SGC

Title

《Simplifying Graph Convolutional Networks》[code]

Summary

作者将 GCN 中的非线性激活函数去掉，然后进行重参数化，将多层变成一层，得到了一个简洁形式的 GCN，速度大大提升。此外还证明了 GCN 实际上是一个低通滤波器，使相邻节点的特征更相似。

Notes

SGC

作者认为非线性激活函数没啥用，去掉之后的GCN长这样：
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其中 S 是带自环的归一化邻接矩阵%22%20aria-hidden%3D%22true%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-53%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-3D%22%20x%3D%22834%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(1890%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-44%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-7E%22%20x%3D%22132%22%20y%3D%22577%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(764%2C623)%22%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2212%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%20x%3D%22778%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2F%22%20x%3D%221279%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-32%22%20x%3D%221779%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3Cg%20transform%3D%22translate(4367%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-41%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(750%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-44%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-7E%22%20x%3D%22132%22%20y%3D%22577%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3Cg%20transform%3D%22translate(1515%2C623)%22%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2212%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%20x%3D%22778%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2F%22%20x%3D%221279%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-32%22%20x%3D%221779%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3C%2Fsvg%3E#card=math&code=%5Cmathrm%7BS%7D%3D%5Cmathrm%7B%5Ctilde%7BD%7D%7D%5E%7B-1%2F2%7D%5Cmathrm%7BA%5Ctilde%7BD%7D%7D%5E%7B-1%2F2%7D&id=uMevi)，可以将这些参数汇聚起来，变成：
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这样就是 Simple Graph Convolution 了。

Spectral Analysis

1. 证明了添加自环会缩小谱半径（例如 Kipf 的重归一化技巧）
2. SGC 起到了一个低通滤波的作用，将特征平滑化，于是相邻的节点会拥有相似的特征。

记 为对称归一化 Laplace矩阵%22%20aria-hidden%3D%22true%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-394%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(833%2C-150)%22%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-73%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-79%22%20x%3D%22394%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-6D%22%20x%3D%22923%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-3D%22%20x%3D%222453%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-49%22%20x%3D%223509%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-2212%22%20x%3D%224093%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(5094%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-44%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(764%2C412)%22%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2212%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%20x%3D%22778%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2F%22%20x%3D%221279%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-32%22%20x%3D%221779%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3Cg%20transform%3D%22translate(7570%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-41%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-44%22%20x%3D%22750%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(1515%2C443)%22%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2212%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%20x%3D%22778%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2F%22%20x%3D%221279%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-32%22%20x%3D%221779%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3C%2Fsvg%3E#card=math&code=%5CDelta%20%7B%5Cmathrm%7Bsym%7D%7D%3D%5Cmathrm%7BI%7D-%5Cmathrm%7BD%7D%5E%7B-1%2F2%7D%5Cmathrm%7BAD%7D%5E%7B-1%2F2%7D&id=FGwM1)的特征值，那么归一化邻接矩阵为%22%20aria-hidden%3D%22true%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-53%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(556%2C-150)%22%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-61%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-64%22%20x%3D%22500%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-6A%22%20x%3D%221057%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-3D%22%20x%3D%221898%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(2954%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-44%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(764%2C412)%22%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2212%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%20x%3D%22778%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2F%22%20x%3D%221279%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-32%22%20x%3D%221779%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3Cg%20transform%3D%22translate(5431%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-41%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-44%22%20x%3D%22750%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(1515%2C443)%22%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2212%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%20x%3D%22778%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2F%22%20x%3D%221279%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-32%22%20x%3D%221779%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3C%2Fsvg%3E#card=math&code=%5Cmathrm%7BS%7D%7B%5Cmathrm%7Badj%7D%7D%3D%5Cmathrm%7BD%7D%5E%7B-1%2F2%7D%5Cmathrm%7BAD%7D%5E%7B-1%2F2%7D&id=Nk605)，那么 %22%20aria-hidden%3D%22true%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-53%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMATHI-4B%22%20x%3D%22787%22%20y%3D%22612%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(556%2C-248)%22%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-61%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-64%22%20x%3D%22500%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-6A%22%20x%3D%221057%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3C%2Fsvg%3E#card=math&code=%5Cmathrm%7BS%7D%7B%5Cmathrm%7Badj%7D%7D%5EK&id=IXzl8) 可以看作图上的一个滤波，滤波函数为：
%20%3D%5Cleft(%201-%5Clambda%20_i%20%5Cright)%20%5EK%3C%2Ftitle%3E%0A%3Cdefs%20aria-hidden%3D%22true%22%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMATHI-67%22%20d%3D%22M311%2043Q296%2030%20267%2015T206%200Q143%200%20105%2045T66%20160Q66%20265%20143%20353T314%20442Q361%20442%20401%20394L404%20398Q406%20401%20409%20404T418%20412T431%20419T447%20422Q461%20422%20470%20413T480%20394Q480%20379%20423%20152T363%20-80Q345%20-134%20286%20-169T151%20-205Q10%20-205%2010%20-137Q10%20-111%2028%20-91T74%20-71Q89%20-71%20102%20-80T116%20-111Q116%20-121%20114%20-130T107%20-144T99%20-154T92%20-162L90%20-164H91Q101%20-167%20151%20-167Q189%20-167%20211%20-155Q234%20-144%20254%20-122T282%20-75Q288%20-56%20298%20-13Q311%2035%20311%2043ZM384%20328L380%20339Q377%20350%20375%20354T369%20368T359%20382T346%20393T328%20402T306%20405Q262%20405%20221%20352Q191%20313%20171%20233T151%20117Q151%2038%20213%2038Q269%2038%20323%20108L331%20118L384%20328Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-28%22%20d%3D%22M94%20250Q94%20319%20104%20381T127%20488T164%20576T202%20643T244%20695T277%20729T302%20750H315H319Q333%20750%20333%20741Q333%20738%20316%20720T275%20667T226%20581T184%20443T167%20250T184%2058T225%20-81T274%20-167T316%20-220T333%20-241Q333%20-250%20318%20-250H315H302L274%20-226Q180%20-141%20137%20-14T94%20250Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMATHI-3BB%22%20d%3D%22M166%20673Q166%20685%20183%20694H202Q292%20691%20316%20644Q322%20629%20373%20486T474%20207T524%2067Q531%2047%20537%2034T546%2015T551%206T555%202T556%20-2T550%20-11H482Q457%203%20450%2018T399%20152L354%20277L340%20262Q327%20246%20293%20207T236%20141Q211%20112%20174%2069Q123%209%20111%20-1T83%20-12Q47%20-12%2047%2020Q47%2037%2061%2052T199%20187Q229%20216%20266%20252T321%20306L338%20322Q338%20323%20288%20462T234%20612Q214%20657%20183%20657Q166%20657%20166%20673Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMATHI-69%22%20d%3D%22M184%20600Q184%20624%20203%20642T247%20661Q265%20661%20277%20649T290%20619Q290%20596%20270%20577T226%20557Q211%20557%20198%20567T184%20600ZM21%20287Q21%20295%2030%20318T54%20369T98%20420T158%20442Q197%20442%20223%20419T250%20357Q250%20340%20236%20301T196%20196T154%2083Q149%2061%20149%2051Q149%2026%20166%2026Q175%2026%20185%2029T208%2043T235%2078T260%20137Q263%20149%20265%20151T282%20153Q302%20153%20302%20143Q302%20135%20293%20112T268%2061T223%2011T161%20-11Q129%20-11%20102%2010T74%2074Q74%2091%2079%20106T122%20220Q160%20321%20166%20341T173%20380Q173%20404%20156%20404H154Q124%20404%2099%20371T61%20287Q60%20286%2059%20284T58%20281T56%20279T53%20278T49%20278T41%20278H27Q21%20284%2021%20287Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-29%22%20d%3D%22M60%20749L64%20750Q69%20750%2074%20750H86L114%20726Q208%20641%20251%20514T294%20250Q294%20182%20284%20119T261%2012T224%20-76T186%20-143T145%20-194T113%20-227T90%20-246Q87%20-249%2086%20-250H74Q66%20-250%2063%20-250T58%20-247T55%20-238Q56%20-237%2066%20-225Q221%20-64%20221%20250T66%20725Q56%20737%2055%20738Q55%20746%2060%20749Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-3D%22%20d%3D%22M56%20347Q56%20360%2070%20367H707Q722%20359%20722%20347Q722%20336%20708%20328L390%20327H72Q56%20332%2056%20347ZM56%20153Q56%20168%2072%20173H708Q722%20163%20722%20153Q722%20140%20707%20133H70Q56%20140%2056%20153Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-31%22%20d%3D%22M213%20578L200%20573Q186%20568%20160%20563T102%20556H83V602H102Q149%20604%20189%20617T245%20641T273%20663Q275%20666%20285%20666Q294%20666%20302%20660V361L303%2061Q310%2054%20315%2052T339%2048T401%2046H427V0H416Q395%203%20257%203Q121%203%20100%200H88V46H114Q136%2046%20152%2046T177%2047T193%2050T201%2052T207%2057T213%2061V578Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-2212%22%20d%3D%22M84%20237T84%20250T98%20270H679Q694%20262%20694%20250T679%20230H98Q84%20237%2084%20250Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMATHI-4B%22%20d%3D%22M285%20628Q285%20635%20228%20637Q205%20637%20198%20638T191%20647Q191%20649%20193%20661Q199%20681%20203%20682Q205%20683%20214%20683H219Q260%20681%20355%20681Q389%20681%20418%20681T463%20682T483%20682Q500%20682%20500%20674Q500%20669%20497%20660Q496%20658%20496%20654T495%20648T493%20644T490%20641T486%20639T479%20638T470%20637T456%20637Q416%20636%20405%20634T387%20623L306%20305Q307%20305%20490%20449T678%20597Q692%20611%20692%20620Q692%20635%20667%20637Q651%20637%20651%20648Q651%20650%20654%20662T659%20677Q662%20682%20676%20682Q680%20682%20711%20681T791%20680Q814%20680%20839%20681T869%20682Q889%20682%20889%20672Q889%20650%20881%20642Q878%20637%20862%20637Q787%20632%20726%20586Q710%20576%20656%20534T556%20455L509%20418L518%20396Q527%20374%20546%20329T581%20244Q656%2067%20661%2061Q663%2059%20666%2057Q680%2047%20717%2046H738Q744%2038%20744%2037T741%2019Q737%206%20731%200H720Q680%203%20625%203Q503%203%20488%200H478Q472%206%20472%209T474%2027Q478%2040%20480%2043T491%2046H494Q544%2046%20544%2071Q544%2075%20517%20141T485%20216L427%20354L359%20301L291%20248L268%20155Q245%2063%20245%2058Q245%2051%20253%2049T303%2046H334Q340%2037%20340%2035Q340%2019%20333%205Q328%200%20317%200Q314%200%20280%201T180%202Q118%202%2085%202T49%201Q31%201%2031%2011Q31%2013%2034%2025Q38%2041%2042%2043T65%2046Q92%2046%20125%2049Q139%2052%20144%2061Q147%2065%20216%20339T285%20628Z%22%3E%3C%2Fpath%3E%0A%3C%2Fdefs%3E%0A%3Cg%20stroke%3D%22currentColor%22%20fill%3D%22currentColor%22%20stroke-width%3D%220%22%20transform%3D%22matrix(1%200%200%20-1%200%200)%22%20aria-hidden%3D%22true%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMATHI-67%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(647%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-28%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(389%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMATHI-3BB%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMATHI-69%22%20x%3D%22825%22%20y%3D%22-213%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-29%22%20x%3D%221317%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-3D%22%20x%3D%222631%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(3688%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-28%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%20x%3D%22389%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-2212%22%20x%3D%221112%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(2112%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMATHI-3BB%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMATHI-69%22%20x%3D%22825%22%20y%3D%22-213%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-29%22%20x%3D%223040%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMATHI-4B%22%20x%3D%224851%22%20y%3D%22675%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3C%2Fsvg%3E#card=math&code=g%5Cleft%28%20%5Clambda%20_i%20%5Cright%29%20%3D%5Cleft%28%201-%5Clambda%20_i%20%5Cright%29%20%5EK&id=e9Obx)
同样的，带自环的归一化邻接矩阵为 %22%20aria-hidden%3D%22true%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-53%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-7E%22%20x%3D%2228%22%20y%3D%22599%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(556%2C-150)%22%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-61%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-64%22%20x%3D%22500%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-6A%22%20x%3D%221057%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-3D%22%20x%3D%221898%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(2954%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-44%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-7E%22%20x%3D%22132%22%20y%3D%22577%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(764%2C623)%22%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2212%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%20x%3D%22778%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2F%22%20x%3D%221279%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-32%22%20x%3D%221779%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3Cg%20transform%3D%22translate(5431%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-41%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(750%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-44%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-7E%22%20x%3D%22132%22%20y%3D%22577%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3Cg%20transform%3D%22translate(1515%2C623)%22%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2212%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%20x%3D%22778%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2F%22%20x%3D%221279%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-32%22%20x%3D%221779%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3C%2Fsvg%3E#card=math&code=%5Cmathrm%7B%5Ctilde%7BS%7D%7D_%7B%5Cmathrm%7Badj%7D%7D%3D%5Cmathrm%7B%5Ctilde%7BD%7D%7D%5E%7B-1%2F2%7D%5Cmathrm%7BA%5Ctilde%7BD%7D%7D%5E%7B-1%2F2%7D&id=azs55)，滤波函数为 %20%3D%5Cleft(%201-%5Cbegin%7Barray%7D%7Bc%7D%20%5Ctilde%7B%5Clambda%7D_i%5C%5C%20%5Cend%7Barray%7D%20%5Cright)%20%5EK%3C%2Ftitle%3E%0A%3Cdefs%20aria-hidden%3D%22true%22%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMATHI-67%22%20d%3D%22M311%2043Q296%2030%20267%2015T206%200Q143%200%20105%2045T66%20160Q66%20265%20143%20353T314%20442Q361%20442%20401%20394L404%20398Q406%20401%20409%20404T418%20412T431%20419T447%20422Q461%20422%20470%20413T480%20394Q480%20379%20423%20152T363%20-80Q345%20-134%20286%20-169T151%20-205Q10%20-205%2010%20-137Q10%20-111%2028%20-91T74%20-71Q89%20-71%20102%20-80T116%20-111Q116%20-121%20114%20-130T107%20-144T99%20-154T92%20-162L90%20-164H91Q101%20-167%20151%20-167Q189%20-167%20211%20-155Q234%20-144%20254%20-122T282%20-75Q288%20-56%20298%20-13Q311%2035%20311%2043ZM384%20328L380%20339Q377%20350%20375%20354T369%20368T359%20382T346%20393T328%20402T306%20405Q262%20405%20221%20352Q191%20313%20171%20233T151%20117Q151%2038%20213%2038Q269%2038%20323%20108L331%20118L384%20328Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-28%22%20d%3D%22M94%20250Q94%20319%20104%20381T127%20488T164%20576T202%20643T244%20695T277%20729T302%20750H315H319Q333%20750%20333%20741Q333%20738%20316%20720T275%20667T226%20581T184%20443T167%20250T184%2058T225%20-81T274%20-167T316%20-220T333%20-241Q333%20-250%20318%20-250H315H302L274%20-226Q180%20-141%20137%20-14T94%20250Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMATHI-3BB%22%20d%3D%22M166%20673Q166%20685%20183%20694H202Q292%20691%20316%20644Q322%20629%20373%20486T474%20207T524%2067Q531%2047%20537%2034T546%2015T551%206T555%202T556%20-2T550%20-11H482Q457%203%20450%2018T399%20152L354%20277L340%20262Q327%20246%20293%20207T236%20141Q211%20112%20174%2069Q123%209%20111%20-1T83%20-12Q47%20-12%2047%2020Q47%2037%2061%2052T199%20187Q229%20216%20266%20252T321%20306L338%20322Q338%20323%20288%20462T234%20612Q214%20657%20183%20657Q166%20657%20166%20673Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-7E%22%20d%3D%22M179%20251Q164%20251%20151%20245T131%20234T111%20215L97%20227L83%20238Q83%20239%2095%20253T121%20283T142%20304Q165%20318%20187%20318T253%20300T320%20282Q335%20282%20348%20288T368%20299T388%20318L402%20306L416%20295Q375%20236%20344%20222Q330%20215%20313%20215Q292%20215%20248%20233T179%20251Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMATHI-69%22%20d%3D%22M184%20600Q184%20624%20203%20642T247%20661Q265%20661%20277%20649T290%20619Q290%20596%20270%20577T226%20557Q211%20557%20198%20567T184%20600ZM21%20287Q21%20295%2030%20318T54%20369T98%20420T158%20442Q197%20442%20223%20419T250%20357Q250%20340%20236%20301T196%20196T154%2083Q149%2061%20149%2051Q149%2026%20166%2026Q175%2026%20185%2029T208%2043T235%2078T260%20137Q263%20149%20265%20151T282%20153Q302%20153%20302%20143Q302%20135%20293%20112T268%2061T223%2011T161%20-11Q129%20-11%20102%2010T74%2074Q74%2091%2079%20106T122%20220Q160%20321%20166%20341T173%20380Q173%20404%20156%20404H154Q124%20404%2099%20371T61%20287Q60%20286%2059%20284T58%20281T56%20279T53%20278T49%20278T41%20278H27Q21%20284%2021%20287Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-29%22%20d%3D%22M60%20749L64%20750Q69%20750%2074%20750H86L114%20726Q208%20641%20251%20514T294%20250Q294%20182%20284%20119T261%2012T224%20-76T186%20-143T145%20-194T113%20-227T90%20-246Q87%20-249%2086%20-250H74Q66%20-250%2063%20-250T58%20-247T55%20-238Q56%20-237%2066%20-225Q221%20-64%20221%20250T66%20725Q56%20737%2055%20738Q55%20746%2060%20749Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-3D%22%20d%3D%22M56%20347Q56%20360%2070%20367H707Q722%20359%20722%20347Q722%20336%20708%20328L390%20327H72Q56%20332%2056%20347ZM56%20153Q56%20168%2072%20173H708Q722%20163%20722%20153Q722%20140%20707%20133H70Q56%20140%2056%20153Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-31%22%20d%3D%22M213%20578L200%20573Q186%20568%20160%20563T102%20556H83V602H102Q149%20604%20189%20617T245%20641T273%20663Q275%20666%20285%20666Q294%20666%20302%20660V361L303%2061Q310%2054%20315%2052T339%2048T401%2046H427V0H416Q395%203%20257%203Q121%203%20100%200H88V46H114Q136%2046%20152%2046T177%2047T193%2050T201%2052T207%2057T213%2061V578Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-2212%22%20d%3D%22M84%20237T84%20250T98%20270H679Q694%20262%20694%20250T679%20230H98Q84%20237%2084%20250Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMATHI-4B%22%20d%3D%22M285%20628Q285%20635%20228%20637Q205%20637%20198%20638T191%20647Q191%20649%20193%20661Q199%20681%20203%20682Q205%20683%20214%20683H219Q260%20681%20355%20681Q389%20681%20418%20681T463%20682T483%20682Q500%20682%20500%20674Q500%20669%20497%20660Q496%20658%20496%20654T495%20648T493%20644T490%20641T486%20639T479%20638T470%20637T456%20637Q416%20636%20405%20634T387%20623L306%20305Q307%20305%20490%20449T678%20597Q692%20611%20692%20620Q692%20635%20667%20637Q651%20637%20651%20648Q651%20650%20654%20662T659%20677Q662%20682%20676%20682Q680%20682%20711%20681T791%20680Q814%20680%20839%20681T869%20682Q889%20682%20889%20672Q889%20650%20881%20642Q878%20637%20862%20637Q787%20632%20726%20586Q710%20576%20656%20534T556%20455L509%20418L518%20396Q527%20374%20546%20329T581%20244Q656%2067%20661%2061Q663%2059%20666%2057Q680%2047%20717%2046H738Q744%2038%20744%2037T741%2019Q737%206%20731%200H720Q680%203%20625%203Q503%203%20488%200H478Q472%206%20472%209T474%2027Q478%2040%20480%2043T491%2046H494Q544%2046%20544%2071Q544%2075%20517%20141T485%20216L427%20354L359%20301L291%20248L268%20155Q245%2063%20245%2058Q245%2051%20253%2049T303%2046H334Q340%2037%20340%2035Q340%2019%20333%205Q328%200%20317%200Q314%200%20280%201T180%202Q118%202%2085%202T49%201Q31%201%2031%2011Q31%2013%2034%2025Q38%2041%2042%2043T65%2046Q92%2046%20125%2049Q139%2052%20144%2061Q147%2065%20216%20339T285%20628Z%22%3E%3C%2Fpath%3E%0A%3C%2Fdefs%3E%0A%3Cg%20stroke%3D%22currentColor%22%20fill%3D%22currentColor%22%20stroke-width%3D%220%22%20transform%3D%22matrix(1%200%200%20-1%200%200)%22%20aria-hidden%3D%22true%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMATHI-67%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(647%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-28%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(556%2C0)%22%3E%0A%3Cg%20transform%3D%22translate(-11%2C0)%22%3E%0A%3Cg%20transform%3D%22translate(0%2C-104)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMATHI-3BB%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-7E%22%20x%3D%2241%22%20y%3D%22588%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMATHI-69%22%20x%3D%22825%22%20y%3D%22-213%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-29%22%20x%3D%221640%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-3D%22%20x%3D%222955%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(4011%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-28%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%20x%3D%22389%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-2212%22%20x%3D%221112%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(2279%2C0)%22%3E%0A%3Cg%20transform%3D%22translate(-11%2C0)%22%3E%0A%3Cg%20transform%3D%22translate(0%2C-104)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMATHI-3BB%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-7E%22%20x%3D%2241%22%20y%3D%22588%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMATHI-69%22%20x%3D%22825%22%20y%3D%22-213%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-29%22%20x%3D%223364%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMATHI-4B%22%20x%3D%225308%22%20y%3D%22750%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3C%2Fsvg%3E#card=math&code=g%5Cleft%28%20%5Cbegin%7Barray%7D%7Bc%7D%20%09%5Ctilde%7B%5Clambda%7D_i%5C%5C%20%5Cend%7Barray%7D%20%5Cright%29%20%3D%5Cleft%28%201-%5Cbegin%7Barray%7D%7Bc%7D%20%09%5Ctilde%7B%5Clambda%7D_i%5C%5C%20%5Cend%7Barray%7D%20%5Cright%29%20%5EK&id=Dc7Hy)。

它们的滤波系数随 的变化如下：

左一是一阶切比雪夫 %22%20aria-hidden%3D%22true%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-53%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(556%2C-150)%22%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2212%22%20x%3D%22500%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(904%2C0)%22%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-6F%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-72%22%20x%3D%22500%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-64%22%20x%3D%22892%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-65%22%20x%3D%221449%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-72%22%20x%3D%221894%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-3D%22%20x%3D%223455%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-49%22%20x%3D%224511%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-2B%22%20x%3D%225095%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(6096%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-44%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(764%2C412)%22%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2212%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%20x%3D%22778%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2F%22%20x%3D%221279%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-32%22%20x%3D%221779%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3Cg%20transform%3D%22translate(8572%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-41%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-44%22%20x%3D%22750%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(1515%2C443)%22%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2212%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%20x%3D%22778%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-2F%22%20x%3D%221279%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMAIN-32%22%20x%3D%221779%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3C%2Fsvg%3E#card=math&code=%5Cmathrm%7BS%7D%7B1-%5Cmathrm%7Border%7D%7D%3D%5Cmathrm%7BI%7D%2B%5Cmathrm%7BD%7D%5E%7B-1%2F2%7D%5Cmathrm%7BAD%7D%5E%7B-1%2F2%7D&id=wpc6F)，滤波函数为 %20%3D%5Cleft(%202-%5Clambda%20_i%20%5Cright)%20%5EK%3C%2Ftitle%3E%0A%3Cdefs%20aria-hidden%3D%22true%22%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMATHI-67%22%20d%3D%22M311%2043Q296%2030%20267%2015T206%200Q143%200%20105%2045T66%20160Q66%20265%20143%20353T314%20442Q361%20442%20401%20394L404%20398Q406%20401%20409%20404T418%20412T431%20419T447%20422Q461%20422%20470%20413T480%20394Q480%20379%20423%20152T363%20-80Q345%20-134%20286%20-169T151%20-205Q10%20-205%2010%20-137Q10%20-111%2028%20-91T74%20-71Q89%20-71%20102%20-80T116%20-111Q116%20-121%20114%20-130T107%20-144T99%20-154T92%20-162L90%20-164H91Q101%20-167%20151%20-167Q189%20-167%20211%20-155Q234%20-144%20254%20-122T282%20-75Q288%20-56%20298%20-13Q311%2035%20311%2043ZM384%20328L380%20339Q377%20350%20375%20354T369%20368T359%20382T346%20393T328%20402T306%20405Q262%20405%20221%20352Q191%20313%20171%20233T151%20117Q151%2038%20213%2038Q269%2038%20323%20108L331%20118L384%20328Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-28%22%20d%3D%22M94%20250Q94%20319%20104%20381T127%20488T164%20576T202%20643T244%20695T277%20729T302%20750H315H319Q333%20750%20333%20741Q333%20738%20316%20720T275%20667T226%20581T184%20443T167%20250T184%2058T225%20-81T274%20-167T316%20-220T333%20-241Q333%20-250%20318%20-250H315H302L274%20-226Q180%20-141%20137%20-14T94%20250Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMATHI-3BB%22%20d%3D%22M166%20673Q166%20685%20183%20694H202Q292%20691%20316%20644Q322%20629%20373%20486T474%20207T524%2067Q531%2047%20537%2034T546%2015T551%206T555%202T556%20-2T550%20-11H482Q457%203%20450%2018T399%20152L354%20277L340%20262Q327%20246%20293%20207T236%20141Q211%20112%20174%2069Q123%209%20111%20-1T83%20-12Q47%20-12%2047%2020Q47%2037%2061%2052T199%20187Q229%20216%20266%20252T321%20306L338%20322Q338%20323%20288%20462T234%20612Q214%20657%20183%20657Q166%20657%20166%20673Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMATHI-69%22%20d%3D%22M184%20600Q184%20624%20203%20642T247%20661Q265%20661%20277%20649T290%20619Q290%20596%20270%20577T226%20557Q211%20557%20198%20567T184%20600ZM21%20287Q21%20295%2030%20318T54%20369T98%20420T158%20442Q197%20442%20223%20419T250%20357Q250%20340%20236%20301T196%20196T154%2083Q149%2061%20149%2051Q149%2026%20166%2026Q175%2026%20185%2029T208%2043T235%2078T260%20137Q263%20149%20265%20151T282%20153Q302%20153%20302%20143Q302%20135%20293%20112T268%2061T223%2011T161%20-11Q129%20-11%20102%2010T74%2074Q74%2091%2079%20106T122%20220Q160%20321%20166%20341T173%20380Q173%20404%20156%20404H154Q124%20404%2099%20371T61%20287Q60%20286%2059%20284T58%20281T56%20279T53%20278T49%20278T41%20278H27Q21%20284%2021%20287Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-29%22%20d%3D%22M60%20749L64%20750Q69%20750%2074%20750H86L114%20726Q208%20641%20251%20514T294%20250Q294%20182%20284%20119T261%2012T224%20-76T186%20-143T145%20-194T113%20-227T90%20-246Q87%20-249%2086%20-250H74Q66%20-250%2063%20-250T58%20-247T55%20-238Q56%20-237%2066%20-225Q221%20-64%20221%20250T66%20725Q56%20737%2055%20738Q55%20746%2060%20749Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-3D%22%20d%3D%22M56%20347Q56%20360%2070%20367H707Q722%20359%20722%20347Q722%20336%20708%20328L390%20327H72Q56%20332%2056%20347ZM56%20153Q56%20168%2072%20173H708Q722%20163%20722%20153Q722%20140%20707%20133H70Q56%20140%2056%20153Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-32%22%20d%3D%22M109%20429Q82%20429%2066%20447T50%20491Q50%20562%20103%20614T235%20666Q326%20666%20387%20610T449%20465Q449%20422%20429%20383T381%20315T301%20241Q265%20210%20201%20149L142%2093L218%2092Q375%2092%20385%2097Q392%2099%20409%20186V189H449V186Q448%20183%20436%2095T421%203V0H50V19V31Q50%2038%2056%2046T86%2081Q115%20113%20136%20137Q145%20147%20170%20174T204%20211T233%20244T261%20278T284%20308T305%20340T320%20369T333%20401T340%20431T343%20464Q343%20527%20309%20573T212%20619Q179%20619%20154%20602T119%20569T109%20550Q109%20549%20114%20549Q132%20549%20151%20535T170%20489Q170%20464%20154%20447T109%20429Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-2212%22%20d%3D%22M84%20237T84%20250T98%20270H679Q694%20262%20694%20250T679%20230H98Q84%20237%2084%20250Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMATHI-4B%22%20d%3D%22M285%20628Q285%20635%20228%20637Q205%20637%20198%20638T191%20647Q191%20649%20193%20661Q199%20681%20203%20682Q205%20683%20214%20683H219Q260%20681%20355%20681Q389%20681%20418%20681T463%20682T483%20682Q500%20682%20500%20674Q500%20669%20497%20660Q496%20658%20496%20654T495%20648T493%20644T490%20641T486%20639T479%20638T470%20637T456%20637Q416%20636%20405%20634T387%20623L306%20305Q307%20305%20490%20449T678%20597Q692%20611%20692%20620Q692%20635%20667%20637Q651%20637%20651%20648Q651%20650%20654%20662T659%20677Q662%20682%20676%20682Q680%20682%20711%20681T791%20680Q814%20680%20839%20681T869%20682Q889%20682%20889%20672Q889%20650%20881%20642Q878%20637%20862%20637Q787%20632%20726%20586Q710%20576%20656%20534T556%20455L509%20418L518%20396Q527%20374%20546%20329T581%20244Q656%2067%20661%2061Q663%2059%20666%2057Q680%2047%20717%2046H738Q744%2038%20744%2037T741%2019Q737%206%20731%200H720Q680%203%20625%203Q503%203%20488%200H478Q472%206%20472%209T474%2027Q478%2040%20480%2043T491%2046H494Q544%2046%20544%2071Q544%2075%20517%20141T485%20216L427%20354L359%20301L291%20248L268%20155Q245%2063%20245%2058Q245%2051%20253%2049T303%2046H334Q340%2037%20340%2035Q340%2019%20333%205Q328%200%20317%200Q314%200%20280%201T180%202Q118%202%2085%202T49%201Q31%201%2031%2011Q31%2013%2034%2025Q38%2041%2042%2043T65%2046Q92%2046%20125%2049Q139%2052%20144%2061Q147%2065%20216%20339T285%20628Z%22%3E%3C%2Fpath%3E%0A%3C%2Fdefs%3E%0A%3Cg%20stroke%3D%22currentColor%22%20fill%3D%22currentColor%22%20stroke-width%3D%220%22%20transform%3D%22matrix(1%200%200%20-1%200%200)%22%20aria-hidden%3D%22true%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMATHI-67%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(647%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-28%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(389%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMATHI-3BB%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMATHI-69%22%20x%3D%22825%22%20y%3D%22-213%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-29%22%20x%3D%221317%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-3D%22%20x%3D%222631%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(3688%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-28%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-32%22%20x%3D%22389%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-2212%22%20x%3D%221112%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(2112%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMATHI-3BB%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMATHI-69%22%20x%3D%22825%22%20y%3D%22-213%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-29%22%20x%3D%223040%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMATHI-4B%22%20x%3D%224851%22%20y%3D%22675%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fg%3E%0A%3C%2Fsvg%3E#card=math&code=g%5Cleft%28%20%5Clambda%20_i%20%5Cright%29%20%3D%5Cleft%28%202-%5Clambda%20_i%20%5Cright%29%20%5EK&id=r9B21)，在 时会将特征值放得特别大。
右一是 ，由于添加自环的原因，最小特征值 仍是0，但最大特征值被压缩到了1.5左右，因此实际上起到了一个低通滤波器的作用，将 0~1.5 以外频段的信号都过滤掉了。（图中红色部分可能代表滤波后的特征）

对比实验

可以看到：

1. 添加了自环的确效果更好
2. 在低频部分的滤波系数非常大，导致在层数更深时性能明显下降。