{"id":1064147,"date":"2024-12-31T16:06:42","date_gmt":"2024-12-31T08:06:42","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1064147.html"},"modified":"2024-12-31T16:06:44","modified_gmt":"2024-12-31T08:06:44","slug":"python%e5%a6%82%e4%bd%95%e7%94%bb%e4%b8%80%e6%9d%a1%e6%8b%9f%e5%90%88%e7%ba%bf","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1064147.html","title":{"rendered":"python\u5982\u4f55\u753b\u4e00\u6761\u62df\u5408\u7ebf"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-docs.pingcode.com\/wp-content\/uploads\/2024\/12\/cd44dcb0-03b5-4991-8c29-459136b7fbcf.webp?x-oss-process=image\/auto-orient,1\/format,webp\" alt=\"python\u5982\u4f55\u753b\u4e00\u6761\u62df\u5408\u7ebf\" \/><\/p>\n<p><p> <strong>Python\u753b\u4e00\u6761\u62df\u5408\u7ebf\u7684\u6b65\u9aa4\u4e3b\u8981\u5305\u62ec\uff1a\u5bfc\u5165\u5fc5\u8981\u7684\u5e93\u3001\u51c6\u5907\u6570\u636e\u3001\u6267\u884c\u7ebf\u6027\u56de\u5f52\u3001\u7ed8\u5236\u62df\u5408\u7ebf\u3001\u89e3\u91ca\u7ed3\u679c\u3002<\/strong> \u5176\u4e2d\uff0c\u6700\u5e38\u7528\u7684\u5e93\u662fMatplotlib\u548cNumPy\uff0c\u4ee5\u53ca\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u5e38\u7528\u7684\u5e93Scikit-learn\u3002\u6211\u4eec\u5c06\u8be6\u7ec6\u63cf\u8ff0\u5982\u4f55\u901a\u8fc7\u8fd9\u4e9b\u6b65\u9aa4\u5b9e\u73b0\u4e00\u4e2a\u62df\u5408\u7ebf\u7684\u7ed8\u5236\uff0c\u5e76\u89e3\u91ca\u5404\u4e2a\u6b65\u9aa4\u7684\u7ec6\u8282\u3002<\/p>\n<\/p>\n<p><h2>\u4e00\u3001\u5bfc\u5165\u5fc5\u8981\u7684\u5e93<\/h2>\n<\/p>\n<p><p>\u5728\u7ed8\u5236\u62df\u5408\u7ebf\u4e4b\u524d\uff0c\u6211\u4eec\u9700\u8981\u5bfc\u5165\u4e00\u4e9b\u5e38\u7528\u7684Python\u5e93\uff0c\u8fd9\u4e9b\u5e93\u5305\u62ec\uff1aNumPy\u7528\u4e8e\u6570\u636e\u5904\u7406\uff0cMatplotlib\u7528\u4e8e\u7ed8\u56fe\uff0cScikit-learn\u7528\u4e8e\u6267\u884c\u7ebf\u6027\u56de\u5f52\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>import matplotlib.pyplot as plt<\/p>\n<p>from sklearn.linear_model import LinearRegression<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h2>\u4e8c\u3001\u51c6\u5907\u6570\u636e<\/h2>\n<\/p>\n<p><p>\u51c6\u5907\u6570\u636e\u662f\u7ed8\u5236\u62df\u5408\u7ebf\u7684\u7b2c\u4e00\u6b65\u3002\u6211\u4eec\u9700\u8981\u6709\u4e00\u7ec4\u8f93\u5165\u6570\u636e\uff08\u81ea\u53d8\u91cfX\uff09\u548c\u5bf9\u5e94\u7684\u8f93\u51fa\u6570\u636e\uff08\u56e0\u53d8\u91cfY\uff09\u3002\u8fd9\u4e9b\u6570\u636e\u53ef\u4ee5\u662f\u4ece\u5b9e\u9a8c\u4e2d\u83b7\u5f97\u7684\uff0c\u4e5f\u53ef\u4ee5\u662f\u901a\u8fc7\u67d0\u4e9b\u51fd\u6570\u751f\u6210\u7684\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u751f\u6210\u793a\u4f8b\u6570\u636e<\/p>\n<p>np.random.seed(0)<\/p>\n<p>X = 2 * np.random.rand(100, 1)<\/p>\n<p>Y = 4 + 3 * X + np.random.randn(100, 1)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528NumPy\u751f\u6210\u4e86\u4e00\u7ec4\u968f\u673a\u6570\u636e\u3002<code>X<\/code>\u662f\u4e00\u4e2a\u5305\u542b100\u4e2a\u968f\u673a\u6570\u7684\u6570\u7ec4\uff0c\u8fd9\u4e9b\u6570\u503c\u57280\u52302\u4e4b\u95f4\u3002<code>Y<\/code>\u662f\u4e00\u4e2a\u901a\u8fc7\u7ebf\u6027\u65b9\u7a0b<code>4 + 3 * X<\/code>\u52a0\u4e0a\u4e00\u4e9b\u968f\u673a\u566a\u58f0\u751f\u6210\u7684\u6570\u7ec4\u3002<\/p>\n<\/p>\n<p><h2>\u4e09\u3001\u6267\u884c\u7ebf\u6027\u56de\u5f52<\/h2>\n<\/p>\n<p><p>\u6709\u4e86\u6570\u636e\u4e4b\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528Scikit-learn\u5e93\u4e2d\u7684\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u6765\u62df\u5408\u8fd9\u4e9b\u6570\u636e\u3002\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u80fd\u591f\u627e\u5230\u6700\u9002\u5408\u8fd9\u4e9b\u6570\u636e\u7684\u76f4\u7ebf\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u521b\u5efa\u7ebf\u6027\u56de\u5f52\u6a21\u578b<\/p>\n<p>lin_reg = LinearRegression()<\/p>\n<p>lin_reg.fit(X, Y)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u521b\u5efa\u4e86\u4e00\u4e2a<code>LinearRegression<\/code>\u5bf9\u8c61\uff0c\u5e76\u4f7f\u7528<code>fit<\/code>\u65b9\u6cd5\u6765\u62df\u5408\u6570\u636e\u3002\u62df\u5408\u8fc7\u7a0b\u5b9e\u9645\u4e0a\u662f\u5728\u8ba1\u7b97\u6700\u9002\u5408\u6570\u636e\u7684\u76f4\u7ebf\u7684\u659c\u7387\u548c\u622a\u8ddd\u3002<\/p>\n<\/p>\n<p><h2>\u56db\u3001\u7ed8\u5236\u62df\u5408\u7ebf<\/h2>\n<\/p>\n<p><p>\u62df\u5408\u5b8c\u6210\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528Matplotlib\u5e93\u6765\u7ed8\u5236\u62df\u5408\u7ebf\u548c\u6570\u636e\u70b9\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u7ed8\u5236\u6570\u636e\u70b9<\/p>\n<p>plt.scatter(X, Y, color=&#39;blue&#39;, label=&#39;Data points&#39;)<\/p>\n<h2><strong>\u7ed8\u5236\u62df\u5408\u7ebf<\/strong><\/h2>\n<p>X_new = np.array([[0], [2]])<\/p>\n<p>Y_predict = lin_reg.predict(X_new)<\/p>\n<p>plt.plot(X_new, Y_predict, color=&#39;red&#39;, linewidth=2, label=&#39;Fit line&#39;)<\/p>\n<p>plt.xlabel(&#39;X&#39;)<\/p>\n<p>plt.ylabel(&#39;Y&#39;)<\/p>\n<p>plt.legend()<\/p>\n<p>plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u9996\u5148\u4f7f\u7528<code>scatter<\/code>\u51fd\u6570\u7ed8\u5236\u6570\u636e\u70b9\uff0c\u7136\u540e\u4f7f\u7528<code>plot<\/code>\u51fd\u6570\u7ed8\u5236\u62df\u5408\u7ebf\u3002\u62df\u5408\u7ebf\u7684\u4e24\u4e2a\u7aef\u70b9\u5206\u522b\u662f<code>X_new<\/code>\u4e2d\u7684\u4e24\u4e2a\u70b9\uff080\u548c2\uff09\uff0c\u5bf9\u5e94\u7684\u9884\u6d4b\u503c\u662f<code>Y_predict<\/code>\u3002<\/p>\n<\/p>\n<p><h2>\u4e94\u3001\u89e3\u91ca\u7ed3\u679c<\/h2>\n<\/p>\n<p><p>\u901a\u8fc7\u4e0a\u8ff0\u6b65\u9aa4\uff0c\u6211\u4eec\u7ed8\u5236\u4e86\u4e00\u6761\u62df\u5408\u7ebf\u3002\u62df\u5408\u7ebf\u7684\u659c\u7387\u548c\u622a\u8ddd\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u4ee3\u7801\u83b7\u53d6\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">print(&#39;Slope:&#39;, lin_reg.coef_)<\/p>\n<p>print(&#39;Intercept:&#39;, lin_reg.intercept_)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u8fd9\u4e9b\u503c\u8868\u793a\u4e86\u62df\u5408\u7ebf\u7684\u65b9\u7a0b\u3002\u659c\u7387\uff08Slope\uff09\u8868\u793a\u4e86X\u548cY\u4e4b\u95f4\u7684\u7ebf\u6027\u5173\u7cfb\uff0c\u800c\u622a\u8ddd\uff08Intercept\uff09\u8868\u793a\u4e86\u62df\u5408\u7ebf\u5728Y\u8f74\u4e0a\u7684\u8d77\u70b9\u3002<\/p>\n<\/p>\n<p><h3>\u8fdb\u4e00\u6b65\u63d0\u9ad8\u6a21\u578b\u7684\u51c6\u786e\u6027<\/h3>\n<\/p>\n<p><p>\u867d\u7136\u7b80\u5355\u7684\u7ebf\u6027\u56de\u5f52\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u6570\u636e\u4e2d\u7684\u7ebf\u6027\u5173\u7cfb\uff0c\u4f46\u5b9e\u9645\u5e94\u7528\u4e2d\u53ef\u80fd\u9700\u8981\u66f4\u590d\u6742\u7684\u6a21\u578b\u6765\u63d0\u9ad8\u9884\u6d4b\u51c6\u786e\u6027\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u65b9\u5f0f\u63d0\u9ad8\u6a21\u578b\u7684\u6027\u80fd\uff1a<\/p>\n<\/p>\n<ol>\n<li><strong>\u591a\u9879\u5f0f\u56de\u5f52<\/strong>\uff1a\u5982\u679c\u6570\u636e\u5448\u73b0\u975e\u7ebf\u6027\u5173\u7cfb\uff0c\u53ef\u4ee5\u5c1d\u8bd5\u591a\u9879\u5f0f\u56de\u5f52\u3002Scikit-learn\u63d0\u4f9b\u4e86<code>PolynomialFeatures<\/code>\u7c7b\u6765\u751f\u6210\u591a\u9879\u5f0f\u7279\u5f81\u3002<\/li>\n<li><strong>\u6b63\u5219\u5316<\/strong>\uff1a\u4f7f\u7528\u6b63\u5219\u5316\u65b9\u6cd5\uff08\u5982Lasso\u6216Ridge\u56de\u5f52\uff09\u53ef\u4ee5\u9632\u6b62\u8fc7\u62df\u5408\uff0c\u63d0\u9ad8\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/li>\n<li><strong>\u4ea4\u53c9\u9a8c\u8bc1<\/strong>\uff1a\u4f7f\u7528\u4ea4\u53c9\u9a8c\u8bc1\u53ef\u4ee5\u66f4\u53ef\u9760\u5730\u8bc4\u4f30\u6a21\u578b\u7684\u6027\u80fd\uff0c\u5e76\u9009\u62e9\u6700\u4f73\u7684\u8d85\u53c2\u6570\u3002<\/li>\n<\/ol>\n<p><pre><code class=\"language-python\">from sklearn.preprocessing import PolynomialFeatures<\/p>\n<p>from sklearn.linear_model import Ridge<\/p>\n<p>from sklearn.model_selection import cross_val_score<\/p>\n<h2><strong>\u591a\u9879\u5f0f\u56de\u5f52\u793a\u4f8b<\/strong><\/h2>\n<p>poly_features = PolynomialFeatures(degree=2, include_bias=False)<\/p>\n<p>X_poly = poly_features.fit_transform(X)<\/p>\n<p>ridge_reg = Ridge(alpha=1, solver=&quot;cholesky&quot;)<\/p>\n<p>ridge_reg.fit(X_poly, Y)<\/p>\n<p>print(&#39;Ridge Regression Slope:&#39;, ridge_reg.coef_)<\/p>\n<p>print(&#39;Ridge Regression Intercept:&#39;, ridge_reg.intercept_)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u901a\u8fc7\u4ee5\u4e0a\u65b9\u6cd5\uff0c\u6211\u4eec\u53ef\u4ee5\u8fdb\u4e00\u6b65\u63d0\u9ad8\u6a21\u578b\u7684\u51c6\u786e\u6027\u548c\u7a33\u5b9a\u6027\uff0c\u83b7\u5f97\u66f4\u6709\u4ef7\u503c\u7684\u9884\u6d4b\u7ed3\u679c\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> <strong>\u5982\u4f55\u4f7f\u7528Python\u7ed8\u5236\u6570\u636e\u7684\u62df\u5408\u7ebf\uff1f<\/strong><br \/>\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u5229\u7528\u591a\u79cd\u5e93\u7ed8\u5236\u62df\u5408\u7ebf\u3002\u6700\u5e38\u7528\u7684\u5e93\u6709Matplotlib\u548cNumPy\u3002\u901a\u5e38\uff0c\u60a8\u9700\u8981\u5148\u4f7f\u7528NumPy\u7684polyfit\u51fd\u6570\u6765\u8ba1\u7b97\u62df\u5408\u7ebf\u7684\u53c2\u6570\uff0c\u7136\u540e\u4f7f\u7528Matplotlib\u7ed8\u5236\u6570\u636e\u70b9\u548c\u62df\u5408\u7ebf\u3002\u4ee5\u4e0b\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u793a\u4f8b\u4ee3\u7801\uff1a<\/p>\n<pre><code class=\"language-python\">import numpy as np\nimport matplotlib.pyplot as plt\n\n# \u793a\u4f8b\u6570\u636e\nx = np.array([1, 2, 3, 4, 5])\ny = np.array([2.2, 2.8, 3.6, 4.5, 5.1])\n\n# \u8ba1\u7b97\u62df\u5408\u7ebf\u7684\u7cfb\u6570\ncoefficients = np.polyfit(x, y, 1)  # 1\u8868\u793a\u7ebf\u6027\u62df\u5408\nfit_line = np.polyval(coefficients, x)\n\n# \u7ed8\u5236\u6570\u636e\u70b9\u548c\u62df\u5408\u7ebf\nplt.scatter(x, y, color=&#39;blue&#39;, label=&#39;\u6570\u636e\u70b9&#39;)\nplt.plot(x, fit_line, color=&#39;red&#39;, label=&#39;\u62df\u5408\u7ebf&#39;)\nplt.legend()\nplt.xlabel(&#39;X\u8f74&#39;)\nplt.ylabel(&#39;Y\u8f74&#39;)\nplt.title(&#39;\u6570\u636e\u4e0e\u62df\u5408\u7ebf&#39;)\nplt.show()\n<\/code><\/pre>\n<p><strong>\u62df\u5408\u7ebf\u7684\u7c7b\u578b\u6709\u54ea\u4e9b\uff0c\u5982\u4f55\u9009\u62e9\u5408\u9002\u7684\u62df\u5408\u65b9\u6cd5\uff1f<\/strong><br \/>\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u6839\u636e\u6570\u636e\u7684\u7279\u6027\u9009\u62e9\u4e0d\u540c\u7684\u62df\u5408\u65b9\u6cd5\u3002\u5e38\u89c1\u7684\u62df\u5408\u7c7b\u578b\u5305\u62ec\u7ebf\u6027\u62df\u5408\u3001\u591a\u9879\u5f0f\u62df\u5408\u3001\u6307\u6570\u62df\u5408\u548c\u5bf9\u6570\u62df\u5408\u7b49\u3002\u7ebf\u6027\u62df\u5408\u9002\u7528\u4e8e\u6570\u636e\u8d8b\u52bf\u8f83\u4e3a\u7ebf\u6027\u7684\u60c5\u51b5\uff0c\u800c\u591a\u9879\u5f0f\u62df\u5408\u9002\u5408\u4e8e\u5b58\u5728\u66f4\u590d\u6742\u5173\u7cfb\u7684\u6570\u636e\u3002\u9009\u62e9\u5408\u9002\u7684\u62df\u5408\u65b9\u6cd5\u53ef\u4ee5\u901a\u8fc7\u53ef\u89c6\u5316\u6570\u636e\u70b9\u5e76\u89c2\u5bdf\u5176\u5206\u5e03\u8d8b\u52bf\u6765\u5b9e\u73b0\uff0c\u4f7f\u7528scikit-learn\u7b49\u5e93\u4e5f\u53ef\u4ee5\u65b9\u4fbf\u5730\u8fdb\u884c\u6a21\u578b\u9009\u62e9\u548c\u8bc4\u4f30\u3002<\/p>\n<p><strong>\u5982\u4f55\u8bc4\u4f30\u62df\u5408\u7ebf\u7684\u51c6\u786e\u6027\uff1f<\/strong><br 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