{"id":1048768,"date":"2024-12-31T13:53:56","date_gmt":"2024-12-31T05:53:56","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1048768.html"},"modified":"2024-12-31T13:54:00","modified_gmt":"2024-12-31T05:54:00","slug":"%e5%a6%82%e4%bd%95%e7%94%a8python%e8%bf%9b%e8%a1%8c%e5%a5%87%e5%bc%82%e5%80%bc%e5%88%86%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1048768.html","title":{"rendered":"\u5982\u4f55\u7528python\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3"},"content":{"rendered":"

\"\u5982\u4f55\u7528python\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\"<\/p>\n

\u5947\u5f02\u503c\u5206\u89e3\uff08SVD\uff09<\/strong>\u662f\u4e00\u79cd\u91cd\u8981\u7684\u77e9\u9635\u5206\u89e3\u6280\u672f\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u6570\u636e\u964d\u7ef4\u3001\u56fe\u50cf\u5904\u7406\u3001\u63a8\u8350\u7cfb\u7edf\u7b49\u9886\u57df\u3002\u5728Python\u4e2d\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\uff0c\u53ef\u4ee5\u4f7f\u7528NumPy\u5e93\u3001SciPy\u5e93\u3001scikit-learn\u5e93<\/strong>\u3002\u5176\u4e2d\uff0cNumPy\u5e93\u6700\u4e3a\u5e38\u7528\uff0c\u4f7f\u7528\u65b9\u4fbf\u3002\u672c\u6587\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u5982\u4f55\u5728Python\u4e2d\u4f7f\u7528\u8fd9\u4e09\u79cd\u5e93\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\uff0c\u5e76\u7ed3\u5408\u5b9e\u9645\u5e94\u7528\u573a\u666f\u8fdb\u884c\u8bf4\u660e\u3002<\/p>\n<\/p>\n

\u4e00\u3001NUMPY\u5e93\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3<\/p>\n<\/p>\n

NumPy\u662fPython\u79d1\u5b66\u8ba1\u7b97\u7684\u57fa\u7840\u5e93\uff0c\u63d0\u4f9b\u4e86\u5927\u91cf\u7684\u6570\u5b66\u51fd\u6570\u548c\u64cd\u4f5c\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528NumPy\u5e93\u4e2d\u7684linalg.svd<\/code>\u51fd\u6570\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\u3002<\/p>\n<\/p>\n

1. \u5b89\u88c5\u548c\u5bfc\u5165NumPy\u5e93<\/h3>\n<\/p>\n

\u5728\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\u4e4b\u524d\uff0c\u9700\u8981\u786e\u4fdd\u5df2\u7ecf\u5b89\u88c5\u4e86NumPy\u5e93\u3002\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u5b89\u88c5NumPy\uff1a<\/p>\n<\/p>\n

pip install numpy<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5b89\u88c5\u5b8c\u6210\u540e\uff0c\u5728\u4ee3\u7801\u4e2d\u5bfc\u5165NumPy\u5e93\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
<\/code><\/pre>\n<\/p>\n
2. \u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3<\/h3>\n<\/p>\n
\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u77e9\u9635A\uff0c\u60f3\u5bf9\u5176\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\u3002\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u4ee3\u7801\uff1a<\/p>\n<\/p>\n
# \u521b\u5efa\u4e00\u4e2a\u77e9\u9635<\/p>\n
A = np.array([[1, 2, 3], <\/p>\n
              [4, 5, 6], <\/p>\n
              [7, 8, 9]])<\/p>\n
\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3<\/strong><\/h2>\n
U, S, VT = np.linalg.svd(A)<\/p>\n
print("U\u77e9\u9635\uff1a\\n", U)<\/p>\n
print("\u5947\u5f02\u503c\uff1a\\n", S)<\/p>\n
print("V^T\u77e9\u9635\uff1a\\n", VT)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0cnp.linalg.svd(A)<\/code>\u51fd\u6570\u8fd4\u56de\u4e09\u4e2a\u503c\uff1aU\u77e9\u9635\u3001\u5947\u5f02\u503c\u5411\u91cfS\u3001V^T\u77e9\u9635\u3002U\u77e9\u9635\u548cV^T\u77e9\u9635\u662f\u6b63\u4ea4\u77e9\u9635\uff0cS\u662f\u5947\u5f02\u503c\u7684\u5bf9\u89d2\u7ebf\u5143\u7d20\u3002<\/p>\n<\/p>\n
3. \u8fd8\u539f\u539f\u59cb\u77e9\u9635<\/h3>\n<\/p>\n
\u53ef\u4ee5\u4f7f\u7528\u5206\u89e3\u5f97\u5230\u7684U\u77e9\u9635\u3001\u5947\u5f02\u503c\u5411\u91cfS\u3001V^T\u77e9\u9635\u8fd8\u539f\u539f\u59cb\u77e9\u9635A\uff1a<\/p>\n<\/p>\n
# \u6784\u9020\u5bf9\u89d2\u77e9\u9635<\/p>\n
Sigma = np.zeros((A.shape[0], A.shape[1]))<\/p>\n
np.fill_diagonal(Sigma, S)<\/p>\n
\u8fd8\u539f\u539f\u59cb\u77e9\u9635<\/strong><\/h2>\n
A_reconstructed = np.dot(U, np.dot(Sigma, VT))<\/p>\n
print("\u8fd8\u539f\u7684\u77e9\u9635\uff1a\\n", A_reconstructed)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e8c\u3001SCIPY\u5e93\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3<\/p>\n<\/p>\n
SciPy\u662f\u57fa\u4e8eNumPy\u7684\u4e00\u4e2a\u79d1\u5b66\u8ba1\u7b97\u5e93\uff0c\u63d0\u4f9b\u4e86\u66f4\u591a\u7684\u6570\u5b66\u7b97\u6cd5\u548c\u51fd\u6570\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528SciPy\u5e93\u4e2d\u7684svd<\/code>\u51fd\u6570\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\u3002<\/p>\n<\/p>\n
1. \u5b89\u88c5\u548c\u5bfc\u5165SciPy\u5e93<\/h3>\n<\/p>\n
\u5728\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\u4e4b\u524d\uff0c\u9700\u8981\u786e\u4fdd\u5df2\u7ecf\u5b89\u88c5\u4e86SciPy\u5e93\u3002\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u5b89\u88c5SciPy\uff1a<\/p>\n<\/p>\n
pip install scipy<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5b89\u88c5\u5b8c\u6210\u540e\uff0c\u5728\u4ee3\u7801\u4e2d\u5bfc\u5165SciPy\u5e93\uff1a<\/p>\n<\/p>\n
from scipy.linalg import svd<\/p>\n
<\/code><\/pre>\n<\/p>\n
2. \u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3<\/h3>\n<\/p>\n
\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u77e9\u9635A\uff0c\u60f3\u5bf9\u5176\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\u3002\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u4ee3\u7801\uff1a<\/p>\n<\/p>\n
# \u521b\u5efa\u4e00\u4e2a\u77e9\u9635<\/p>\n
A = np.array([[1, 2, 3], <\/p>\n
              [4, 5, 6], <\/p>\n
              [7, 8, 9]])<\/p>\n
\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3<\/strong><\/h2>\n
U, S, VT = svd(A)<\/p>\n
print("U\u77e9\u9635\uff1a\\n", U)<\/p>\n
print("\u5947\u5f02\u503c\uff1a\\n", S)<\/p>\n
print("V^T\u77e9\u9635\uff1a\\n", VT)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0csvd(A)<\/code>\u51fd\u6570\u8fd4\u56de\u4e09\u4e2a\u503c\uff1aU\u77e9\u9635\u3001\u5947\u5f02\u503c\u5411\u91cfS\u3001V^T\u77e9\u9635\u3002U\u77e9\u9635\u548cV^T\u77e9\u9635\u662f\u6b63\u4ea4\u77e9\u9635\uff0cS\u662f\u5947\u5f02\u503c\u7684\u5bf9\u89d2\u7ebf\u5143\u7d20\u3002<\/p>\n<\/p>\n
3. \u8fd8\u539f\u539f\u59cb\u77e9\u9635<\/h3>\n<\/p>\n
\u53ef\u4ee5\u4f7f\u7528\u5206\u89e3\u5f97\u5230\u7684U\u77e9\u9635\u3001\u5947\u5f02\u503c\u5411\u91cfS\u3001V^T\u77e9\u9635\u8fd8\u539f\u539f\u59cb\u77e9\u9635A\uff1a<\/p>\n<\/p>\n
# \u6784\u9020\u5bf9\u89d2\u77e9\u9635<\/p>\n
Sigma = np.zeros((A.shape[0], A.shape[1]))<\/p>\n
np.fill_diagonal(Sigma, S)<\/p>\n
\u8fd8\u539f\u539f\u59cb\u77e9\u9635<\/strong><\/h2>\n
A_reconstructed = np.dot(U, np.dot(Sigma, VT))<\/p>\n
print("\u8fd8\u539f\u7684\u77e9\u9635\uff1a\\n", A_reconstructed)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e09\u3001SCIKIT-LEARN\u5e93\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3<\/p>\n<\/p>\n
scikit-learn\u662fPython\u4e2d\u4e00\u4e2a\u5f3a\u5927\u7684\u673a\u5668\u5b66\u4e60<\/a>\u5e93\uff0c\u63d0\u4f9b\u4e86\u5927\u91cf\u7684\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u548c\u5de5\u5177\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528scikit-learn\u5e93\u4e2d\u7684TruncatedSVD<\/code>\u7c7b\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\u3002<\/p>\n<\/p>\n
1. \u5b89\u88c5\u548c\u5bfc\u5165scikit-learn\u5e93<\/h3>\n<\/p>\n
\u5728\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\u4e4b\u524d\uff0c\u9700\u8981\u786e\u4fdd\u5df2\u7ecf\u5b89\u88c5\u4e86scikit-learn\u5e93\u3002\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u5b89\u88c5scikit-learn\uff1a<\/p>\n<\/p>\n
pip install scikit-learn<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5b89\u88c5\u5b8c\u6210\u540e\uff0c\u5728\u4ee3\u7801\u4e2d\u5bfc\u5165scikit-learn\u5e93\uff1a<\/p>\n<\/p>\n
from sklearn.decomposition import TruncatedSVD<\/p>\n
<\/code><\/pre>\n<\/p>\n
2. \u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3<\/h3>\n<\/p>\n
\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u77e9\u9635A\uff0c\u60f3\u5bf9\u5176\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\u3002\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u4ee3\u7801\uff1a<\/p>\n<\/p>\n
# \u521b\u5efa\u4e00\u4e2a\u77e9\u9635<\/p>\n
A = np.array([[1, 2, 3], <\/p>\n
              [4, 5, 6], <\/p>\n
              [7, 8, 9]])<\/p>\n
\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3<\/strong><\/h2>\n
svd = TruncatedSVD(n_components=2)<\/p>\n
U = svd.fit_transform(A)<\/p>\n
S = svd.singular_values_<\/p>\n
VT = svd.components_<\/p>\n
print("U\u77e9\u9635\uff1a\\n", U)<\/p>\n
print("\u5947\u5f02\u503c\uff1a\\n", S)<\/p>\n
print("V^T\u77e9\u9635\uff1a\\n", VT)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0cTruncatedSVD(n_components=2)<\/code>\u521b\u5efa\u4e86\u4e00\u4e2aTruncatedSVD\u5bf9\u8c61\uff0cfit_transform(A)<\/code>\u51fd\u6570\u5bf9\u77e9\u9635A\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\uff0c\u5e76\u8fd4\u56deU\u77e9\u9635\uff0csingular_values_<\/code>\u5c5e\u6027\u8fd4\u56de\u5947\u5f02\u503c\u5411\u91cfS\uff0ccomponents_<\/code>\u5c5e\u6027\u8fd4\u56deV^T\u77e9\u9635\u3002<\/p>\n<\/p>\n
3. \u8fd8\u539f\u539f\u59cb\u77e9\u9635<\/h3>\n<\/p>\n
\u53ef\u4ee5\u4f7f\u7528\u5206\u89e3\u5f97\u5230\u7684U\u77e9\u9635\u3001\u5947\u5f02\u503c\u5411\u91cfS\u3001V^T\u77e9\u9635\u8fd8\u539f\u539f\u59cb\u77e9\u9635A\uff1a<\/p>\n<\/p>\n
# \u6784\u9020\u5bf9\u89d2\u77e9\u9635<\/p>\n
Sigma = np.zeros((U.shape[1], VT.shape[0]))<\/p>\n
np.fill_diagonal(Sigma, S)<\/p>\n
\u8fd8\u539f\u539f\u59cb\u77e9\u9635<\/strong><\/h2>\n
A_reconstructed = np.dot(U, np.dot(Sigma, VT))<\/p>\n
print("\u8fd8\u539f\u7684\u77e9\u9635\uff1a\\n", A_reconstructed)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u56db\u3001\u5947\u5f02\u503c\u5206\u89e3\u7684\u5b9e\u9645\u5e94\u7528<\/p>\n<\/p>\n
1. \u6570\u636e\u964d\u7ef4<\/h3>\n<\/p>\n
\u5947\u5f02\u503c\u5206\u89e3\u53ef\u4ee5\u7528\u4e8e\u6570\u636e\u964d\u7ef4\uff0c\u5c06\u9ad8\u7ef4\u6570\u636e\u6620\u5c04\u5230\u4f4e\u7ef4\u7a7a\u95f4\uff0c\u4fdd\u7559\u4e3b\u8981\u4fe1\u606f\uff0c\u53bb\u9664\u566a\u58f0\u3002\u4ee5\u4e0b\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\uff1a<\/p>\n<\/p>\n
from sklearn.datasets import load_iris<\/p>\n
from sklearn.decomposition import TruncatedSVD<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
\u52a0\u8f7d\u6570\u636e\u96c6<\/strong><\/h2>\n
iris = load_iris()<\/p>\n
X = iris.data<\/p>\n
\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\u964d\u7ef4<\/strong><\/h2>\n
svd = TruncatedSVD(n_components=2)<\/p>\n
X_reduced = svd.fit_transform(X)<\/p>\n
\u53ef\u89c6\u5316\u964d\u7ef4\u540e\u7684\u6570\u636e<\/strong><\/h2>\n
plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=iris.target)<\/p>\n
plt.xlabel('Component 1')<\/p>\n
plt.ylabel('Component 2')<\/p>\n
plt.title('SVD Dimensionality Reduction')<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u4e86TruncatedSVD<\/code>\u7c7b\u5c06iris\u6570\u636e\u96c6\u4ece\u56db\u7ef4\u964d\u5230\u4e8c\u7ef4\uff0c\u5e76\u5bf9\u964d\u7ef4\u540e\u7684\u6570\u636e\u8fdb\u884c\u53ef\u89c6\u5316\u3002<\/p>\n<\/p>\n
2. \u56fe\u50cf\u538b\u7f29<\/h3>\n<\/p>\n
\u5947\u5f02\u503c\u5206\u89e3\u53ef\u4ee5\u7528\u4e8e\u56fe\u50cf\u538b\u7f29\uff0c\u5c06\u539f\u59cb\u56fe\u50cf\u5206\u89e3\u4e3a\u4f4e\u79e9\u8fd1\u4f3c\u77e9\u9635\u3002\u4ee5\u4e0b\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\uff1a<\/p>\n<\/p>\n
from skimage import data<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
\u52a0\u8f7d\u56fe\u50cf<\/strong><\/h2>\n
image = data.camera()<\/p>\n
U, S, VT = np.linalg.svd(image, full_matrices=False)<\/p>\n
\u4f7f\u7528\u524dk\u4e2a\u5947\u5f02\u503c\u8fdb\u884c\u91cd\u6784<\/strong><\/h2>\n
k = 50<\/p>\n
reconstructed_image = np.dot(U[:, :k], np.dot(np.diag(S[:k]), VT[:k, :]))<\/p>\n
\u663e\u793a\u539f\u59cb\u56fe\u50cf\u548c\u91cd\u6784\u56fe\u50cf<\/strong><\/h2>\n
plt.subplot(1, 2, 1)<\/p>\n
plt.title('Original Image')<\/p>\n
plt.imshow(image, cmap='gray')<\/p>\n
plt.subplot(1, 2, 2)<\/p>\n
plt.title('Reconstructed Image')<\/p>\n
plt.imshow(reconstructed_image, cmap='gray')<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u4e86\u524d50\u4e2a\u5947\u5f02\u503c\u5bf9\u56fe\u50cf\u8fdb\u884c\u91cd\u6784\uff0c\u5f97\u5230\u4e86\u538b\u7f29\u540e\u7684\u56fe\u50cf\u3002<\/p>\n<\/p>\n
3. \u63a8\u8350\u7cfb\u7edf<\/h3>\n<\/p>\n
\u5947\u5f02\u503c\u5206\u89e3\u53ef\u4ee5\u7528\u4e8e\u63a8\u8350\u7cfb\u7edf\uff0c\u901a\u8fc7\u5206\u89e3\u7528\u6237-\u7269\u54c1\u77e9\u9635\uff0c\u9884\u6d4b\u7528\u6237\u672a\u8bc4\u5206\u7684\u7269\u54c1\u8bc4\u5206\u3002\u4ee5\u4e0b\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
\u521b\u5efa\u7528\u6237-\u7269\u54c1\u77e9\u9635<\/strong><\/h2>\n
R = np.array([[5, 3, 0, 1],<\/p>\n
              [4, 0, 0, 1],<\/p>\n
              [1, 1, 0, 5],<\/p>\n
              [1, 0, 0, 4],<\/p>\n
              [0, 1, 5, 4]])<\/p>\n
\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3<\/strong><\/h2>\n
U, S, VT = np.linalg.svd(R, full_matrices=False)<\/p>\n
\u4f7f\u7528\u524dk\u4e2a\u5947\u5f02\u503c\u8fdb\u884c\u91cd\u6784<\/strong><\/h2>\n
k = 2<\/p>\n
R_reconstructed = np.dot(U[:, :k], np.dot(np.diag(S[:k]), VT[:k, :]))<\/p>\n
print("\u539f\u59cb\u77e9\u9635\uff1a\\n", R)<\/p>\n
print("\u91cd\u6784\u77e9\u9635\uff1a\\n", R_reconstructed)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u4e86\u524d2\u4e2a\u5947\u5f02\u503c\u5bf9\u7528\u6237-\u7269\u54c1\u77e9\u9635\u8fdb\u884c\u91cd\u6784\uff0c\u53ef\u4ee5\u7528\u4e8e\u9884\u6d4b\u7528\u6237\u672a\u8bc4\u5206\u7684\u7269\u54c1\u8bc4\u5206\u3002<\/p>\n<\/p>\n
\u7efc\u4e0a\u6240\u8ff0\uff0c\u5947\u5f02\u503c\u5206\u89e3\u662f\u4e00\u79cd\u91cd\u8981\u7684\u77e9\u9635\u5206\u89e3\u6280\u672f<\/strong>\uff0c\u5728\u6570\u636e\u964d\u7ef4\u3001\u56fe\u50cf\u538b\u7f29\u3001\u63a8\u8350\u7cfb\u7edf\u7b49\u9886\u57df\u6709\u5e7f\u6cdb\u5e94\u7528\u3002\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528NumPy\u5e93\u3001SciPy\u5e93\u3001scikit-learn\u5e93\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3<\/strong>\uff0c\u672c\u6587\u8be6\u7ec6\u4ecb\u7ecd\u4e86\u5982\u4f55\u4f7f\u7528\u8fd9\u4e09\u79cd\u5e93\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\u53ca\u5176\u5b9e\u9645\u5e94\u7528\u3002\u5e0c\u671b\u672c\u6587\u5bf9\u4f60\u6709\u6240\u5e2e\u52a9\u3002<\/p>\n<\/p>\n
\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
 \u5947\u5f02\u503c\u5206\u89e3\u5728Python\u4e2d\u6709\u4ec0\u4e48\u5e94\u7528\u573a\u666f\uff1f<\/strong>
\u5947\u5f02\u503c\u5206\u89e3\uff08SVD\uff09\u662f\u4e00\u79cd\u5f3a\u5927\u7684\u6570\u5b66\u5de5\u5177\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u6570\u636e\u964d\u7ef4\u3001\u56fe\u50cf\u5904\u7406\u3001\u63a8\u8350\u7cfb\u7edf\u548c\u81ea\u7136\u8bed\u8a00\u5904\u7406\u7b49\u9886\u57df\u3002\u5728\u6570\u636e\u5206\u6790\u4e2d\uff0cSVD\u80fd\u591f\u5e2e\u52a9\u6211\u4eec\u8bc6\u522b\u6570\u636e\u4e2d\u7684\u6f5c\u5728\u7ed3\u6784\uff0c\u964d\u4f4e\u8ba1\u7b97\u590d\u6742\u5ea6\u3002\u5728\u56fe\u50cf\u5904\u7406\u4e2d\uff0cSVD\u53ef\u4ee5\u7528\u4e8e\u56fe\u50cf\u538b\u7f29\uff0c\u901a\u8fc7\u53bb\u9664\u4e0d\u91cd\u8981\u7684\u7279\u5f81\u6765\u51cf\u5c0f\u6587\u4ef6\u5927\u5c0f\u3002\u63a8\u8350\u7cfb\u7edf\u4e2d\uff0cSVD\u88ab\u7528\u6765\u6316\u6398\u7528\u6237\u548c\u7269\u54c1\u4e4b\u95f4\u7684\u6f5c\u5728\u5173\u7cfb\uff0c\u4ece\u800c\u63d0\u9ad8\u63a8\u8350\u7684\u51c6\u786e\u6027\u3002<\/p>\n
\u5728Python\u4e2d\u5982\u4f55\u5b9e\u73b0\u5947\u5f02\u503c\u5206\u89e3\uff1f<\/strong>
\u5728Python\u4e2d\uff0c\u6700\u5e38\u7528\u7684\u5b9e\u73b0\u5947\u5f02\u503c\u5206\u89e3\u7684\u5e93\u662fNumPy\u548cSciPy\u3002\u4f7f\u7528NumPy\u7684numpy.linalg.svd()<\/code>\u51fd\u6570\uff0c\u53ef\u4ee5\u65b9\u4fbf\u5730\u5bf9\u77e9\u9635\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\u3002\u5176\u8fd4\u56de\u503c\u5305\u62ec\u5947\u5f02\u503c\u3001\u5de6\u5947\u5f02\u5411\u91cf\u548c\u53f3\u5947\u5f02\u5411\u91cf\u3002\u793a\u4f8b\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n
import numpy as np\n\n# \u521b\u5efa\u4e00\u4e2a\u77e9\u9635\nA = np.array([[1, 2], [3, 4], [5, 6]])\n\n# \u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\nU, S, VT = np.linalg.svd(A)\n\nprint("\u5de6\u5947\u5f02\u5411\u91cf U:\\n", U)\nprint("\u5947\u5f02\u503c S:\\n", S)\nprint("\u53f3\u5947\u5f02\u5411\u91cf VT:\\n", VT)\n<\/code><\/pre>\n
\u8be5\u4ee3\u7801\u5c55\u793a\u4e86\u5982\u4f55\u5bf9\u4e00\u4e2a\u7b80\u5355\u7684\u77e9\u9635\u8fdb\u884cSVD\uff0c\u5e76\u8f93\u51fa\u5206\u89e3\u7ed3\u679c\u3002<\/p>\n
\u5728\u4f7f\u7528\u5947\u5f02\u503c\u5206\u89e3\u65f6\u9700\u8981\u6ce8\u610f\u54ea\u4e9b\u4e8b\u9879\uff1f<\/strong>
\u8fdb\u884c\u5947\u5f02\u503c\u5206\u89e3\u65f6\uff0c\u6709\u51e0\u4e2a\u5173\u952e\u70b9\u9700\u8981\u5173\u6ce8\u3002\u9996\u5148\uff0c\u8f93\u5165\u7684\u77e9\u9635\u5e94\u4e3a\u4e8c\u7ef4\u6570\u7ec4\uff0c\u4e14\u5efa\u8bae\u8fdb\u884c\u6807\u51c6\u5316\u5904\u7406\uff0c\u4ee5\u63d0\u9ad8\u5206\u89e3\u7684\u7a33\u5b9a\u6027\u548c\u51c6\u786e\u6027\u3002\u5176\u6b21\uff0c\u5947\u5f02\u503c\u5206\u89e3\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\u8f83\u9ad8\uff0c\u5728\u5904\u7406\u5927\u89c4\u6a21\u6570\u636e\u65f6\uff0c\u53ef\u80fd\u5bfc\u81f4\u6027\u80fd\u95ee\u9898\u3002\u53ef\u4ee5\u8003\u8651\u4f7f\u7528\u589e\u91cf\u5f0fSVD\u6216\u5176\u4ed6\u8fd1\u4f3c\u7b97\u6cd5\u6765\u63d0\u9ad8\u6548\u7387\u3002\u6b64\u5916\uff0c\u5904\u7406\u540e\u7684\u5947\u5f02\u503c\u5e94\u6839\u636e\u5177\u4f53\u5e94\u7528\u8fdb\u884c\u9009\u62e9\uff0c\u4ee5\u907f\u514d\u8fc7\u62df\u5408\u6216\u4fe1\u606f\u635f\u5931\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u5947\u5f02\u503c\u5206\u89e3\uff08SVD\uff09\u662f\u4e00\u79cd\u91cd\u8981\u7684\u77e9\u9635\u5206\u89e3\u6280\u672f\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u6570\u636e\u964d\u7ef4\u3001\u56fe\u50cf\u5904\u7406\u3001\u63a8\u8350\u7cfb\u7edf\u7b49\u9886\u57df\u3002\u5728Python\u4e2d\u8fdb […]","protected":false},"author":3,"featured_media":1048785,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1048768"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=1048768"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1048768\/revisions"}],"predecessor-version":[{"id":1048789,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1048768\/revisions\/1048789"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1048785"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1048768"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1048768"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1048768"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}