版权声明：此文章有作者原创，涉及相关版本问题可以联系作者，[email protected] https://blog.csdn.net/weixin_42600072/article/details/88644881
import numpy as np
import pandas as pd
df = pd.read_csv('./data/iris.data')
print(df.head())
5.1 3.5 1.4 0.2 Iris-setosa
0 4.9 3.0 1.4 0.2 Iris-setosa
1 4.7 3.2 1.3 0.2 Iris-setosa
2 4.6 3.1 1.5 0.2 Iris-setosa
3 5.0 3.6 1.4 0.2 Iris-setosa
4 5.4 3.9 1.7 0.4 Iris-setosa
df.columns=['sepal_len', 'sepal_wid', 'petal_len', 'petal_wid', 'class']
print(df.head())
sepal_len sepal_wid petal_len petal_wid class
0 4.9 3.0 1.4 0.2 Iris-setosa
1 4.7 3.2 1.3 0.2 Iris-setosa
2 4.6 3.1 1.5 0.2 Iris-setosa
3 5.0 3.6 1.4 0.2 Iris-setosa
4 5.4 3.9 1.7 0.4 Iris-setosa
将数据分为数据X和数据标签Y
X = df.iloc[:,0:4].values
Y = df.iloc[:,4].values
from matplotlib import pyplot as plt
import math
label_dict = {1: 'Iris-Setosa',
2: 'Iris-Versicolor',
3: 'Iris-Virgnica'}
feature_dict = {0: 'sepal length [cm]',
1: 'sepal width [cm]',
2: 'petal length [cm]',
3: 'petal width [cm]'}
plt.figure(figsize=(8, 6))
for cnt in range(4):
plt.subplot(2, 2, cnt+1)
for lab in ('Iris-setosa', 'Iris-versicolor', 'Iris-virginica'):
plt.hist(X[y==lab, cnt],
label=lab,
bins=10,
alpha=0.3,)
plt.xlabel(feature_dict[cnt])
plt.legend(loc='upper right', fancybox=True, fontsize=8)
plt.tight_layout()
plt.show()
from sklearn.preprocessing import StandardScaler
X_std = StandardScaler().fit_transform(X)
print (X_std)
[[-1.1483555 -0.11805969 -1.35396443 -1.32506301]
[-1.3905423 0.34485856 -1.41098555 -1.32506301]
[-1.51163569 0.11339944 -1.29694332 -1.32506301]
[-1.02726211 1.27069504 -1.35396443 -1.32506301]
[-0.54288852 1.9650724 -1.18290109 -1.0614657 ]
[-1.51163569 0.8077768 -1.35396443 -1.19326436]
[-1.02726211 0.8077768 -1.29694332 -1.32506301]
[-1.75382249 -0.34951881 -1.35396443 -1.32506301]
[-1.1483555 0.11339944 -1.29694332 -1.45686167]
[-0.54288852 1.50215416 -1.29694332 -1.32506301]
[-1.2694489 0.8077768 -1.23992221 -1.32506301]
[-1.2694489 -0.11805969 -1.35396443 -1.45686167]
[-1.87491588 -0.11805969 -1.52502777 -1.45686167]
[-0.05851493 2.19653152 -1.46800666 -1.32506301]
[-0.17960833 3.122368 -1.29694332 -1.0614657 ]
[-0.54288852 1.9650724 -1.41098555 -1.0614657 ]
[-0.90616871 1.03923592 -1.35396443 -1.19326436]
[-0.17960833 1.73361328 -1.18290109 -1.19326436]
[-0.90616871 1.73361328 -1.29694332 -1.19326436]
[-0.54288852 0.8077768 -1.18290109 -1.32506301]
[-0.90616871 1.50215416 -1.29694332 -1.0614657 ]
[-1.51163569 1.27069504 -1.58204889 -1.32506301]
[-0.90616871 0.57631768 -1.18290109 -0.92966704]
[-1.2694489 0.8077768 -1.06885886 -1.32506301]
[-1.02726211 -0.11805969 -1.23992221 -1.32506301]
[-1.02726211 0.8077768 -1.23992221 -1.0614657 ]
[-0.78507531 1.03923592 -1.29694332 -1.32506301]
[-0.78507531 0.8077768 -1.35396443 -1.32506301]
[-1.3905423 0.34485856 -1.23992221 -1.32506301]
[-1.2694489 0.11339944 -1.23992221 -1.32506301]
[-0.54288852 0.8077768 -1.29694332 -1.0614657 ]
[-0.78507531 2.42799064 -1.29694332 -1.45686167]
[-0.42179512 2.65944976 -1.35396443 -1.32506301]
[-1.1483555 0.11339944 -1.29694332 -1.45686167]
[-1.02726211 0.34485856 -1.46800666 -1.32506301]
[-0.42179512 1.03923592 -1.41098555 -1.32506301]
[-1.1483555 0.11339944 -1.29694332 -1.45686167]
[-1.75382249 -0.11805969 -1.41098555 -1.32506301]
[-0.90616871 0.8077768 -1.29694332 -1.32506301]
[-1.02726211 1.03923592 -1.41098555 -1.19326436]
[-1.63272909 -1.73827353 -1.41098555 -1.19326436]
[-1.75382249 0.34485856 -1.41098555 -1.32506301]
[-1.02726211 1.03923592 -1.23992221 -0.79786838]
[-0.90616871 1.73361328 -1.06885886 -1.0614657 ]
[-1.2694489 -0.11805969 -1.35396443 -1.19326436]
[-0.90616871 1.73361328 -1.23992221 -1.32506301]
[-1.51163569 0.34485856 -1.35396443 -1.32506301]
[-0.66398191 1.50215416 -1.29694332 -1.32506301]
[-1.02726211 0.57631768 -1.35396443 -1.32506301]
[ 1.39460583 0.34485856 0.52773232 0.25652088]
[ 0.66804545 0.34485856 0.41369009 0.38831953]
[ 1.27351244 0.11339944 0.64177455 0.38831953]
[-0.42179512 -1.73827353 0.12858453 0.12472222]
[ 0.78913885 -0.58097793 0.47071121 0.38831953]
[-0.17960833 -0.58097793 0.41369009 0.12472222]
[ 0.54695205 0.57631768 0.52773232 0.52011819]
[-1.1483555 -1.50681441 -0.27056327 -0.27067375]
[ 0.91023225 -0.34951881 0.47071121 0.12472222]
[-0.78507531 -0.81243705 0.07156341 0.25652088]
[-1.02726211 -2.43265089 -0.15652104 -0.27067375]
[ 0.06257847 -0.11805969 0.24262675 0.38831953]
[ 0.18367186 -1.96973265 0.12858453 -0.27067375]
[ 0.30476526 -0.34951881 0.52773232 0.25652088]
[-0.30070172 -0.34951881 -0.09949993 0.12472222]
[ 1.03132564 0.11339944 0.35666898 0.25652088]
[-0.30070172 -0.11805969 0.41369009 0.38831953]
[-0.05851493 -0.81243705 0.18560564 -0.27067375]
[ 0.42585866 -1.96973265 0.41369009 0.38831953]
[-0.30070172 -1.27535529 0.07156341 -0.1388751 ]
[ 0.06257847 0.34485856 0.58475344 0.78371551]
[ 0.30476526 -0.58097793 0.12858453 0.12472222]
[ 0.54695205 -1.27535529 0.64177455 0.38831953]
[ 0.30476526 -0.58097793 0.52773232 -0.00707644]
[ 0.66804545 -0.34951881 0.29964787 0.12472222]
[ 0.91023225 -0.11805969 0.35666898 0.25652088]
[ 1.15241904 -0.58097793 0.58475344 0.25652088]
[ 1.03132564 -0.11805969 0.69879566 0.65191685]
[ 0.18367186 -0.34951881 0.41369009 0.38831953]
[-0.17960833 -1.04389617 -0.15652104 -0.27067375]
[-0.42179512 -1.50681441 0.0145423 -0.1388751 ]
[-0.42179512 -1.50681441 -0.04247882 -0.27067375]
[-0.05851493 -0.81243705 0.07156341 -0.00707644]
[ 0.18367186 -0.81243705 0.75581678 0.52011819]
[-0.54288852 -0.11805969 0.41369009 0.38831953]
[ 0.18367186 0.8077768 0.41369009 0.52011819]
[ 1.03132564 0.11339944 0.52773232 0.38831953]
[ 0.54695205 -1.73827353 0.35666898 0.12472222]
[-0.30070172 -0.11805969 0.18560564 0.12472222]
[-0.42179512 -1.27535529 0.12858453 0.12472222]
[-0.42179512 -1.04389617 0.35666898 -0.00707644]
[ 0.30476526 -0.11805969 0.47071121 0.25652088]
[-0.05851493 -1.04389617 0.12858453 -0.00707644]
[-1.02726211 -1.73827353 -0.27056327 -0.27067375]
[-0.30070172 -0.81243705 0.24262675 0.12472222]
[-0.17960833 -0.11805969 0.24262675 -0.00707644]
[-0.17960833 -0.34951881 0.24262675 0.12472222]
[ 0.42585866 -0.34951881 0.29964787 0.12472222]
[-0.90616871 -1.27535529 -0.44162661 -0.1388751 ]
[-0.17960833 -0.58097793 0.18560564 0.12472222]
[ 0.54695205 0.57631768 1.2690068 1.70630611]
[-0.05851493 -0.81243705 0.75581678 0.91551417]
[ 1.51569923 -0.11805969 1.21198569 1.17911148]
[ 0.54695205 -0.34951881 1.04092235 0.78371551]
[ 0.78913885 -0.11805969 1.15496457 1.31091014]
[ 2.12116622 -0.11805969 1.61113348 1.17911148]
[-1.1483555 -1.27535529 0.41369009 0.65191685]
[ 1.75788602 -0.34951881 1.44007014 0.78371551]
[ 1.03132564 -1.27535529 1.15496457 0.78371551]
[ 1.63679263 1.27069504 1.32602791 1.70630611]
[ 0.78913885 0.34485856 0.75581678 1.04731282]
[ 0.66804545 -0.81243705 0.869859 0.91551417]
[ 1.15241904 -0.11805969 0.98390123 1.17911148]
[-0.17960833 -1.27535529 0.69879566 1.04731282]
[-0.05851493 -0.58097793 0.75581678 1.57450745]
[ 0.66804545 0.34485856 0.869859 1.4427088 ]
[ 0.78913885 -0.11805969 0.98390123 0.78371551]
[ 2.24225961 1.73361328 1.6681546 1.31091014]
[ 2.24225961 -1.04389617 1.78219682 1.4427088 ]
[ 0.18367186 -1.96973265 0.69879566 0.38831953]
[ 1.27351244 0.34485856 1.09794346 1.4427088 ]
[-0.30070172 -0.58097793 0.64177455 1.04731282]
[ 2.24225961 -0.58097793 1.6681546 1.04731282]
[ 0.54695205 -0.81243705 0.64177455 0.78371551]
[ 1.03132564 0.57631768 1.09794346 1.17911148]
[ 1.63679263 0.34485856 1.2690068 0.78371551]
[ 0.42585866 -0.58097793 0.58475344 0.78371551]
[ 0.30476526 -0.11805969 0.64177455 0.78371551]
[ 0.66804545 -0.58097793 1.04092235 1.17911148]
[ 1.63679263 -0.11805969 1.15496457 0.52011819]
[ 1.87897942 -0.58097793 1.32602791 0.91551417]
[ 2.48444641 1.73361328 1.49709126 1.04731282]
[ 0.66804545 -0.58097793 1.04092235 1.31091014]
[ 0.54695205 -0.58097793 0.75581678 0.38831953]
[ 0.30476526 -1.04389617 1.04092235 0.25652088]
[ 2.24225961 -0.11805969 1.32602791 1.4427088 ]
[ 0.54695205 0.8077768 1.04092235 1.57450745]
[ 0.66804545 0.11339944 0.98390123 0.78371551]
[ 0.18367186 -0.11805969 0.58475344 0.78371551]
[ 1.27351244 0.11339944 0.92688012 1.17911148]
[ 1.03132564 0.11339944 1.04092235 1.57450745]
[ 1.27351244 0.11339944 0.75581678 1.4427088 ]
[-0.05851493 -0.81243705 0.75581678 0.91551417]
[ 1.15241904 0.34485856 1.21198569 1.4427088 ]
[ 1.03132564 0.57631768 1.09794346 1.70630611]
[ 1.03132564 -0.11805969 0.81283789 1.4427088 ]
[ 0.54695205 -1.27535529 0.69879566 0.91551417]
[ 0.78913885 -0.11805969 0.81283789 1.04731282]
[ 0.42585866 0.8077768 0.92688012 1.4427088 ]
[ 0.06257847 -0.11805969 0.75581678 0.78371551]]
求解协方差
mean_vec = np.mean(X_std, axis=0)
print(mean_vec)
[ 2.38437160e-16 2.38437160e-17 -9.53748639e-17 -1.43062296e-16]
cov_mat = (X_std - mean_vec).T.dot(X_std - mean_vec) / (X_std.shape[0]-1)
print('Covariance matrix \n%s' %cov_mat)
Covariance matrix
[[ 1.00675676 -0.10448539 0.87716999 0.82249094]
[-0.10448539 1.00675676 -0.41802325 -0.35310295]
[ 0.87716999 -0.41802325 1.00675676 0.96881642]
[ 0.82249094 -0.35310295 0.96881642 1.00675676]]
print('NumPy covariance matrix: \n%s' %np.cov(X_std.T))
NumPy covariance matrix:
[[ 1.00675676 -0.10448539 0.87716999 0.82249094]
[-0.10448539 1.00675676 -0.41802325 -0.35310295]
[ 0.87716999 -0.41802325 1.00675676 0.96881642]
[ 0.82249094 -0.35310295 0.96881642 1.00675676]]
求解特征向量和特征值
cov_mat = np.cov(X_std.T)
eig_vals, eig_vecs = np.linalg.eig(cov_mat)
print('Eigenvectors \n%s' %eig_vecs)
print('Eigenvalues \n%s' %eig_vals)
Eigenvectors
[[ 0.52308496 -0.36956962 -0.72154279 0.26301409]
[-0.25956935 -0.92681168 0.2411952 -0.12437342]
[ 0.58184289 -0.01912775 0.13962963 -0.80099722]
[ 0.56609604 -0.06381646 0.63380158 0.52321917]]
Eigenvalues
[2.92442837 0.93215233 0.14946373 0.02098259]
# Make a list of (eigenvalue, eigenvector) tuples
eig_pairs = [(np.abs(eig_vals[i]), eig_vecs[:,i]) for i in range(len(eig_vals))]
print (eig_pairs)
print ('----------')
# Sort the (eigenvalue, eigenvector) tuples from high to low
eig_pairs.sort(key=lambda x: x[0], reverse=True)
# Visually confirm that the list is correctly sorted by decreasing eigenvalues
print('Eigenvalues in descending order:')
for i in eig_pairs:
print(i[0])
[(2.9244283691111144, array([ 0.52308496, -0.25956935, 0.58184289, 0.56609604])), (0.932152330253508, array([-0.36956962, -0.92681168, -0.01912775, -0.06381646])), (0.14946373489813417, array([-0.72154279, 0.2411952 , 0.13962963, 0.63380158])), (0.02098259276427019, array([ 0.26301409, -0.12437342, -0.80099722, 0.52321917]))]
----------
Eigenvalues in descending order:
2.9244283691111144
0.932152330253508
0.14946373489813417
0.02098259276427019
tot = sum(eig_vals)
var_exp = [(i / tot)*100 for i in sorted(eig_vals, reverse=True)]
print (var_exp)
cum_var_exp = np.cumsum(var_exp)
cum_var_exp
[72.62003332692029, 23.147406858644157, 3.7115155645845395, 0.5210442498510046]
array([ 72.62003333, 95.76744019, 99.47895575, 100. ])
plt.figure(figsize=(6, 4))
plt.bar(range(4), var_exp, alpha=0.5, align='center',
label='individual explained variance')
plt.step(range(4), cum_var_exp, where='mid',
label='cumulative explained variance')
plt.ylabel('Explained variance ratio')
plt.xlabel('Principal components')
plt.legend(loc='best')
plt.tight_layout()
plt.show()
matrix_w = np.hstack((eig_pairs[0][1].reshape(4,1), eig_pairs[1][1].reshape(4,1)))
print('Matrix W:\n', matrix_w)
Matrix W:
[[ 0.52308496 -0.36956962]
[-0.25956935 -0.92681168]
[ 0.58184289 -0.01912775]
[ 0.56609604 -0.06381646]]
Y = X_std.dot(matrix_w)
Y
array([[-2.10795032, 0.64427554],
[-2.38797131, 0.30583307],
[-2.32487909, 0.56292316],
[-2.40508635, -0.687591 ],
[-2.08320351, -1.53025171],
[-2.4636848 , -0.08795413],
[-2.25174963, -0.25964365],
[-2.3645813 , 1.08255676],
[-2.20946338, 0.43707676],
[-2.17862017, -1.08221046],
[-2.34525657, -0.17122946],
[-2.24590315, 0.6974389 ],
[-2.66214582, 0.92447316],
[-2.2050227 , -1.90150522],
[-2.25993023, -2.73492274],
[-2.21591283, -1.52588897],
[-2.20705382, -0.52623535],
[-1.9077081 , -1.4415791 ],
[-2.35411558, -1.17088308],
[-1.93202643, -0.44083479],
[-2.21942518, -0.96477499],
[-2.79116421, -0.50421849],
[-1.83814105, -0.11729122],
[-2.24572458, -0.17450151],
[-1.97825353, 0.59734172],
[-2.06935091, -0.27755619],
[-2.18514506, -0.56366755],
[-2.15824269, -0.34805785],
[-2.28843932, 0.30256102],
[-2.16501749, 0.47232759],
[-1.8491597 , -0.45547527],
[-2.62023392, -1.84237072],
[-2.44885384, -2.1984673 ],
[-2.20946338, 0.43707676],
[-2.23112223, 0.17266644],
[-2.06147331, -0.6957435 ],
[-2.20946338, 0.43707676],
[-2.45783833, 0.86912843],
[-2.1884075 , -0.30439609],
[-2.30357329, -0.48039222],
[-1.89932763, 2.31759817],
[-2.57799771, 0.4400904 ],
[-1.98020921, -0.50889705],
[-2.14679556, -1.18365675],
[-2.09668176, 0.68061705],
[-2.39554894, -1.16356284],
[-2.41813611, 0.34949483],
[-2.24196231, -1.03745802],
[-2.22484727, -0.04403395],
[ 1.09225538, -0.86148748],
[ 0.72045861, -0.59920238],
[ 1.2299583 , -0.61280832],
[ 0.37598859, 1.756516 ],
[ 1.05729685, 0.21303055],
[ 0.36816104, 0.58896262],
[ 0.73800214, -0.77956125],
[-0.52021731, 1.84337921],
[ 0.9113379 , -0.02941906],
[-0.01292322, 1.02537703],
[-0.15020174, 2.65452146],
[ 0.42437533, 0.05686991],
[ 0.52894687, 1.77250558],
[ 0.70241525, 0.18484154],
[-0.05385675, 0.42901221],
[ 0.86277668, -0.50943908],
[ 0.33388091, 0.18785518],
[ 0.13504146, 0.7883247 ],
[ 1.19457128, 1.63549265],
[ 0.13677262, 1.30063807],
[ 0.72711201, -0.40394501],
[ 0.45564294, 0.41540628],
[ 1.21038365, 0.94282042],
[ 0.61327355, 0.4161824 ],
[ 0.68512164, 0.06335788],
[ 0.85951424, -0.25016762],
[ 1.23906722, 0.08500278],
[ 1.34575245, -0.32669695],
[ 0.64732915, 0.22336443],
[-0.06728496, 1.05414028],
[ 0.10033285, 1.56100021],
[-0.00745518, 1.57050182],
[ 0.2179082 , 0.77368423],
[ 1.04116321, 0.63744742],
[ 0.20719664, 0.27736006],
[ 0.42154138, -0.85764157],
[ 1.03691937, -0.52112206],
[ 1.015435 , 1.39413373],
[ 0.0519502 , 0.20903977],
[ 0.25582921, 1.32747797],
[ 0.25384813, 1.11700714],
[ 0.60915822, -0.02858679],
[ 0.31116522, 0.98711256],
[-0.39679548, 2.01314578],
[ 0.26536661, 0.85150613],
[ 0.07385897, 0.17160757],
[ 0.20854936, 0.37771566],
[ 0.55843737, 0.15286277],
[-0.47853403, 1.53421644],
[ 0.23545172, 0.59332536],
[ 1.8408037 , -0.86943848],
[ 1.13831104, 0.70171953],
[ 2.19615974, -0.54916658],
[ 1.42613827, 0.05187679],
[ 1.8575403 , -0.28797217],
[ 2.74511173, -0.78056359],
[ 0.34010583, 1.5568955 ],
[ 2.29180093, -0.40328242],
[ 1.98618025, 0.72876171],
[ 2.26382116, -1.91685818],
[ 1.35591821, -0.69255356],
[ 1.58471851, 0.43102351],
[ 1.87342402, -0.41054652],
[ 1.23656166, 1.16818977],
[ 1.45128483, 0.4451459 ],
[ 1.58276283, -0.67521526],
[ 1.45956552, -0.25105642],
[ 2.43560434, -2.55096977],
[ 3.29752602, 0.01266612],
[ 1.23377366, 1.71954411],
[ 2.03218282, -0.90334021],
[ 0.95980311, 0.57047585],
[ 2.88717988, -0.38895776],
[ 1.31405636, 0.48854962],
[ 1.69619746, -1.01153249],
[ 1.94868773, -0.99881497],
[ 1.1574572 , 0.31987373],
[ 1.007133 , -0.06550254],
[ 1.7733922 , 0.19641059],
[ 1.85327106, -0.55077372],
[ 2.4234788 , -0.2397454 ],
[ 2.31353522, -2.62038074],
[ 1.84800289, 0.18799967],
[ 1.09649923, 0.29708201],
[ 1.1812503 , 0.81858241],
[ 2.79178861, -0.83668445],
[ 1.57340399, -1.07118383],
[ 1.33614369, -0.420823 ],
[ 0.91061354, -0.01965942],
[ 1.84350913, -0.66872729],
[ 2.00701161, -0.60663655],
[ 1.89319854, -0.68227708],
[ 1.13831104, 0.70171953],
[ 2.03519535, -0.86076914],
[ 1.99464025, -1.04517619],
[ 1.85977129, -0.37934387],
[ 1.54200377, 0.90808604],
[ 1.50925493, -0.26460621],
[ 1.3690965 , -1.01583909],
[ 0.94680339, 0.02182097]])
plt.figure(figsize=(6, 4))
for lab, col in zip(('Iris-setosa', 'Iris-versicolor', 'Iris-virginica'),
('blue', 'red', 'green')):
plt.scatter(X[y==lab, 0],
X[y==lab, 1],
label=lab,
c=col)
plt.xlabel('sepal_len')
plt.ylabel('sepal_wid')
plt.legend(loc='best')
plt.tight_layout()
plt.show()
plt.figure(figsize=(6, 4))
for lab, col in zip(('Iris-setosa', 'Iris-versicolor', 'Iris-virginica'),
('blue', 'red', 'green')):
plt.scatter(Y[y==lab, 0],
Y[y==lab, 1],
label=lab,
c=col)
plt.xlabel('Principal Component 1')
plt.ylabel('Principal Component 2')
plt.legend(loc='lower center')
plt.tight_layout()
plt.show()
