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xlink:href=\"#E51-MJMATHI-6A\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E51-MJMAIN-3D\" x=\"412\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E51-MJMAIN-31\" x=\"1189\" y=\"0\"><\/use><\/g><use transform=\"scale(0.707)\" xlink:href=\"#E51-MJMATHI-6D\" x=\"582\" y=\"1626\"><\/use><\/g><g transform=\"translate(7673,0)\"><use xlink:href=\"#E51-MJMATHBI-57\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(1093,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#E51-MJMATHI-69\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E51-MJMATHI-6A\" x=\"345\" y=\"0\"><\/use><\/g><\/g><use xlink:href=\"#E51-MJMAIN-28\" x=\"9401\" y=\"0\"><\/use><use xlink:href=\"#E51-MJMATHI-66\" x=\"9790\" y=\"0\"><\/use><use xlink:href=\"#E51-MJMAIN-28\" x=\"10340\" y=\"0\"><\/use><g transform=\"translate(10729,0)\"><use xlink:href=\"#E51-MJMATHBI-78\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E51-MJMATHI-69\" x=\"931\" y=\"-213\"><\/use><\/g><use xlink:href=\"#E51-MJMAIN-29\" x=\"11732\" y=\"0\"><\/use><use xlink:href=\"#E51-MJMAIN-2212\" x=\"12344\" y=\"0\"><\/use><use xlink:href=\"#E51-MJMATHI-66\" x=\"13344\" y=\"0\"><\/use><use xlink:href=\"#E51-MJMAIN-28\" x=\"13894\" y=\"0\"><\/use><g transform=\"translate(14283,0)\"><use xlink:href=\"#E51-MJMATHBI-78\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E51-MJMATHI-6A\" x=\"931\" y=\"-213\"><\/use><\/g><use xlink:href=\"#E51-MJMAIN-29\" x=\"15333\" y=\"0\"><\/use><g transform=\"translate(15722,0)\"><use xlink:href=\"#E51-MJMAIN-29\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E51-MJMAIN-32\" x=\"550\" y=\"583\"><\/use><\/g><\/g><\/svg><\/span><script type=\"math\/tex\">\\displaystyle E(f)=\\frac12\\sum\\limits_{i=1}^m\\sum\\limits_{j=1}^m\\boldsymbol W_{ij}(f(\\boldsymbol x_i)-f(\\boldsymbol x_j))^2<\/script><\/p>\n<p>\u5176\u4e2d<span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.014ex\" height=\"2.577ex\" viewBox=\"0 -755.9 1728.3 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.822ex;\"><defs><path stroke-width=\"0\" id=\"E52-MJMATHBI-57\" d=\"M111 624Q109 624 102 624T91 623Q61 623 61 640Q61 660 70 678Q78 686 98 686Q140 684 239 684Q277 684 309 684T360 685T383 686H385Q407 686 407 668Q404 634 391 626Q387 624 348 624Q307 624 307 622Q307 618 332 409Q359 198 359 195L570 532L564 576L558 622V624H522H504Q472 624 472 641Q475 678 488 684L493 686L529 685Q551 684 645 684Q716 684 753 685T795 686Q818 686 818 669Q815 632 802 626Q798 624 759 624Q718 624 718 622Q718 615 743 410Q770 199 770 196Q770 195 806 253T903 406Q1035 618 1035 619Q1025 624 968 624Q943 624 943 641Q943 648 946 659Q950 675 952 679T963 686L998 685Q1020 684 1093 684Q1113 684 1139 685T1173 686Q1207 686 1207 669Q1207 664 1204 652Q1199 631 1194 628T1164 624Q1113 622 1101 615Q1098 612 905 305Q715 -1 709 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286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#E52-MJMATHBI-57\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(1093,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#E52-MJMATHI-69\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E52-MJMATHI-6A\" x=\"345\" y=\"0\"><\/use><\/g><\/g><\/svg><\/span><script type=\"math\/tex\">\\boldsymbol W_{ij}<\/script>\u7528\u4e8e\u8868\u793ai\u4e0ej\u4e24\u4e2a\u6837\u672c\u4e4b\u95f4\u7684\u4eb2\u548c\u5ea6\uff0c\u5373\u8282\u70b9\u4e4b\u95f4\u7684\u5173\u8054\u6027\uff0c\u88ab\u8868\u793a\u4e3a\u56fe\u7684\u8fb9\uff0c\u5177\u4f53\u5b9a\u4e49\u5982\u4e0b<\/p>\n<p><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"30.703ex\" height=\"7.48ex\" viewBox=\"0 -1861.6 13219.4 3220.6\" role=\"img\" focusable=\"false\" style=\"vertical-align: -3.156ex;\"><defs><path stroke-width=\"0\" id=\"E53-MJMATHBI-57\" d=\"M111 624Q109 624 102 624T91 623Q61 623 61 640Q61 660 70 678Q78 686 98 686Q140 684 239 684Q277 684 309 684T360 685T383 686H385Q407 686 407 668Q404 634 391 626Q387 624 348 624Q307 624 307 622Q307 618 332 409Q359 198 359 195L570 532L564 576L558 622V624H522H504Q472 624 472 641Q475 678 488 684L493 686L529 685Q551 684 645 684Q716 684 753 685T795 686Q818 686 818 669Q815 632 802 626Q798 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xlink:href=\"#E77-MJMATHI-6C\" x=\"572\" y=\"0\"><\/use><\/g><\/g><g transform=\"translate(13653,0)\"><use xlink:href=\"#E77-MJMATHBI-66\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E77-MJMATHI-6C\" x=\"803\" y=\"-213\"><\/use><\/g><use xlink:href=\"#E77-MJMAIN-2B\" x=\"14754\" y=\"0\"><\/use><g transform=\"translate(15754,0)\"><use xlink:href=\"#E77-MJMATHBI-66\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E77-MJMAIN-54\" x=\"906\" y=\"487\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E77-MJMATHI-75\" x=\"803\" y=\"-210\"><\/use><\/g><g transform=\"translate(17172,0)\"><use xlink:href=\"#E77-MJMAIN-28\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(389,0)\"><use xlink:href=\"#E77-MJMATHBI-44\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(938,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#E77-MJMATHI-75\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E77-MJMATHI-75\" x=\"572\" y=\"0\"><\/use><\/g><\/g><use xlink:href=\"#E77-MJMAIN-2212\" x=\"2458\" y=\"0\"><\/use><g transform=\"translate(3458,0)\"><use xlink:href=\"#E77-MJMATHBI-57\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(1093,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#E77-MJMATHI-75\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E77-MJMATHI-75\" x=\"572\" y=\"0\"><\/use><\/g><\/g><use xlink:href=\"#E77-MJMAIN-29\" x=\"5460\" y=\"0\"><\/use><\/g><g transform=\"translate(23188,0)\"><use xlink:href=\"#E77-MJMATHBI-66\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E77-MJMATHI-75\" x=\"803\" y=\"-213\"><\/use><\/g><\/g><\/g><\/g><\/g><\/svg><\/span><\/div><script type=\"math\/tex; mode=display\" id=\"MathJax-Element-74\">\\begin{aligned}\nE(f) &=\\left(\\boldsymbol{f}_{l}^{\\mathrm{T}} \\boldsymbol{f}_{u}^{\\mathrm{T}}\\right)\\left(\\left[\\begin{array}{ll}\n\\mathbf{D}_{l l} & \\mathbf{0}_{l u} \\\\\n\\mathbf{0}_{u l} & \\mathbf{D}_{u u}\n\\end{array}\\right]-\\left[\\begin{array}{ll}\n\\mathbf{W}_{l l} & \\mathbf{W}_{l u} \\\\\n\\mathbf{W}_{u l} & \\mathbf{W}_{u u}\n\\end{array}\\right]\\right)\\left[\\begin{array}{l}\n\\boldsymbol{f}_{l} \\\\\n\\boldsymbol{f}_{u}\n\\end{array}\\right] \\\\&=\\left[\\begin{array}{ll}\n\\boldsymbol{f}_{l}^{\\mathrm{T}} & \\boldsymbol{f}_{u}^{\\mathrm{T}}\n\\end{array}\\right]\\left[\\begin{array}{cc}\n\\boldsymbol{D}_{l l}-\\boldsymbol{W}_{l l} & -\\boldsymbol{W}_{l u} \\\\\n-\\boldsymbol{W}_{u l} & \\boldsymbol{D}_{u u}-\\boldsymbol{W}_{u u}\n\\end{array}\\right]\\left[\\begin{array}{l}\n\\boldsymbol{f}_{l} \\\\\n\\boldsymbol{f}_{u}\n\\end{array}\\right] \\\\\n&=\\left[\\begin{array}{ll}\\boldsymbol{f}_{l}^{\\mathrm{T}}\\left(\\boldsymbol{D}_{l l}-\\boldsymbol{W}_{l l}\\right)-\\boldsymbol{f}_{u}^{\\mathrm{T}} \\boldsymbol{W}_{u l} & -\\boldsymbol{f}_{l}^{\\mathrm{T}} \\boldsymbol{W}_{l u}+\\boldsymbol{f}_{u}^{\\mathrm{T}}\\left(\\boldsymbol{D}_{u u}-\\boldsymbol{W}_{u u}\\right)\\end{array}\\right]\\left[\\begin{array}{l}\n\\boldsymbol{f}_{l} \\\\\n\\boldsymbol{f}_{u}\n\\end{array}\\right] \\\\\n&=\\left(\\boldsymbol{f}_{l}^{\\mathrm{T}}\\left(\\boldsymbol{D}_{l l}-\\boldsymbol{W}_{l l}\\right)-\\boldsymbol{f}_{u}^{\\mathrm{T}} \\boldsymbol{W}_{u l}\\right) \\boldsymbol{f}_{l}+\\left(-\\boldsymbol{f}_{l}^{\\mathrm{T}} \\boldsymbol{W}_{l u}+\\boldsymbol{f}_{u}^{\\mathrm{T}}\\left(\\boldsymbol{D}_{u u}-\\boldsymbol{W}_{u u}\\right)\\right) \\boldsymbol{f}_{u} \\\\\n&=\\boldsymbol{f}_{l}^{\\mathrm{T}}\\left(\\boldsymbol{D}_{l l}-\\boldsymbol{W}_{l l}\\right) \\boldsymbol{f}_{l}-\\boldsymbol{f}_{u}^{\\mathrm{T}} \\boldsymbol{W}_{u l} \\boldsymbol{f}_{l}-\\boldsymbol{f}_{l}^{\\mathrm{T}} \\boldsymbol{W}_{l u} \\boldsymbol{f}_{u}+\\boldsymbol{f}_{u}^{\\mathrm{T}}\\left(\\boldsymbol{D}_{u u}-\\boldsymbol{W}_{u u}\\right) \\boldsymbol{f}_{u} \\\\\n&=\\boldsymbol{f}_{l}^{\\mathrm{T}}\\left(\\boldsymbol{D}_{l l}-\\boldsymbol{W}_{l l}\\right) \\boldsymbol{f}_{l}-2 \\boldsymbol{f}_{u}^{\\mathrm{T}} \\boldsymbol{W}_{u l} \\boldsymbol{f}_{l}+\\boldsymbol{f}_{u}^{\\mathrm{T}}\\left(\\boldsymbol{D}_{u u}-\\boldsymbol{W}_{u u}\\right) \\boldsymbol{f}_{u}\n\\end{aligned}<\/script><\/div><\/div>\n<p>\u7531\u4e8e\u6211\u4eec\u7684\u76ee\u6807\u662f\u83b7\u53d6<span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.859ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2092 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E54-MJMATHI-45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 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y=\"-213\"><\/use><use xlink:href=\"#E57-MJMAIN-3D\" x=\"1350\" y=\"0\"><\/use><g transform=\"translate(2406,0)\"><use xlink:href=\"#E57-MJMAIN-28\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(389,0)\"><use xlink:href=\"#E57-MJMAINB-44\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(882,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMATHI-75\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMATHI-75\" x=\"572\" y=\"0\"><\/use><\/g><\/g><use xlink:href=\"#E57-MJMAIN-2212\" x=\"2402\" y=\"0\"><\/use><g transform=\"translate(3402,0)\"><use xlink:href=\"#E57-MJMAINB-57\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(1189,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMATHI-75\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMATHI-75\" x=\"572\" y=\"0\"><\/use><\/g><\/g><use xlink:href=\"#E57-MJMAIN-29\" x=\"5500\" y=\"0\"><\/use><g transform=\"translate(5889,476)\"><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMAIN-2212\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMAIN-31\" x=\"778\" y=\"0\"><\/use><\/g><\/g><g transform=\"translate(9299,0)\"><use xlink:href=\"#E57-MJMAINB-57\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(1189,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMATHI-75\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMATHI-6C\" x=\"572\" y=\"0\"><\/use><\/g><\/g><g transform=\"translate(11203,0)\"><use xlink:href=\"#E57-MJMATHBI-66\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMATHI-6C\" x=\"803\" y=\"-213\"><\/use><\/g><\/g><\/svg><\/span><script type=\"math\/tex\">\\boldsymbol{f}_{u}=\\left(\\mathbf{D}_{u u}-\\mathbf{W}_{u u}\\right)^{-1} \\mathbf{W}_{u l} \\boldsymbol{f}_{l}<\/script>\uff0c\u4f9d\u6b64\u901a\u8fc7\u5df2\u77e5\u7684<span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg 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type=\"math\/tex\">F_i(F_{i1},F_{i2},\\cdots,F_{i|\\gamma|})<\/script>\uff0c\u8868\u793a\u7b2ci\u4e2a\u6837\u672c\u4e0a\u03b3\u4e2a\u6807\u7b7e\u5206\u5e03\u7684\u6982\u7387\uff0c\u4f5c\u4e3a<span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"2.329ex\" height=\"1.76ex\" viewBox=\"0 -504.6 1003 757.9\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.588ex;\"><defs><path stroke-width=\"0\" id=\"E61-MJMATHBI-78\" d=\"M74 282H63Q43 282 43 296Q43 298 45 307T56 332T76 365T110 401T159 433Q200 451 233 451H236Q273 451 282 450Q358 437 382 400L392 410Q434 452 483 452Q538 452 568 421T599 346Q599 303 573 280T517 256Q494 256 478 270T462 308Q462 343 488 367Q501 377 520 385Q520 386 516 389T502 396T480 400T462 398Q429 383 415 341Q354 116 354 80T405 44Q449 44 485 74T535 142Q539 156 542 159T562 162H568H579Q599 162 599 148Q599 135 586 111T550 60T485 12T397 -8Q313 -8 266 35L258 44Q215 -7 161 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j\\leq|\\gamma|}F_{ij}<\/script>\uff0c\u5373\u6700\u5927\u6982\u7387\u7c7b<\/p>\n<p>\u6839\u636e\u5df2\u77e5\u7684y\u6807\u7b7e\uff0c\u6211\u4eec\u5bf9F\u8fdb\u884c\u521d\u503c\u8d4b\u4e88\u3002\u968f\u540e\uff0c\u6211\u4eec\u8981\u5c06F\u7684\u6807\u7b7e\u4fe1\u606f\u5728\u56fe\u4e0a\u8fdb\u884c\u8fed\u4ee3\u4f20\u64ad\uff0c\u4ece\u800c\u4f7f\u672a\u6807\u8bb0\u6837\u672c\u83b7\u53d6\u6807\u7b7e\u4fe1\u606f<\/p>\n<p>\u6211\u4eec\u5b9a\u4e49\u5728\u56fe\u4e0a\u7684\u6b63\u5219\u5316\u4f20\u64ad\u77e9\u9635\u4e3a<span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"16.729ex\" height=\"2.928ex\" viewBox=\"0 -1158 7202.8 1260.5\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E63-MJMATHI-53\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 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type=\"math\/tex\">\\displaystyle E(f)=\\frac12\\sum\\limits_{i=1}^m\\sum\\limits_{j=1}^m\\boldsymbol W_{ij}(f(\\boldsymbol x_i)-f(\\boldsymbol x_j))^2<\/script><\/p>\n<p>\u5176\u4e2d<span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.014ex\" height=\"2.577ex\" viewBox=\"0 -755.9 1728.3 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.822ex;\"><defs><path stroke-width=\"0\" id=\"E52-MJMATHBI-57\" d=\"M111 624Q109 624 102 624T91 623Q61 623 61 640Q61 660 70 678Q78 686 98 686Q140 684 239 684Q277 684 309 684T360 685T383 686H385Q407 686 407 668Q404 634 391 626Q387 624 348 624Q307 624 307 622Q307 618 332 409Q359 198 359 195L570 532L564 576L558 622V624H522H504Q472 624 472 641Q475 678 488 684L493 686L529 685Q551 684 645 684Q716 684 753 685T795 686Q818 686 818 669Q815 632 802 626Q798 624 759 624Q718 624 718 622Q718 615 743 410Q770 199 770 196Q770 195 806 253T903 406Q1035 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y=\"0\"><\/use><\/g><\/g><\/svg><\/span><script type=\"math\/tex\">\\boldsymbol W_{ij}<\/script>\u7528\u4e8e\u8868\u793ai\u4e0ej\u4e24\u4e2a\u6837\u672c\u4e4b\u95f4\u7684\u4eb2\u548c\u5ea6\uff0c\u5373\u8282\u70b9\u4e4b\u95f4\u7684\u5173\u8054\u6027\uff0c\u88ab\u8868\u793a\u4e3a\u56fe\u7684\u8fb9\uff0c\u5177\u4f53\u5b9a\u4e49\u5982\u4e0b<\/p>\n<p><span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"30.703ex\" height=\"7.48ex\" viewBox=\"0 -1861.6 13219.4 3220.6\" role=\"img\" focusable=\"false\" style=\"vertical-align: -3.156ex;\"><defs><path stroke-width=\"0\" id=\"E53-MJMATHBI-57\" d=\"M111 624Q109 624 102 624T91 623Q61 623 61 640Q61 660 70 678Q78 686 98 686Q140 684 239 684Q277 684 309 684T360 685T383 686H385Q407 686 407 668Q404 634 391 626Q387 624 348 624Q307 624 307 622Q307 618 332 409Q359 198 359 195L570 532L564 576L558 622V624H522H504Q472 624 472 641Q475 678 488 684L493 686L529 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xlink:href=\"#E76-MJMAIN-29\" x=\"5709\" y=\"0\"><\/use><use xlink:href=\"#E76-MJMATHI-66\" x=\"6098\" y=\"0\"><\/use><\/g><\/g><\/g><\/g><\/svg><\/span><\/div><script type=\"math\/tex; mode=display\" id=\"MathJax-Element-73\">\\begin{array}\\\\ \\displaystyle E(f)&=\\frac12\\sum\\limits_{i=1}^m\\sum\\limits_{j=1}^m\\boldsymbol W_{ij}(f(\\boldsymbol x_i)-f(\\boldsymbol x_j))^2 \\\\ &=\\frac12\\left( \\sum\\limits_{i=1}^md_if^2(x_i)+\\sum\\limits_{j=1}^md_jf^2(x_j) -2\\sum\\limits_{i=1}^m\\sum\\limits_{j=1}^m\\boldsymbol W_{ij}f(\\boldsymbol x_i)f(\\boldsymbol x_j) \\right)\\\\&=\\sum\\limits_{i=1}^md_if^2(x_i) -\\sum\\limits_{i=1}^m\\sum\\limits_{j=1}^m\\boldsymbol W_{ij}f(\\boldsymbol x_i)f(\\boldsymbol x_j)\\\\&=f^TDf-f^TWf \\\\&= f^{T}(D-W)f\\end{array}<\/script><\/div><\/div>\n<p>\u5176\u4e2dD\u4e3a\u5ea6\u77e9\u9635\uff0cW\u4e3a\u90bb\u63a5\u77e9\u9635\uff0c\u5408\u8ba1\u8868\u793a\u4e3a\u62c9\u666e\u62c9\u65af\u77e9\u9635L=D-W\uff0c\u53e6\u5916\u6709d<sub>i<\/sub>\u4e3aW\u77e9\u9635i\u884c\u5143\u7d20\u4e4b\u548c<\/p>\n<p>\u53e6\u5916\uff0c\u7531\u4e8e\u5168\u8fde\u63a5\u7279\u6027\uff0cD\u7684\u503c\u4e0d\u4e3a\u90bb\u63a5\u8282\u70b9\u4e2a\u6570\uff0c\u800c\u662f\u603b\u8fde\u63a5\u6743\u503c<\/p>\n<p>\u4f46\u662f\u8fd9\u4e2a\u7ed3\u6784\u7684\u76ee\u6807\u662f\u4ec0\u4e48\u5462\uff1f\u6211\u4eec\u5df2\u77e5\u4e86\u90e8\u5206\u6620\u5c04\u60c5\u51b5\uff0c\u5e76\u5e0c\u671b\u6839\u636e\u5df2\u77e5\u77e5\u8bc6\u8fdb\u884c\u63a8\u5e7f\uff0c\u83b7\u53d6\u672a\u77e5\u90e8\u5206\u7684\u6620\u5c04\u51fd\u6570<\/p>\n<p>\u901a\u8fc7\u5206\u5757\u77e9\u9635\u7684\u65b9\u5f0f\uff0c\u53ef\u4ee5\u5c06\u539f\u5f0f\u6539\u5199\u6210<\/p>\n<div contenteditable=\"false\" spellcheck=\"false\" class=\"mathjax-block 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xlink:href=\"#E77-MJMATHI-6C\" x=\"572\" y=\"0\"><\/use><\/g><\/g><g transform=\"translate(13653,0)\"><use xlink:href=\"#E77-MJMATHBI-66\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E77-MJMATHI-6C\" x=\"803\" y=\"-213\"><\/use><\/g><use xlink:href=\"#E77-MJMAIN-2B\" x=\"14754\" y=\"0\"><\/use><g transform=\"translate(15754,0)\"><use xlink:href=\"#E77-MJMATHBI-66\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E77-MJMAIN-54\" x=\"906\" y=\"487\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E77-MJMATHI-75\" x=\"803\" y=\"-210\"><\/use><\/g><g transform=\"translate(17172,0)\"><use xlink:href=\"#E77-MJMAIN-28\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(389,0)\"><use xlink:href=\"#E77-MJMATHBI-44\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(938,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#E77-MJMATHI-75\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E77-MJMATHI-75\" x=\"572\" y=\"0\"><\/use><\/g><\/g><use xlink:href=\"#E77-MJMAIN-2212\" x=\"2458\" y=\"0\"><\/use><g transform=\"translate(3458,0)\"><use xlink:href=\"#E77-MJMATHBI-57\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(1093,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#E77-MJMATHI-75\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E77-MJMATHI-75\" x=\"572\" y=\"0\"><\/use><\/g><\/g><use xlink:href=\"#E77-MJMAIN-29\" x=\"5460\" y=\"0\"><\/use><\/g><g transform=\"translate(23188,0)\"><use xlink:href=\"#E77-MJMATHBI-66\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E77-MJMATHI-75\" x=\"803\" y=\"-213\"><\/use><\/g><\/g><\/g><\/g><\/g><\/svg><\/span><\/div><script type=\"math\/tex; mode=display\" id=\"MathJax-Element-74\">\\begin{aligned}\nE(f) &=\\left(\\boldsymbol{f}_{l}^{\\mathrm{T}} \\boldsymbol{f}_{u}^{\\mathrm{T}}\\right)\\left(\\left[\\begin{array}{ll}\n\\mathbf{D}_{l l} & \\mathbf{0}_{l u} \\\\\n\\mathbf{0}_{u l} & \\mathbf{D}_{u u}\n\\end{array}\\right]-\\left[\\begin{array}{ll}\n\\mathbf{W}_{l l} & \\mathbf{W}_{l u} \\\\\n\\mathbf{W}_{u l} & \\mathbf{W}_{u u}\n\\end{array}\\right]\\right)\\left[\\begin{array}{l}\n\\boldsymbol{f}_{l} \\\\\n\\boldsymbol{f}_{u}\n\\end{array}\\right] \\\\&=\\left[\\begin{array}{ll}\n\\boldsymbol{f}_{l}^{\\mathrm{T}} & \\boldsymbol{f}_{u}^{\\mathrm{T}}\n\\end{array}\\right]\\left[\\begin{array}{cc}\n\\boldsymbol{D}_{l l}-\\boldsymbol{W}_{l l} & -\\boldsymbol{W}_{l u} \\\\\n-\\boldsymbol{W}_{u l} & \\boldsymbol{D}_{u u}-\\boldsymbol{W}_{u u}\n\\end{array}\\right]\\left[\\begin{array}{l}\n\\boldsymbol{f}_{l} \\\\\n\\boldsymbol{f}_{u}\n\\end{array}\\right] \\\\\n&=\\left[\\begin{array}{ll}\\boldsymbol{f}_{l}^{\\mathrm{T}}\\left(\\boldsymbol{D}_{l l}-\\boldsymbol{W}_{l l}\\right)-\\boldsymbol{f}_{u}^{\\mathrm{T}} \\boldsymbol{W}_{u l} & -\\boldsymbol{f}_{l}^{\\mathrm{T}} \\boldsymbol{W}_{l u}+\\boldsymbol{f}_{u}^{\\mathrm{T}}\\left(\\boldsymbol{D}_{u u}-\\boldsymbol{W}_{u u}\\right)\\end{array}\\right]\\left[\\begin{array}{l}\n\\boldsymbol{f}_{l} \\\\\n\\boldsymbol{f}_{u}\n\\end{array}\\right] \\\\\n&=\\left(\\boldsymbol{f}_{l}^{\\mathrm{T}}\\left(\\boldsymbol{D}_{l l}-\\boldsymbol{W}_{l l}\\right)-\\boldsymbol{f}_{u}^{\\mathrm{T}} \\boldsymbol{W}_{u l}\\right) \\boldsymbol{f}_{l}+\\left(-\\boldsymbol{f}_{l}^{\\mathrm{T}} \\boldsymbol{W}_{l u}+\\boldsymbol{f}_{u}^{\\mathrm{T}}\\left(\\boldsymbol{D}_{u u}-\\boldsymbol{W}_{u u}\\right)\\right) \\boldsymbol{f}_{u} \\\\\n&=\\boldsymbol{f}_{l}^{\\mathrm{T}}\\left(\\boldsymbol{D}_{l l}-\\boldsymbol{W}_{l l}\\right) \\boldsymbol{f}_{l}-\\boldsymbol{f}_{u}^{\\mathrm{T}} \\boldsymbol{W}_{u l} \\boldsymbol{f}_{l}-\\boldsymbol{f}_{l}^{\\mathrm{T}} \\boldsymbol{W}_{l u} \\boldsymbol{f}_{u}+\\boldsymbol{f}_{u}^{\\mathrm{T}}\\left(\\boldsymbol{D}_{u u}-\\boldsymbol{W}_{u u}\\right) \\boldsymbol{f}_{u} \\\\\n&=\\boldsymbol{f}_{l}^{\\mathrm{T}}\\left(\\boldsymbol{D}_{l l}-\\boldsymbol{W}_{l l}\\right) \\boldsymbol{f}_{l}-2 \\boldsymbol{f}_{u}^{\\mathrm{T}} \\boldsymbol{W}_{u l} \\boldsymbol{f}_{l}+\\boldsymbol{f}_{u}^{\\mathrm{T}}\\left(\\boldsymbol{D}_{u u}-\\boldsymbol{W}_{u u}\\right) \\boldsymbol{f}_{u}\n\\end{aligned}<\/script><\/div><\/div>\n<p>\u7531\u4e8e\u6211\u4eec\u7684\u76ee\u6807\u662f\u83b7\u53d6<span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"4.859ex\" height=\"2.577ex\" viewBox=\"0 -806.1 2092 1109.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.705ex;\"><defs><path stroke-width=\"0\" id=\"E54-MJMATHI-45\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 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y=\"-213\"><\/use><use xlink:href=\"#E57-MJMAIN-3D\" x=\"1350\" y=\"0\"><\/use><g transform=\"translate(2406,0)\"><use xlink:href=\"#E57-MJMAIN-28\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(389,0)\"><use xlink:href=\"#E57-MJMAINB-44\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(882,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMATHI-75\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMATHI-75\" x=\"572\" y=\"0\"><\/use><\/g><\/g><use xlink:href=\"#E57-MJMAIN-2212\" x=\"2402\" y=\"0\"><\/use><g transform=\"translate(3402,0)\"><use xlink:href=\"#E57-MJMAINB-57\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(1189,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMATHI-75\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMATHI-75\" x=\"572\" y=\"0\"><\/use><\/g><\/g><use xlink:href=\"#E57-MJMAIN-29\" x=\"5500\" y=\"0\"><\/use><g transform=\"translate(5889,476)\"><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMAIN-2212\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMAIN-31\" x=\"778\" y=\"0\"><\/use><\/g><\/g><g transform=\"translate(9299,0)\"><use xlink:href=\"#E57-MJMAINB-57\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(1189,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMATHI-75\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMATHI-6C\" x=\"572\" y=\"0\"><\/use><\/g><\/g><g transform=\"translate(11203,0)\"><use xlink:href=\"#E57-MJMATHBI-66\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E57-MJMATHI-6C\" x=\"803\" y=\"-213\"><\/use><\/g><\/g><\/svg><\/span><script type=\"math\/tex\">\\boldsymbol{f}_{u}=\\left(\\mathbf{D}_{u u}-\\mathbf{W}_{u u}\\right)^{-1} \\mathbf{W}_{u l} \\boldsymbol{f}_{l}<\/script>\uff0c\u4f9d\u6b64\u901a\u8fc7\u5df2\u77e5\u7684<span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg 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type=\"math\/tex\">F_i(F_{i1},F_{i2},\\cdots,F_{i|\\gamma|})<\/script>\uff0c\u8868\u793a\u7b2ci\u4e2a\u6837\u672c\u4e0a\u03b3\u4e2a\u6807\u7b7e\u5206\u5e03\u7684\u6982\u7387\uff0c\u4f5c\u4e3a<span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"2.329ex\" height=\"1.76ex\" viewBox=\"0 -504.6 1003 757.9\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.588ex;\"><defs><path stroke-width=\"0\" id=\"E61-MJMATHBI-78\" d=\"M74 282H63Q43 282 43 296Q43 298 45 307T56 332T76 365T110 401T159 433Q200 451 233 451H236Q273 451 282 450Q358 437 382 400L392 410Q434 452 483 452Q538 452 568 421T599 346Q599 303 573 280T517 256Q494 256 478 270T462 308Q462 343 488 367Q501 377 520 385Q520 386 516 389T502 396T480 400T462 398Q429 383 415 341Q354 116 354 80T405 44Q449 44 485 74T535 142Q539 156 542 159T562 162H568H579Q599 162 599 148Q599 135 586 111T550 60T485 12T397 -8Q313 -8 266 35L258 44Q215 -7 161 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j\\leq|\\gamma|}F_{ij}<\/script>\uff0c\u5373\u6700\u5927\u6982\u7387\u7c7b<\/p>\n<p>\u6839\u636e\u5df2\u77e5\u7684y\u6807\u7b7e\uff0c\u6211\u4eec\u5bf9F\u8fdb\u884c\u521d\u503c\u8d4b\u4e88\u3002\u968f\u540e\uff0c\u6211\u4eec\u8981\u5c06F\u7684\u6807\u7b7e\u4fe1\u606f\u5728\u56fe\u4e0a\u8fdb\u884c\u8fed\u4ee3\u4f20\u64ad\uff0c\u4ece\u800c\u4f7f\u672a\u6807\u8bb0\u6837\u672c\u83b7\u53d6\u6807\u7b7e\u4fe1\u606f<\/p>\n<p>\u6211\u4eec\u5b9a\u4e49\u5728\u56fe\u4e0a\u7684\u6b63\u5219\u5316\u4f20\u64ad\u77e9\u9635\u4e3a<span class=\"MathJax_SVG\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"16.729ex\" height=\"2.928ex\" viewBox=\"0 -1158 7202.8 1260.5\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.238ex;\"><defs><path stroke-width=\"0\" id=\"E63-MJMATHI-53\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 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