{"id":106728,"date":"2026-09-18T08:08:35","date_gmt":"2026-09-18T00:08:35","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/106728.html"},"modified":"2026-09-18T08:08:35","modified_gmt":"2026-09-18T00:08:35","slug":"ai%e5%a4%a7%e6%a8%a1%e5%9e%8b%e4%b8%8e%e6%95%b0%e5%ad%a6%ef%bd%9c%e7%ac%ac81%e5%a4%a9-%e8%af%be%e7%a8%8b%ef%bc%9a%e6%ad%a3%e4%ba%a4%e5%90%91%e9%87%8f%e3%80%81%e6%ad%a3%e4%ba%a4%e5%9f%ba%e3%80%81","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/106728.html","title":{"rendered":"AI\u5927\u6a21\u578b\u4e0e\u6570\u5b66\uff5c\u7b2c81\u5929 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j<\/p>\n<p>\u79f0\u4e3a\u6b63\u4ea4\u5411\u91cf\u7ec4\u3002<\/p>\n<\/p>\n<p>\u91cd\u8981\u5b9a\u7406&#xff1a;\u6b63\u4ea4\u5411\u91cf\u7ec4\u4e00\u5b9a\u7ebf\u6027\u65e0\u5173\u3002<\/p>\n<p>\u8fd9\u662f\u5de8\u5927\u4f18\u52bf&#xff1a;\u53ea\u8981\u4e24\u4e24\u6b63\u4ea4&#xff0c;\u5c31\u81ea\u52a8\u662f\u65e0\u5173\u7ec4&#xff0c;\u4e0d\u7528\u518d\u7b97\u884c\u5217\u5f0f\u5224\u65ad\u7ebf\u6027\u76f8\u5173\u6027\u3002<\/p>\n<\/p>\n<p>\u6807\u51c6\u6b63\u4ea4\u5411\u91cf\u7ec4&#xff08;\u5355\u4f4d\u6b63\u4ea4&#xff09;<\/p>\n<\/p>\n<p>\u6b63\u4ea4\u57fa\u7840\u4e0a&#xff0c;\u6bcf\u4e00\u4e2a\u5411\u91cf\u81ea\u8eab\u957f\u5ea6&#xff08;\u8303\u6570&#xff09;\u4e3a1&#xff1a;<\/p>\n<p>\\\\|\\\\boldsymbol v_i\\\\|&#061;\\\\sqrt{\\\\boldsymbol v_i^\\\\mathrm T\\\\boldsymbol v_i}&#061;1<\/p>\n<p>\u4e24\u4e24\u5185\u79ef\u6ee1\u8db3&#xff1a;<\/p>\n<\/p>\n<p>\\\\boldsymbol v_i^\\\\mathrm T\\\\boldsymbol v_j&#061;<\/p>\n<p>\\\\begin{cases}<\/p>\n<p>1,&amp;i&#061;j\\\\\\\\<\/p>\n<p>0,&amp;i\\\\neq j<\/p>\n<p>\\\\end{cases}<\/p>\n<\/p>\n<\/p>\n<p>2\u3001\u6b63\u4ea4\u57fa &amp; \u6807\u51c6\u6b63\u4ea4\u57fa<\/p>\n<\/p>\n<p>\u57fa\u56de\u987e<\/p>\n<\/p>\n<p>R^n\u7a7a\u95f4\u4e00\u7ec4\u57fa&#xff1a;n\u4e2a\u7ebf\u6027\u65e0\u5173\u5411\u91cf&#xff0c;\u53ef\u4ee5\u628a\u7a7a\u95f4\u4e2d\u4efb\u610f\u5411\u91cf&#xff0c;\u5199\u6210\u8fd9\u7ec4\u57fa\u7684\u7ebf\u6027\u7ec4\u5408\u3002<\/p>\n<\/p>\n<p>1.\u00a0\u6b63\u4ea4\u57fa&#xff1a;\u4e00\u7ec4\u57fa&#xff0c;\u540c\u65f6\u53c8\u662f\u6b63\u4ea4\u5411\u91cf\u7ec4\u3002<\/p>\n<p>2.\u00a0\u6807\u51c6\u6b63\u4ea4\u57fa&#xff1a;\u4e00\u7ec4\u57fa&#xff0c;\u4e24\u4e24\u6b63\u4ea4&#xff0c;\u5e76\u4e14\u6bcf\u4e2a\u5411\u91cf\u957f\u5ea6\u7b49\u4e8e1\u3002<\/p>\n<\/p>\n<p>\u6807\u51c6\u6b63\u4ea4\u57fa\u5de8\u5927\u597d\u5904&#xff08;AI\u9ad8\u9891&#xff09;<\/p>\n<\/p>\n<p>\u5982\u679c \\\\{\\\\boldsymbol e_1,\\\\boldsymbol e_2\\\\dots,\\\\boldsymbol e_n\\\\} \u662f\u6807\u51c6\u6b63\u4ea4\u57fa\u3002<\/p>\n<p>\u4efb\u610f\u5411\u91cf \\\\boldsymbol x \u505a\u5206\u89e3&#xff1a;<\/p>\n<p>\\\\boldsymbol x &#061; c_1\\\\boldsymbol e_1 &#043; c_2\\\\boldsymbol e_2&#043;\\\\dots&#043;c_n\\\\boldsymbol e_n<\/p>\n<p>\u7cfb\u6570\u76f4\u63a5\u7528\u5185\u79ef\u7b97\u51fa&#xff1a;<\/p>\n<p>c_i&#061;\\\\boldsymbol x^\\\\mathrm T \\\\boldsymbol e_i<\/p>\n<\/p>\n<p>\u666e\u901a\u57fa\u6c42\u7cfb\u6570\u9700\u8981\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4&#xff1b;\u6807\u51c6\u6b63\u4ea4\u57fa\u76f4\u63a5\u70b9\u79ef\u5c31\u5f97\u5230\u7cfb\u6570&#xff0c;\u8ba1\u7b97\u91cf\u5927\u5e45\u4e0b\u964d\u3002<\/p>\n<\/p>\n<p>\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48AI\u5927\u91cf\u8ffd\u6c42\u6b63\u4ea4&#xff1a;\u7b80\u5316\u9ad8\u7ef4\u5411\u91cf\u6295\u5f71\u3001\u5206\u89e3\u3001\u76f8\u4f3c\u5ea6\u8ba1\u7b97\u3002<\/p>\n<\/p>\n<p>\u77e9\u9635\u5f62\u5f0f&#xff1a;\u6b63\u4ea4\u77e9\u9635<\/p>\n<\/p>\n<p>\u628a\u6807\u51c6\u6b63\u4ea4\u57fa\u6309\u5217\u62fc\u6210\u77e9\u9635 Q&#xff1a;<\/p>\n<p>Q&#061;\\\\begin{bmatrix}\\\\boldsymbol 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v_1\u6b63\u4ea4\u7684\\\\boldsymbol v_2<\/p>\n<\/p>\n<p>\\\\boldsymbol v_2&#061;\\\\boldsymbol a_2<\/p>\n<p>-\\\\frac{\\\\boldsymbol a_2^\\\\mathrm T\\\\boldsymbol v_1}{\\\\boldsymbol v_1^\\\\mathrm T \\\\boldsymbol v_1}\\\\boldsymbol v_1<\/p>\n<\/p>\n<p>3.\u00a0\u7b2c\u4e09\u4e2a\u5411\u91cf&#xff1a;\\\\boldsymbol a_3&#xff0c;\u51cf\u53bb\u5b83\u5728\\\\boldsymbol v_1\u6295\u5f71&#xff0c;\u518d\u51cf\u53bb\u5728\\\\boldsymbol v_2\u6295\u5f71<\/p>\n<\/p>\n<p>\\\\boldsymbol v_3&#061;\\\\boldsymbol a_3<\/p>\n<p>-\\\\frac{\\\\boldsymbol a_3^\\\\mathrm T\\\\boldsymbol v_1}{\\\\boldsymbol v_1^\\\\mathrm T \\\\boldsymbol v_1}\\\\boldsymbol v_1<\/p>\n<p>-\\\\frac{\\\\boldsymbol a_3^\\\\mathrm T\\\\boldsymbol v_2}{\\\\boldsymbol v_2^\\\\mathrm T \\\\boldsymbol v_2}\\\\boldsymbol v_2<\/p>\n<\/p>\n<p>4.\u00a0\u901a\u7528\u9012\u63a8\u516c\u5f0f<\/p>\n<\/p>\n<p>\\\\boldsymbol v_k&#061;\\\\boldsymbol a_k-\\\\sum_{i&#061;1}^{k-1}<\/p>\n<p>\\\\frac{\\\\boldsymbol a_k^\\\\mathrm T \\\\boldsymbol v_i}{\\\\boldsymbol v_i^\\\\mathrm T\\\\boldsymbol v_i}\\\\boldsymbol v_i<\/p>\n<\/p>\n<p>\u51e0\u4f55\u7406\u89e3&#xff1a;\u6bcf\u4e00\u6b65&#xff0c;\u628a\u65b0\u5411\u91cf&#xff0c;\u51cf\u53bb\u5411\u524d\u9762\u6240\u6709\u5df2\u7ecf\u5f97\u5230\u6b63\u4ea4\u5411\u91cf\u4e0a\u7684\u6295\u5f71\u5206\u91cf&#xff0c;\u5269\u4e0b\u7684\u6b8b\u5dee\u90e8\u5206\u5c31\u548c\u524d\u9762\u5168\u90e8\u6b63\u4ea4\u3002<\/p>\n<\/p>\n<p>\u5f97\u5230\u6b63\u4ea4\u7ec4\\\\boldsymbol v_1,\\\\boldsymbol v_2\\\\dots\u4e4b\u540e&#xff0c;\u505a\u5355\u4f4d\u5316&#xff0c;\u5f97\u5230\u6807\u51c6\u6b63\u4ea4\u5411\u91cf&#xff1a;<\/p>\n<p>\\\\boldsymbol e_i&#061;\\\\frac{\\\\boldsymbol v_i}{\\\\|\\\\boldsymbol v_i\\\\|}<\/p>\n<\/p>\n<p>2\u9636\u5b8c\u6574\u624b\u7b97\u4f8b\u9898<\/p>\n<\/p>\n<p>\u7ed9\u5b9a<\/p>\n<p>\\\\boldsymbol a_1&#061;\\\\begin{pmatrix}1\\\\\\\\1\\\\end{pmatrix},\\\\;<\/p>\n<p>\\\\boldsymbol a_2&#061;\\\\begin{pmatrix}0\\\\\\\\1\\\\end{pmatrix}<\/p>\n<\/p>\n<p>1.\\\\boldsymbol 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