],
[ 1.22020175],
[-1.65008429],
[ 0.45008263],
[ 0.81952325],
[-0.97525438],
[-1.18703817],
[-0.56623865],
[-1.04071217],
[ 3.21066554],
[-0.72887389],
[-0.99124524],
[-4.20525965],
[-1.73441591],
[-0.15464027],
[ 0.32631244],
[-1.36694546],
[-0.16897841],
[ 1.46783557],
[ 0.28316526],
[-0.25870976],
[-0.79050932],
[-0.86808187],
[-2.41534815],
[-0.16271327],
[-0.99406614],
[-0.8221322 ],
[-0.09825589],
[ 2.02265651],
[-0.8596007 ],
[ 0.51713851],
[ 0.24236981],
[ 0.39841078],
[ 1.01361551],
[-0.20272853],
[ 0.37300882],
[-1.5802361 ],
[ 1.05843709],
[ 1.10599465],
[-0.01991832],
[ 0.14456892],
[-0.56400755],
[ 0.74296475],
[-0.71388053],
[ 1.15764504],
[-0.68104578],
[-0.02367192],
[-0.40098541],
[-0.45004564],
[-1.80451501],
[ 0.67611791],
[-1.84718826],
[-0.84972083],
[-1.27350394],
[-0.33970734],
[ 0.96318898],
[-2.19867349]])
4.2 验证 X_train_lda 的由来
In [11]:
X_train.shape
Out[11]:
In [12]:
# 转换系数
scalings = lda.scalings_
In [13]:
scalings
Out[13]:
In [14]:
verify_matrix = X_train.dot(scalings)
In [15]:
verify_matrix
Out[15]:
array([[-7.09580575e-01],
[-1.25232619e+00],
[-7.59813997e-01],
[ 2.24487957e+00],
[-1.83472235e+00],
[ 1.72713900e+00],
[-7.01671717e-01],
[-3.75717668e+00],
[-4.42372899e-02],
[-1.44707200e+00],
[-3.64381132e-01],
[-1.22559889e+00],
[-4.34165087e-01],
[ 2.62545954e+00],
[ 5.29809659e-02],
[-1.28741643e+00],
[-1.33326464e-01],
[ 1.32496639e+00],
[-8.41212474e-01],
[-5.80913765e-01],
[-9.31947468e-01],
[-4.71240842e-01],
[ 6.01506952e-01],
[ 8.09658116e-02],
[-5.36135643e-01],
[-1.24878685e+00],
[-8.74004230e-01],
[-1.38735113e+00],
[ 1.87812923e+00],
[ 3.34056050e-01],
[-1.65936332e+00],
[-1.55708389e+00],
[-1.03447627e+00],
[ 2.78128145e-01],
[-1.07863887e+00],
[ 9.24997670e-01],
[-4.40200308e-01],
[-7.82628235e-01],
[ 6.24893963e-01],
[ 1.37482261e+00],
[ 4.83817890e-01],
[ 1.18420457e-01],
[ 1.93598829e-01],
[-1.38235717e-01],
[-4.45815683e-01],
[-1.73559267e+00],
[-4.53253421e-01],
[ 1.36693114e+00],
[-1.11857616e+00],
[-9.27818986e-01],
[ 9.03495498e-01],
[-2.08423086e-01],
[ 1.09073837e+00],
[-1.78992797e-01],
[-1.81685894e-01],
[ 1.55669292e+00],
[ 1.70649911e+00],
[-8.30370459e-01],
[ 1.74389260e+00],
[-4.38333981e-01],
[-1.32175889e+00],
[-1.17902590e+00],
[-1.27970387e+00],
[ 2.64997197e-01],
[ 1.83927441e+00],
[ 2.87603583e+00],
[ 1.32747827e+00],
[-1.23317807e+00],
[-6.38667579e-01],
[-2.49730690e+00],
[-7.50335687e-01],
[ 1.13819241e+00],
[-1.51819792e+00],
[ 3.48699578e-01],
[ 2.07291912e+00],
[ 1.18872205e+00],
[-1.26752930e+00],
[-9.61061338e-01],
[-1.48481631e+00],
[-6.16788749e-01],
[ 1.00107373e+00],
[ 1.64183047e+00],
[ 7.62485249e-01],
[-9.05966168e-01],
[-1.76583480e+00],
[ 1.15119270e+00],
[-5.71248022e-01],
[ 2.82671522e-01],
[ 1.58923966e+00],
[ 3.89370865e-02],
[ 6.95987190e-04],
[ 2.38587148e-02],
[ 4.33294099e-01],
[-1.61807242e+00],
[-3.75036587e-02],
[ 1.45518668e+00],
[-9.09626996e-01],
[-9.00170742e-01],
[ 2.02443108e+00],
[-6.88335740e-01],
[ 2.33687536e+00],
[-2.14774953e-01],
[ 4.22766244e-01],
[-7.44887303e-01],
[ 1.78782795e-02],
[-1.05789594e+00],
[-1.48150473e+00],
[-1.45801198e+00],
[ 2.11355083e+00],
[-5.60956835e-01],
[-7.99557384e-01],
[-2.53714672e+00],
[ 1.15827139e-01],
[-2.85981257e-01],
[ 1.20870045e-01],
[-1.50249259e-01],
[ 1.28325311e+00],
[-9.10469484e-01],
[-2.04100810e-01],
[ 3.04926411e-01],
[-6.13533181e-01],
[-1.13799972e+00],
[ 1.85069640e+00],
[-9.52159360e-01],
[-1.07072549e+00],
[ 1.54132020e+00],
[-2.25155103e-01],
[ 9.42723622e-01],
[ 2.33261633e+00],
[-2.50335599e+00],
[-1.71081917e+00],
[-5.69055863e-01],
[-7.86551181e-02],
[ 8.59624336e-01],
[-1.27175612e+00],
[-7.32892454e-01],
[ 1.62806827e+00],
[-1.73505213e+00],
[ 5.89219216e-01],
[ 9.61940538e-01],
[ 1.21978497e+00],
[-1.23402059e-01],
[ 5.58089135e-01],
[-1.97372406e+00],
[-3.54738583e-01],
[ 1.07679503e+00],
[ 3.30921389e-02],
[ 3.51641156e+00],
[ 2.01319999e+00],
[-4.79608603e-01],
[-1.54500904e+00],
[ 7.28837498e-01],
[-7.68164175e-01],
[ 6.03755150e-01],
[-5.79291694e-01],
[ 1.09312454e+00],
[-7.60263201e-01],
[ 6.99167689e-01],
[ 1.37164718e+00],
[ 1.31225828e+00],
[-8.40653172e-01],
[ 2.91430119e-02],
[-8.29551054e-01],
[-8.52135872e-01],
[ 2.42179542e+00],
[ 1.19833768e-01],
[ 1.34468182e+00],
[ 3.31802548e-01],
[ 8.84131097e-01],
[-1.08418018e+00],
[ 3.16804052e-01],
[ 1.95699099e-01],
[ 1.18224504e+00],
[-4.76551929e-02],
[ 2.32738728e-01],
[ 2.17302678e-01],
[-5.89237273e-01],
[ 1.85849443e-01],
[-1.54979285e+00],
[ 9.82798488e-01],
[-5.83740225e-01],
[-6.00824976e-01],
[ 1.74716312e+00],
[-8.40349063e-01],
[-1.92108538e-01],
[-6.60931850e-01],
[-1.09416397e+00],
[ 1.07363466e+00],
[-7.56504146e-01],
[ 4.81118721e-01],
[ 4.58322441e-02],
[-5.30149132e-02],
[-9.83533399e-01],
[-1.18611803e+00],
[ 8.97981571e-01],
[-1.38655961e+00],
[ 8.65977388e-02],
[-1.29923057e+00],
[-2.00106616e-01],
[-8.84903649e-01],
[-1.01814576e+00],
[-6.73380309e-01],
[-2.57345929e-01],
[-6.09999516e-01],
[-9.99780327e-01],
[ 1.42422789e+00],
[-2.44448484e-01],
[-1.13703421e+00],
[-6.42258506e-01],
[ 2.25918605e-01],
[ 5.65663441e-01],
[ 1.23524077e-01],
[ 1.08528225e+00],
[ 2.19363184e+00],
[ 1.01163253e+00],
[-7.94344125e-01],
[-9.53004876e-01],
[ 7.66628719e-01],
[ 2.17274216e+00],
[ 1.40669491e-01],
[ 5.94159896e-01],
[-5.55446317e-01],
[ 3.51591179e-01],
[ 1.50546591e+00],
[ 5.66679498e-01],
[ 3.85443340e-01],
[-1.15721046e+00],
[ 1.92121722e+00],
[ 5.79754177e-01],
[ 1.61088688e-01],
[ 6.40910989e-02],
[-4.15781837e-03],
[ 1.20911354e+00],
[ 5.81706676e-01],
[ 9.29316806e-01],
[-6.49635760e-01],
[-1.29028128e+00],
[ 1.19743896e+00],
[ 1.73958239e+00],
[ 1.06273540e+00],
[-5.78708212e-01],
[-5.91652462e-01],
[-1.06403705e+00],
[ 8.48748221e-01],
[ 1.84245259e+00],
[-1.12241556e+00],
[-3.92319922e-01],
[-5.06398050e-01],
[-8.01740487e-01],
[ 2.81827862e-01],
[-3.73194844e-01],
[ 1.27356384e-01],
[ 1.38348151e+00],
[-1.95791710e+00],
[-1.69343253e+00],
[ 1.57912787e+00],
[ 1.56905793e+00],
[-4.81162123e-01],
[ 7.14304828e-01],
[ 1.67063463e+00],
[-7.24911993e-01],
[ 1.00982197e+00],
[-1.99039022e-01],
[-9.26955565e-01],
[ 2.98929969e+00],
[ 2.66203782e-01],
[-1.90022216e-01],
[ 1.21421832e+00],
[ 1.48219197e+00],
[ 4.29338339e-01],
[ 1.25202834e+00],
[ 2.31888566e+00],
[-1.81524331e-01],
[ 4.03757358e-01],
[-2.37300773e+00],
[-5.05502452e-01],
[ 1.57620164e+00],
[-7.44501998e-01],
[-2.78989955e+00],
[-7.48811082e-01],
[ 9.34453007e-03],
[-8.86760850e-01],
[ 2.40821378e+00],
[ 7.52828238e-01],
[ 1.01930801e+00],
[-1.11676970e+00],
[ 1.16286127e+00],
[-1.38072161e+00],
[ 5.06045144e-02],
[ 1.28447844e+00],
[ 1.10147534e+00],
[-6.99471941e-01],
[-3.95475313e-01],
[-2.33814898e+00],
[-5.58885514e-01],
[-1.62515502e+00],
[-4.80031790e-02],
[-1.22933421e+00],
[-1.43289330e+00],
[ 3.82368455e-01],
[-4.78784838e-01],
[ 3.11226395e+00],
[-2.19872519e-01],
[-8.66012695e-02],
[-8.61030811e-01],
[-1.79659712e-02],
[ 5.63343238e-01],
[ 1.15772339e-01],
[ 1.33832964e+00],
[-9.20451870e-01],
[-1.94203663e+00],
[-2.10981127e+00],
[-8.96254271e-01],
[-1.01096412e+00],
[-7.96968176e-01],
[ 1.53526922e+00],
[ 2.96828601e+00],
[-2.37340281e+00],
[-5.39905276e-01],
[ 8.05031504e-03],
[ 6.19929863e-02],
[-4.07763181e-01],
[-7.69899804e-01],
[-1.06445126e-01],
[ 2.44923107e+00],
[-8.64897290e-01],
[-9.61107269e-01],
[ 1.12928198e+00],
[-6.93799633e-01],
[ 9.12263450e-02],
[-1.65662030e+00],
[ 1.23445066e+00],
[-2.29989521e+00],
[-6.67210528e-01],
[ 1.39505120e+00],
[-5.90146656e-01],
[ 1.91599297e+00],
[-3.07105657e-02],
[-1.86495725e+00],
[-4.10045496e-03],
[ 1.95146853e+00],
[-6.63388932e-01],
[-1.25932062e-01],
[-1.95617520e+00],
[-7.24067222e-01],
[ 1.68597191e+00],
[ 7.67739195e-01],
[ 1.50844457e+00],
[-1.39040166e+00],
[-5.28317583e-01],
[-7.98163950e-01],
[-2.05966934e+00],
[-5.00389045e-01],
[-3.08430392e-01],
[-4.55409643e-01],
[ 1.22705948e-01],
[-6.42465319e-01],
[-5.16243197e-01],
[-1.36050953e+00],
[-5.87265409e-01],
[ 4.00535897e-01],
[-2.11442799e-01],
[-2.42412529e-02],
[-1.86695525e+00],
[-3.71845160e-01],
[ 1.66009450e+00],
[-3.22778860e-01],
[-4.78111890e-01],
[-9.44115662e-01],
[-1.77911788e-01],
[ 3.24741813e-01],
[ 2.61166483e+00],
[ 6.15827866e-01],
[ 1.62305833e+00],
[ 6.56975069e-01],
[ 1.07649474e+00],
[ 8.93244246e-01],
[ 2.37038946e+00],
[-1.00074397e+00],
[-6.94135081e-02],
[ 1.90692835e+00],
[-4.16046203e-01],
[-2.97009267e-01],
[ 1.12324933e-02],
[-1.73948585e+00],
[ 1.83169245e+00],
[-7.15739584e-01],
[ 2.84526872e-01],
[-2.08984309e-01],
[ 6.05826777e-01],
[-5.55760348e-02],
[-1.60536248e+00],
[-1.94578868e-01],
[ 4.14010014e-01],
[-4.67234277e-01],
[-1.15041532e+00],
[ 7.12527823e-01],
[-1.13330316e+00],
[-1.86227991e-01],
[ 1.23994415e+00],
[-4.75961697e-01],
[-6.50655572e-01],
[ 1.39405031e-01],
[-1.36545193e-01],
[-1.31667319e+00],
[-1.32598029e+00],
[ 2.76684219e+00],
[-4.30281832e-01],
[-1.12095251e+00],
[ 9.24204330e-01],
[ 8.88934406e-01],
[-7.26751047e-01],
[-1.51174785e+00],
[ 1.02899443e+00],
[-9.73167110e-01],
[-5.71899107e-01],
[ 1.33454081e-01],
[ 1.34722884e+00],
[ 6.89644744e-01],
[ 5.02219295e-01],
[ 3.37284935e-02],
[ 6.68072083e-01],
[-9.99431928e-01],
[-6.88682252e-02],
[ 5.87800737e-01],
[ 1.13551804e+00],
[-9.69739531e-01],
[ 1.35179142e+00],
[-6.42954624e-01],
[-2.86754040e+00],
[ 2.68309817e+00],
[-1.47644791e-01],
[ 1.24845834e+00],
[-2.00060393e-01],
[-9.38918894e-01],
[ 1.55394617e-01],
[ 6.31910785e-01],
[-1.98269993e-01],
[-8.00913625e-01],
[-6.20856966e-01],
[ 1.64681002e+00],
[ 1.49248533e-01],
[ 2.05856664e+00],
[ 2.28501757e-01],
[ 1.26712150e+00],
[ 2.20072239e+00],
[ 5.81895837e-01],
[ 1.06678143e-01],
[-1.65841961e+00],
[-1.56672936e+00],
[ 2.90378758e+00],
[ 7.13023519e-01],
[ 4.16240180e-01],
[ 4.62021431e-02],
[ 8.60391305e-01],
[ 2.49707361e-01],
[ 6.66174264e-01],
[-1.63443218e+00],
[ 8.37298226e-01],
[-2.60832143e-01],
[-1.33690413e+00],
[-6.87726315e-01],
[-5.31041667e-01],
[-1.35290111e+00],
[ 1.01610162e+00],
[ 6.55533597e-01],
[-2.70433334e-01],
[-2.35219615e-01],
[-1.75888819e+00],
[-4.96974980e-01],
[-1.73030175e+00],
[-4.24685451e-02],
[ 1.32843562e+00],
[-2.37166763e+00],
[ 1.15280234e+00],
[-1.42122878e+00],
[ 8.11785345e-02],
[ 8.19612421e-01],
[-8.10324318e-02],
[-1.25420996e+00],
[-5.80349398e-01],
[ 5.63437412e-01],
[ 3.68698998e-01],
[-4.32464214e-01],
[ 7.62099838e-02],
[ 1.73401319e+00],
[-1.24552882e+00],
[ 4.18891453e-01],
[ 5.67174434e-01],
[-1.04944480e-01],
[-1.34731409e+00],
[ 2.21294924e+00],
[-1.28471417e+00],
[ 1.25266601e-01],
[-1.44224174e+00],
[ 6.94186682e-01],
[ 1.60084914e+00],
[ 2.67248641e-01],
[-1.03952728e+00],
[ 2.99739857e+00],
[-1.02794271e+00],
[ 1.79446876e-01],
[ 2.12152257e+00],
[ 2.75108497e+00],
[-2.37792113e-01],
[-1.19692643e+00],
[ 8.44240581e-03],
[ 1.38150735e+00],
[ 4.76567951e-01],
[ 2.30817722e-01],
[-3.63383497e-01],
[ 8.60257816e-01],
[ 1.33933041e+00],
[-2.33511323e+00],
[ 6.41327648e-01],
[-5.97981270e-01],
[ 7.06612394e-03],
[ 1.78549835e+00],
[-4.50443316e-01],
[ 2.46076001e+00],
[ 3.14286397e+00],
[ 5.15128810e-01],
[-7.36301241e-01],
[-1.53678504e+00],
[-5.16439953e-01],
[-1.01638759e+00],
[-7.14951518e-01],
[-1.43208616e+00],
[ 2.97381260e-01],
[ 4.60258527e-01],
[ 1.02833264e+00],
[ 7.20033713e-01],
[-2.95789628e+00],
[-2.48030655e+00],
[-5.25886784e-01],
[-1.03345724e+00],
[ 2.70684733e+00],
[ 2.27077719e+00],
[-3.34526528e-01],
[ 1.85632789e+00],
[ 8.87559816e-01],
[-1.28839425e+00],
[-1.74355748e+00],
[ 5.82635695e-01],
[-2.48169766e-01],
[ 1.86653912e+00],
[ 1.91423697e+00],
[-6.60352751e-02],
[-2.42946132e-01],
[-1.19462005e+00],
[-1.53502969e+00],
[-1.26999357e+00],
[-6.08695437e-01],
[-5.27683110e-02],
[-9.58823996e-01],
[-1.59605519e+00],
[ 2.50713959e+00],
[ 2.31244994e-01],
[-9.64885912e-01],
[ 1.65566514e+00],
[-1.16556071e+00],
[ 1.14036484e+00],
[-4.50863671e-01],
[-1.11290322e+00],
[ 7.58411586e-01],
[ 2.10724977e+00],
[ 1.11431659e+00],
[ 1.63000004e+00],
[ 1.27068286e+00],
[-1.77190314e+00],
[ 1.89336165e+00],
[-1.33850008e+00],
[ 2.35563680e-01],
[-2.14887731e+00],
[ 9.57504839e-01],
[ 5.94126455e-02],
[ 7.78023301e-01],
[ 8.33093082e-02],
[-3.74606796e-01],
[-1.16487681e+00],
[ 1.59009255e+00],
[ 1.80771965e+00],
[-1.12090536e-01],
[ 1.72760476e+00],
[-3.25051722e-01],
[-1.41500859e+00],
[ 2.10646634e+00],
[-9.18720227e-01],
[ 2.09695993e+00],
[-1.13254653e+00],
[-1.38245096e+00],
[ 1.27808119e+00],
[-1.27616927e+00],
[ 1.87341790e-01],
[-8.75253440e-01],
[ 1.36278834e+00],
[-2.56058432e-01],
[ 3.19885136e-01],
[-1.76746338e+00],
[ 6.75854994e-02],
[-8.54493505e-01],
[-1.79006175e+00],
[-3.79361869e-01],
[-3.16685196e-02],
[ 4.17079705e-01],
[ 1.89624404e+00],
[-4.18415837e+00],
[-2.05042882e+00],
[ 1.11891988e-01],
[-8.26401841e-01],
[ 3.89660783e-02],
[ 4.18491480e-01],
[-9.90051172e-01],
[-2.99557217e-01]])
5. 构建逻辑回归模型
5.1 使用原始数据构建逻辑回归模型
In [16]:
# 构建模型
from sklearn.linear_model import LogisticRegression
classifier = LogisticRegression(penalty='l2', C=1, class_weight='balanced', random_state = 0)
classifier.fit(X_train, y_train)
Out[16]:
In [17]:
# 预测测试集
y_pred = classifier.predict(X_test)
In [18]:
# 评估模型性能
from sklearn.metrics import accuracy_score
print(accuracy_score(y_test, y_pred))
In [19]:
# 评估模型性能
from sklearn.metrics import classification_report
print(classification_report(y_test, y_pred))
5.2 使用降维后数据构建逻辑回归模型
In [20]:
# 构建模型
classifier = LogisticRegression(penalty='l2', C=1,
class_weight='balanced', random_state = 0)
classifier.fit(X_train_lda, y_train)
Out[20]:
In [21]:
# 预测测试集
y_pred = classifier.predict(X_test_lda)
In [27]:
X_test_lda
Out[27]:
array([[-1.60467539, 1. ],
[-0.54969838, 1. ],
[-1.12206744, 1. ],
[-0.2307614 , 1. ],
[ 0.91932074, 1. ],
[-0.9453779 , 1. ],
[-1.37419031, 1. ],
[ 0.42135617, 1. ],
[-1.61099597, 1. ],
[ 0.82831279, 1. ],
[ 0.17838866, 1. ],
[ 0.29813002, 1. ],
[ 1.31341755, 1. ],
[-0.53776713, 1. ],
[-2.27658875, 1. ],
[ 1.73281941, 1. ],
[ 1.97332988, 1. ],
[-1.88303933, 1. ],
[-0.209353 , 1. ],
[ 2.17460238, 1. ],
[ 2.75433054, 1. ],
[ 1.74832377, 1. ],
[-0.90042382, 1. ],
[ 0.30119646, 1. ],
[-1.10762802, 1. ],
[-1.39660502, 1. ],
[ 0.95576581, 1. ],
[ 0.27749218, 1. ],
[-0.54955422, 1. ],
[-0.12667065, 1. ],
[-0.21771912, 1. ],
[ 0.35106332, 1. ],
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[-0.31951318, 1. ],
[ 0.1690599 , 1. ],
[ 2.98109784, 1. ],
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[ 1.47044517, 1. ],
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[-1.10356392, 1. ],
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[ 0.62166903, 1. ],
[ 0.1552929 , 1. ],
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[ 1.17440042, 1. ],
[-0.04360507, 1. ],
[-1.05621687, 1. ],
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[ 0.86559721, 1. ],
[-0.89685648, 1. ],
[-0.1900513 , 1. ],
[-0.47231441, 1. ],
[-1.63402045, 1. ],
[-0.58684382, 1. ],
[ 1.26580498, 1. ],
[-0.00456354, 1. ],
[ 0.79176022, 1. ],
[ 1.22020175, 1. ],
[-1.65008429, 1. ],
[ 0.45008263, 1. ],
[ 0.81952325, 1. ],
[-0.97525438, 1. ],
[-1.18703817, 1. ],
[-0.56623865, 1. ],
[-1.04071217, 1. ],
[ 3.21066554, 1. ],
[-0.72887389, 1. ],
[-0.99124524, 1. ],
[-4.20525965, 1. ],
[-1.73441591, 1. ],
[-0.15464027, 1. ],
[ 0.32631244, 1. ],
[-1.36694546, 1. ],
[-0.16897841, 1. ],
[ 1.46783557, 1. ],
[ 0.28316526, 1. ],
[-0.25870976, 1. ],
[-0.79050932, 1. ],
[-0.86808187, 1. ],
[-2.41534815, 1. ],
[-0.16271327, 1. ],
[-0.99406614, 1. ],
[-0.8221322 , 1. ],
[-0.09825589, 1. ],
[ 2.02265651, 1. ],
[-0.8596007 , 1. ],
[ 0.51713851, 1. ],
[ 0.24236981, 1. ],
[ 0.39841078, 1. ],
[ 1.01361551, 1. ],
[-0.20272853, 1. ],
[ 0.37300882, 1. ],
[-1.5802361 , 1. ],
[ 1.05843709, 1. ],
[ 1.10599465, 1. ],
[-0.01991832, 1. ],
[ 0.14456892, 1. ],
[-0.56400755, 1. ],
[ 0.74296475, 1. ],
[-0.71388053, 1. ],
[ 1.15764504, 1. ],
[-0.68104578, 1. ],
[-0.02367192, 1. ],
[-0.40098541, 1. ],
[-0.45004564, 1. ],
[-1.80451501, 1. ],
[ 0.67611791, 1. ],
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[-1.27350394, 1. ],
[-0.33970734, 1. ],
[ 0.96318898, 1. ],
[-2.19867349, 1. ]])
In [22]:
# 评估模型性能
print(accuracy_score(y_test, y_pred))
In [23]:
# 评估模型性能
print(classification_report(y_test, y_pred))
6. 可视化LDA降维效果
由于X_test_lda是1维的。为了可视化，为X_test_lda扩展1维
In [24]:
# X_test_lda 扩展1维
to_insert = np.ones((X_test_lda.shape[0],1))
X_test_lda = np.c_[X_test_lda, to_insert]
In [25]:
X_test_lda
Out[25]:
array([[-1.60467539, 1. ],
[-0.54969838, 1. ],
[-1.12206744, 1. ],
[-0.2307614 , 1. ],
[ 0.91932074, 1. ],
[-0.9453779 , 1. ],
[-1.37419031, 1. ],
[ 0.42135617, 1. ],
[-1.61099597, 1. ],
[ 0.82831279, 1. ],
[ 0.17838866, 1. ],
[ 0.29813002, 1. ],
[ 1.31341755, 1. ],
[-0.53776713, 1. ],
[-2.27658875, 1. ],
[ 1.73281941, 1. ],
[ 1.97332988, 1. ],
[-1.88303933, 1. ],
[-0.209353 , 1. ],
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[ 2.75433054, 1. ],
[ 1.74832377, 1. ],
[-0.90042382, 1. ],
[ 0.30119646, 1. ],
[-1.10762802, 1. ],
[-1.39660502, 1. ],
[ 0.95576581, 1. ],
[ 0.27749218, 1. ],
[-0.54955422, 1. ],
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[ 0.96318898, 1. ],
[-2.19867349, 1. ]])
In [26]:
# 可视化
from matplotlib.colors import ListedColormap
X_set, y_set = X_test_lda, y_test
for i, j in enumerate(np.unique(y_set)):
plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],
color = ListedColormap(('red', 'blue'))(i), label = j)
plt.title('LDA Viz')
plt.xlabel('LD1')
plt.ylabel('LD2 (Useless)')
plt.legend()
plt.show()
经过LDA降维，自变量由8个变为1个。
肉眼可见，模型性能不错，因为红色的类别集中在左边，蓝色的类别集中在右边。
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