
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 AbaDali: 
 
 
 
 
 
 
 
 Zhen Peng Wenbing Huang Minnan Luo Qinghua Zheng Yu Rong Tingyang Xu Junzhou Huang ISISHWA: Ubuncwane kumxholo weenethiwekhi ezahlukeneyo zolwazi ezifana neenethiwekhi zentlalo kunye neenethiwekhi zonxibelelwano bubonelela ngamandla angaqhelekanga okufunda amakhondo anomgangatho ophezulu ngaphandle kolwaluko lwangaphandle. Eli phepha lihlalutha indlela yokugcina nokukhupha ulwazi olunotyebileyo kwidatha enobume bebungotyelelo kwindawo yokubeka ngaphakathi ngendlela engalwalwanga. Ukwenza oku, siphakamisa igama elitsha, iGraphical Mutual Information (GMI), ukujonga ubudlelwane phakathi kwee-graphs ezingenayo kunye namakhondo aphezulu afihliweyo. I-GMI yandisa ingcamango yolwazi oluqhelekileyo phakathi kokubalwa kwi-vector space ukuya kwisidanga se-graph apho ukujonga ulwazi phakathi kwezimbini zeempawu zenqaku kunye nolwakhiwo lwenqwelomfene kubalulekile. I-GMI ibonisa iinzuzo ezininzi: Okokuqala, ayichaphazeleki ziitshintsho ze-isomorphic ze-graphs ezingenayo—isithintelo esingenakuphetshwa kwiindlela ezininzi ezikhoyo zokufunda amakhondo e-graph; Ngaphandle koko, inokulinganiswa ngokufanelekileyo kwaye yonyuswe ziindlela zokulinganisa ulwazi olufana ne-MINE; Okokugqibela, uhlalutyo lwethu lwethiyori luqinisekisa ukuchaneka kwayo kunye nokufaneleka kwayo. Ngokuncediswa yi-GMI, sivelisa imodeli yokufunda engalwalwanga eqeqeshwe ngokonyusa i-GMI phakathi kokungena kunye nokuphuma kwee-graph neural encoder.  Uvavanyo olukhulu malunga nokuhlolwa kwe-transductive kunye ne-inductive kunye nokubhaliweyo kwenqaku kubonisa ukuba indlela yethu igqitha izinto ezikwi-state-of-the-art ezingalwalwanga, kwaye ngamanye amaxesha idlula nokusebenza kwezobuchwepheshe eziyalwanga. 1      ISINGENISO Ukufikelela kwuhlalutyo olunokuthenjwa lwenani elikhulu leenethiwekhi ezahlukeneyo zolwazi, ukufunda amakhondo aphezulu kwidatha enobume bebungotyelelo kuye kwaba yenye yezona ndawo zinomdla ngoku. Iindlela zamva nje ezijonge le njongo, ezidla ngokubizwa ngokuba ziiGraph Neural Networks (GNNs), zifikelele kwiinguqu ezinkulu kwimisebenzi emininzi yokufunda, njengokuhlolwa kwamanqaku [ ,  ,  ], ukubhaliweyo kwenqaku [ ,  ,  ], ukulungelelanisa i-graph [ ,  ,  ], ukuveliswa kwe-molecule [ ,  ,  ], ukubala nje nje. Nangona kukho inkqubela phambili enentsingiselo, ukuqeqesha ii-GNNs kwiindlela ezikhoyo kudla ngokufuna uhlobo oluthile lolwaluko. Ngaphandle kwamathandabuzo, ulwazi lokuleyibhile lunzima ukulufumana—ukuchazwa ngesandla okanye ukuhlawula imvume, kwaye kunokwenzeka nokuba akunakwenzeka ukufumaneka ngenxa yenkqubo yemfihlo. Singatsho nje ukuba ukuthembeka kwezileyibhile ezinikiweyo ngamanye amaxesha kuyathandabuzeka. Ke ngoko, indlela yokufumana ikhondo elikumgangatho ophezulu ngaphandle kolwaluko iba yimfuneko kwimisebenzi emininzi esebenzayo, ekhuthaza isifundo salo nqaku.  35 42 50 26 27 49 12 19 43 4 5 46 Ngokuhlolisisisa idatha yobume bebungotyelelo esiyiqokeleyo, sifumanisa ukuba ngokuqhelekileyo ivela kwimithombo eyahlukeneyo efana neenethiwekhi zentlalo, iinethiwekhi zezicatshulwa, kunye neenethiwekhi zonxibelelwano apho kukho inani elikhulu lolwazi lomxholo kunye nolwazi olunxibelelanayo. Ngokomzekelo, idatha kumaqonga amaninzi osasazo olufana neTwitter, Flickr, kunye neFacebook ibandakanya iimpawu zabasebenzisi,  ., iinkcukacha zobuqu, izicatshulwa, iifoto, i-IP, kunye nobudlelwane babo,  ., ukuthenga into efanayo, ukuba ngabahlobo. Le datha yomxholo enotyebileyo yanele ukuxhasa imisebenzi yokugraba elandelayo ngaphandle kwesikhokelo esongezelelweyo: ukuba ezimbini izinto zibonisa ukufana okugqithisileyo kwiimpawu, kukho ithuba eliphezulu lenqaku phakathi kwazo (ukubhaliweyo kwenqaku), kwaye kunokwenzeka ukuba zingene kudidi olunye (uhlahlo lolungelo), ukuba ezimbini izinto zombini zinqakamelela into enye, mhlawumbi zinophawu olufanayo (ukucebisa). Ngale ngqiqo, ukugcina nokukhupha ulwazi oluninzi kangangoko kwiinethiwekhi zolwazi kwindawo yokubeka ngaphakathi kwenza kube lula ukufunda amakhondo anomgangatho ophezulu abonisa ukusebenza okufunekayo kwimisebenzi yokugraba ngaphandle kwayo nayiphi na inkqubo yolwaluko. Ukufunda amakhondo e-graph okungolwalwanga kukhetho oluthandwayo kwizibonelo ezininzi ngenxa yenkululeko ekususeni izileyibhile, ngakumbi xa sijonge ukuxhamla kwi-data enkulu engalwalwanga yasendle.  umzekelo umzekelo Ukuyiphumeza ngokupheleleyo iminqweno enotyebileyo kwiigrapu, kweli phepha, senza i-graph embedding ngokusekelwe kwi-Mutual Information (MI) maximization, siphefumlelwe yimpumelelo yovavanyo yendlela ye-Deep Info-Max [ ] esebenza kwiifoto. Ukufumana amakhondo aluncedo, i-Deep InfoMax iqeqesha i-encoder ukuba yonyuse i-MI phakathi kwee-inputs zayo ( ., ii-images) kunye neziphumo ( ., iivectori ezifihliweyo). Xa sijonga i-Deep InfoMax kwisidanga se-graph, inyathelo lokuqala ekufuneka silenyathele yindlela yokuchaza i-MI phakathi kwee-graphs kunye nee-vectors ezifihliweyo, ngelixa ulwakhiwo lwee-graphs lunzima kuneefoto (bona Umfanekiso   Enye yemicelimngeni kukuvumela i-MI function phakathi kwenqaku ngalinye le-encoder kunye neempawu zalo ezingqongileyo ukuba zithobele i-symmetric property, okanye ngokulinganayo, ukuba zingachaphazeleki ziintshukumo zengqongileyo. Njengomsebenzi omnye wamva nje ocinga i-MI, i-Deep Graph Infomax (DGI) [ ] kuqala ibeka i-graph engenayo kunye ne-graph echithweyo ehambelanayo, emva koko idibanisa i-graph engenayo kwi-vector nge-readout function, okokugqibela yonyusa i-MI phakathi kwesi sishwankathelo vector kunye namakhondo afihliweyo ngokungahlukaniyo kwi-graph engenayo (isampuli embi) ukusuka kwi-graph echithweyo (isampuli embi). Umfanekiso   ubonelela ngombono oqondakalayo we-DGI. Ukonyusa olu hlobo lwe-MI kuqikelelwa ukuba lulingana nokonyusa olu phakathi kwee-empawu zenqaku kunye nee-vectors ezifihliweyo, kodwa olu linganiselo lusebenza phantsi kweemeko ezithile ezichaziweyo,  ., i-readout function kufuneka ibe yeyona njengoko, nangona kunjalo kubonakala ngathi kunzima kakhulu kwiimeko zokwenyani. Nakuba singaqinisekisa ubukho be-readout function eyeyona njengoko kwiinkalo ezithile,  ., leyo isetyenziswa kwi-DeepSets [ ], ikhono leyona njengoko le-readout function likwaqhutywa luhlobo lwazo oluqeqeshwe ngalo. Oko kukuthi, umsebenzi oweyona njengoko unokuthi ube yinto engengoyona njengoko ukuba uqeqeshwe ngaphandle kolwaluko olongezelelweyo. Kwaye ukuba i-readout function ayiyona eyona njengoko, ulwazi lwe-graph olungenayo olukwisishwankathelo vector luya kuncipha njengoko ubungakanani be-graph bukhula. Ngaphezu koko, i-DGI ihlala ikwii-MI maximization ezingezizo ezigqithisiweyo zegraph/ipatch-level. Ke ngoko kwi-DGI, akukho siqinisekiso sokuba i-encoder ingakwazi ukucola ulwazi olwaneleyo kwidatha engenayo njengoko ingazange idibanise ngokucokisekileyo amakhondo anqamleleneyo kunye nee-inputs zabo zokuqala.  20  Oko.  Oko. 1). 41 1 umzekelo umzekelo 47 Kweli phepha, siphakamisa indlela elula ngakumbi yokujonga i-MI ngokubhekiselele kwizakhiwo zemifanekiso ngaphandle kokusebenzisa nasiphi na isishwankathelo okanye umsebenzi wokuphazamisa. Sivelisa i-MI ngokuthe ngqo ngokuthelekisa i-input ( ., i-sub-graph equka ingqongileyo yokungena) kunye ne-output ( ., ikhondo elifihliweyo lenqaku ngalinye) le-encoder. Kwaye ngokumangalisayo, uhlalutyo lwethu lwethiyori lubonisa ukuba i-MI echazwe ngokuthe ngqo ingahlulwa ibe yisumo enobunzima ye-local MIs phakathi kwempawu nganye engqongileyo kunye ne-vector efihliweyo. Ngale ndlela, sihlule iimpawu zokungena kwaye senze ukubalwa kwe-MI kube lula. Ngaphezu koko, olu hlobo lwe-MI lunokuhlangabezana ngokulula ne-symmetric property ukuba silungisa amaxabiso ezibunzima. Siyayihambisa iinkcukacha ezininzi kwi §   Njengoko i-MI engentla igxininisa kwisidanga sempawu zenqaku, siyibiza nge-Feature Mutual Information (FMI).   Oko.  Oko. 3.1. Imiba emibini eseleyo malunga ne-FMI:   izibunzima zokudibanisa kusaziswa kwaye   ayiqwaleli ulwakhiwo ( ., iimpawu zenqaku) ngaphakathi. Ukujongana nale miba mibini, sichaza imilinganiso yethu ye-Graphical Mutual Information (GMI) ngokusekelwe kwi-FMI. Ngokukodwa, i-GMI isebenzisa ukunika ixabiso eliqhelekileyo ngokubeka izibunzima kwi-FMI zilingane nobude phakathi kwengqongileyo nganye kunye nenqaku elijolise kulo kwindawo yamakhondo. Ngokubhekiselele ekugcineni ulwazi lwakhiwo, i-GMI yongezelela idibanisa ezi zibunzima kunye neeempawu zenqaku engenayo nge-MI term eyongezelelweyo. I-GMI eziphumelayo ayichaphazeleki yi-topological kwaye ikwangabalwa nge-Mutual Information Neural Estimation (MINE)   Iimpawu eziphambili zomsebenzi wethu zizi zilandelayo: 1. 2.  Oko. . •    : Siyandisa ubume obuqhelekileyo bokulinganisa i-MI kwisidanga se-graph kwaye siphakamise ingcamango entsha ye-Graphical Mutual Information (GMI) ngokufanelekileyo. I-GMI ikhululekile kwi  Iingcamango ingxaki enokubakho ebangelwa yi-readout function njengoko ijonga i-MI phakathi kwee-graphs ezingenayo kunye nee-embeddings eziphezulu ngendlela elula. •    : Ngohlalutyo lwethu lwethiyori, sinika ifom enokubalwa kwaye ibalwe ye-GMI ehlula  Iialgorithm i-GMI epheleleyo ibe yisumo enobunzima ye-local MIs. Ngokuncediswa yindlela ye-MINE, i-GMI maximization inokufumaneka ngokulula kwinqanaba lenqaku. •    : Siqinisekisa ukusebenza kwe-GMI kwimisebenzi emininzi yokuhlolwa kwamanqaku kunye nokubhaliweyo kwenqaku  Izifundo zoVavanyo imisebenzi kuquka zombini i-transductive kunye ne-inductive. Uvavanyo lubonisa ukuba indlela yethu ibonelela ngomsebenzi ofanelekileyo kwiinqanaba ezahlukeneyo kwaye ngamanye amaxesha iyadlula namakhondo obuchwepheshe. 2      UMSEBENZI OHAMBANA NAWO Ngokuhambelana nengqwalasela yomsebenzi wethu, sihlola ngokufutshane imisebenzi yangaphambili kwiindawo ezimbini ezilandelayo:   ukulinganisa ulwazi oluhambelanayo, kunye   iinethiwekhi ze-neural zokufunda amakhondo kwiigrapu. 1. 2. 3] ukhuthaza ukonyusa i-MI phakathi kwee-inputs kunye neziphumo zeenethiwekhi ze-neural, iindlela ezininzi ezifana nee-ICA algorithms [ ,  ] zizama ukusebenzisa ingcamango ye-MI ekufundeni kweempawu ezingalwalwanga. Nangona kunjalo, ezi ndlela azinakwanda kwiinethiwekhi ze-neural ezidibeneyo ngokulula ngenxa yobunzima ekubaleni i-MI phakathi kwezinto ezi-dimensional eziqhubekayo. Ngokuthamsanqelayo, i-Mutual Information Neural Estimation (MINE) [ ] yenza ukulinganisa i-MI kwiinethiwekhi ze-neural ezidibeneyo kube lula ngokuqeqesha inethiwekhi yee-statistics njengomahlulo wokwahlula iisampuli ezivela kwi-joint distribution kunye nengxubusho ye-marginal distributions zezinto ezimbini ezijikelezayo. Ngokukodwa, i-MINE isebenzisa i-KL-based formulation ye-MI, ngelixa enye indlela engayi-KL, i-Jensen-Shannon divergence (JSD) [ ], ingasetyenziswa ngaphandle kokukhathazeka malunga nexabiso elichanekileyo le-MI.  1 21 2 30 . Ngophuhliso olukhawulezayo lwee-graph neural networks (GNNs), inani elikhulu leealgorithem zokufunda amakhondo e-graph ezisekelwe kwi-GNNs ziphakanyiswe kwiminyaka yakutshanje, ebonisa ukusebenza okunamandla kuneendlela zakudala ezisekelwe kwi-random walk kunye nezisekelwe kwi-factorization [ ,  ,  ,  ,  ]. Ngokuyimfuneko, ezi ndlela zingahlulwa zibe zizodidi ezilwalwanga kunye nezilwalwanga. Phakathi kwazo, kukho imibhalo eninzi malunga nokufunda amakhondo obuchwepheshe kwiigrapu [ ,  ,  ,  ,  ]. Ngokungafaniyo nokwahluka kwazo kwizakhiwo zenethiwekhi, zifikelela kwimpumelelo yovavanyo ngoncedo lwezileyibhile ezingafumaneki rhoqo kwiimeko zokwenyani. Kule meko, iindlela zokufunda zemifanekiso ezingalwalwanga [ ,  ,  ] zinako ukusetyenziswa ngokubanzi. Indlela eyaziwayo yi-GraphSAGE [ ], isakhelo se-inductive sokuqeqesha ii-GNNs ngomsebenzi wokugqibela we-random-walk kwisimo sayo esingalwalwanga. Kwaye kutshanje, i-DGI [ ] isebenzisa ingcamango ye-MI maximization kwisidanga se-graph kwaye ifumana ukusebenza okunamandla kwisimo esingalwalwanga. Nangona kunjalo, i-DGI isebenzisa i-maximization engekhoyo kakhulu ( ., ukonyisa i-MI kwinqanaba legraph/ipatch) eyenza kube nzima ukugcina ulwazi olucokisekileyo kwi-graph engenayo. Ngaphezu koko, imeko efakwe kwi-readout function esetyenziswa kwi-DGI ibonakala ngathi inobunzima kwiimeko zokwenyani. Ngokungafaniyo, sigxila ekususeni isithintelo se-readout function kwaye sifikelele kwi-graphical mutual information maximization kwinqanaba lenqaku ngokonyisa i-MI phakathi kwee-inputs kunye neziphumo zeree-encoder. Amakhondo afunyenwe yindlela yethu acokisekileyo ekugcineni ulwazi lwe-graph engenayo, oluqinisekisa ukuba inokwenzeka kwimisebenzi yokugraba yemifanekiso elandelayo,  ., uhlahlo lolungelo, ukubhaliweyo kwenqaku, kunye nokucebisa.  Iinethiwekhi ze-neural zokufunda amakhondo e-graph 6 15 33 34 39 7 9 25 40 48 11 16 41 16 41  Oko. umzekelo 3      IGRAFICAL MUTUAL INFORMATION: INKCASO KUNYE NOKUNYUSWA Phambi kokuba siqhubeke, siphakamisa kuqala iingcamango zangaphambili ezisetyenziswa kweli phepha. Makube yiG = (V, E) ibonisa i-graph ene-  amanqaku   ∈ V kunye neenqaku   = (  ,   ) ∈ E. Iimpawu zenqaku, kunye nendlela yokusabalalisa evunywa yovavanyo P, zinikwa yi  ∈ N vi eij vi vj X R  ×  = {  1, · · · ,   } apho   ∈ R  ichaza uphawu lwenqaku   . I-matrix ye-adjacency   ∈ R  ×  ibonisa unxibelelwano lweenqaku, apho   ehambelana nenqaku   ingaba linani lokwenyani okanye i-vector ye-multi-dimensional1. N D x x N xi D vi A N N Aij eij Injongo yokufunda amakhondo e-graph kukuqeqesha i-encoder   : R  ×  × R  ×  → R  × ′, ukuze iivectori ezifihliweyo   = { 1, · · · ,   } =   (  ,  ) ibonise amakhondo aphezulu kuwo wonke amanqaku. Inkqubo yokufaka ngaphakathi ingabhalwa ngokutsha ngendlela yenqaku. f N D N N N D H h hN f X A Ukubonisa oku, sichaza   kunye ne  yenqaku   njengempawu zabalawuli bayo kunye ne-matrix ye-adjacency ehambelanayo Xi Ai i ngokubhekiselele kwimida. Ngokukodwa,   ibandakanya zonke ii-hop neighbours zika-  kunye ne  ≤   xa i-encoder   iyii-  -layer GNN, kwaye ibandakanya inqaku   ngokwalo ukuba songeza ii-self-loops kwi-matrix ye-adjacency. Apha, siyibiza igraph ye-sub-graph ekhutshiweyo yi  kunye ne  njenge  yenqaku  , ibonisiwe yiG  . Ngokuchazwa kwe-support graph, ukufakwa kwenqaku ngalinye liba ngu  =   (G  ) =   (  ,   ).  Xi vi k l f l i Xi Ai support graph i i hi f i f Xi Ai  Kwi-Deep InfoMax [ ], inkqubo yokuqeqesha ye-encoder kukonyisa i-MI phakathi kwee-inputs kunye neziphumo zayo. I-MI iyalinganiswa ngokusebenzisa inethiwekhi yee-statistics njengomahlulo wokwahlula iisampuli ezivela kwi-joint distribution kunye nezivela kwingxubusho yee-marginal distributions. Ngendlela yendalo, xa kusetshintshelwa ingcamango ye-Deep InfoMax kwii-graphs, kufuneka sisongeze i-MI phakathi kwayo amakhondo   kunye ne-support graph G  yenqaku ngalinye. Siyibona le MI ye-graph njenge  (  ; G  ). Nangona kunjalo, akulula ukuchaza I (hi ; Gi ). Ubunzima bubandakanya: Ubunzima ekuchazeni i-graphical mutual information. 20 hi i I hi i •   I-MI ye-graph kufuneka ingachaphazeleki ngesalathiso senqaku. Ngamanye amazwi, kufuneka sibe   (  ; G  ) =   (  ; G′  ), ukuba i-G  kunye ne-G′  ziyafana. I hi i I hi i i i •   Ukuba sisebenzisa indlela ye-MINE yokubalwa kwe-MI, i-discriminator kwi-MINE yamkela kuphela iisampuli ezine-size efanayo. Oku kusengafani ne-G  njengoko ii-G  ezahlukeneyo zihlala zibandakanya amanani ahlukeneyo eenqaku kwaye ngoko ke zinobukhulu obwahlukileyo. i i Ukujongana nomba yobunzima ekuchazeni i-graphical mutual information, eli candelo liqala ngokwazisa ingcamango ye-Feature Mutual Information (FMI) exhomekeke kuphela kwiimpawu zenqaku. Ngokuphefumlelwa yindibaniso ye-FMI, sibe siqamba i-Graphical Mutual Information (GMI), ehlomela zombini iimpawu zenqaku kunye  3.1      FEATURE MUTUAL INFORMATION Siyibonisa indlela yokusabalalisa yempawu zenqaku   njenge (  ), ingqungquthela ye  njenge (  ), kunye nendlela yokusasazwa ngokudibeneyo  (  ,   ). Ngokwe-information theory, i-MI phakathi kwe  kunye ne  ichazwe njenge Xi p Xi hi p hi p hi Xi hi Xi Ngokumangalisayo, sine-theorem yokuhlukana kolwazi oluhambelanayo malunga nokubala   (  ;   ). I hi Xi ITeorema 1 (Uhlukano loLwazi oluHambelanayo).  (  |  )   (  ;   )      , Ukuba i-conditional probability p hi Xi iyakwanda (bona inkcazo yokwanda kwi-[ ]), i-global mutual information I 36 hi Xi echazwe kwi-Eq. (1) ingahlulwa ibe yisumo enobunzima ye-local MIs, Oko.      ≤   ≤ 1  apho, xj iyona nj ye-neighbor yenqaku i, in libala elipheleleyo lezinto ezikwi-Xi , kunye nobunzima wij banelisa 1 wij kangalinye j. Ukufakazela le teoremi, kuqala sizisa ii-lemma ezimbini kunye nenkcazo enye. ILemma 1.  Kulo naliphi na izinto ezijikelezayo X, Y , kunye noZ, sine Ngohlukano kwiTheoremi   sinokubala uhlangothi olusekunene lwe-Eq.   nge-MINE njengee-inputs zesahluli zigqiba zijonge iipareyi ze (  ,   ) ezibukhulu bayo buhlala bugcinwa bufana ( .,   ′-by- ). Ngaphezu koko, sinokulungisa izibunzima ukubonisa utshintsho lwe-isomorphic lwee-graphs ezingenayo. Ngokomzekelo, ukuba i-Xi ibandakanya kuphela ii-hop neighbours zenqaku  , ukubeka zonke izibunzima zilingane kuya kuphumela kwi-MI efanayo kwiinqaku ezingenayo kwiiodolo ezahlukeneyo.  1, (2) hi xj  Oko. D D i Ngaphandle kwezinye iingenelo zoluhlukano, kunzima ukuchaza amaxabiso ezibunzima ezichanekileyo njengoko zihambelana namaxabiso e  (  ;   ) kunye nendlela zabo zokusasaza.  I hi xj Indlela elula kukubeka zonke izibunzima njenge    , emva koko ukonyisa uhlangothi olusekunene lwe-Eq.   kufana nokonyisa umda ongasentla we  (  ;   ), apho i-FMI yokwenyani ikwanyuswa ngandlelanye ethile. Ngaphandle kwale ndlela, sibonelela ngesisombululo esongezelelweyo ngokubandakanya izibunzima njengezinto zokuthotywa eziqeqeshwayo, ekuyisihloko sesahlulo esilandelayo.  1 (2) I hi Xi  Siphefumlelwe yindibaniso kwiTheoremi   sizama ukwak 3.2      Topology-Aware Mutual Information 1,

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