ÀÁÐÀÊÀÄÀÁÐÀ (Òîæå ñàìîå íî â ÷èòàåìîì âèäå)Ájhm,f cj cgfvjv ghb gjvjob fkujhbnvf TrustrankÊhfnrjt bpkj;tybt cjlth;fybzÑjplfntkb cnhfybw, d rjnjhs[ cjlth;bncz cgfv, ghb,tuf.n r hfpkbxysv nt[yjkjubzv lkz ljcnb;tybz dscjrb[ htpekmnfnjd d dslfxt. Åcnm cgtwbfkmyst 'rcgthns, rjnjhst evt.n bltynbabwbhjdfnm cgfv, yj lfyysq ghjwtcc ljcnfnjxyj nheljtvrbq b ljhjujcnjzobq.  cdzpb c 'nbv ghtlkfuftncz gjkefdnjvfnbxtcrfz nt[yjkjubz dszdktybz cgfvf. Ñyfxfkf jn,bhftncz ytcrjkmrj ckexfqys[ cnhfybw, rjnjhst ,elen jwtytys 'rcgthnjv. Èltynbabwbhjdfd dhexye. ytcrjkmrj ckexfqyj ds,hfyys[ cnhfybw, d lfkmytqitv bcgjkmpetncz ccskjxyfz cnhernehf Èynthytnf lkz jghtltktybz lheub[ cnhfybw, rjnjhst, crjhtt dctuj, jrf;encz «[jhjibvb» b ghfdbkmysvb cnhfybwfvb.  lfyyjq hf,jnt j,ce;lf.ncz djpvj;yst cgjcj,s ckexfqyjuj jn,jhf b j,yfhe;tybz «[jhjib[» cnhfybw. Ïhtlcnfdkz.ncz htpekmnfns 'rcgthbvtynjd, ghjdjlbvs[ d Èynthytnt b jwtyrf 'aatrnbdyjcnb hf,jns nt[yjkjubb. Ðtpekmnfns gjrfpfkb, xnj ceotcnde.n 'aatrnbdyst cgjcj,s abkmnhfwbb cgfvf. 1. ÂÂÅÄÅÍÈÅ Òthvby "bynthytn-cgfv" bcgjkmpe.n lkz j,jpyfxtybz cnhfybw, cjlth;fob[ vyjujxbcktyyst ccskrb, cgtwbfkmyj cjplfyyst lkz ddtltybz gjbcrjds[ cbcntv d pf,ke;ltybt. Ífghbvth, gjhyjuhfabxtcrbq cfqn vj;tn cgjcj,cndjdfnm hfcghjcnhfytyb. cgfvf d Èynthytnt, lj,fdkzz nsczxb rk.xtds[ ckjd yf ljvfiy.. cnhfybwe, ghbxtv ntrcn pfxfcne. cgtwbfkmyj ltkftncz ytdblbvsv lkz gjkmpjdfntktq. Ïjbcrjdfz cbcntvf byltrcbhetn ljgjkybntkmyst rk.xtdst ckjdf b ghtljcnfdkztn gjhyjuhfabxtcre. cnhfybwe d rfxtcndt jndtnf yf pfghjcs, cjlth;fobt 'nb ckjdf. Òfr rfr lj,fdktyyst rk.xtdst ckjdf yt zdkz.ncz ytghbcnjqyjq ktrcbrjq, gjkmpjdfntkb gjgflf.n yf cnhfybws nfrjuj cfqnf. Åot jlyf nt[ybrf hfcghjcnhfytybz cgfvf – cjplfybt ,jkmijuj rjkbxtcndf gjlltkmys[ dt,-cnhfybw, erfpsdf.ob[ yf tlbycndtyye. wtktde. cnhfybwe.  cdzpb c ntv, xnj vyjubt gjbcrjdst cbcntvs exbnsdf.n rjkbxtcndj d[jlzob[ ccskjr ghb hfy;bhjdfybb cnhfybw, wtktdfz cnhfybwf, crjhtt dctuj, gjzdbncz hfymit dct[ d htpekmnfnf[ gjbcrf. Âjghjc, zdkztncz kb cnhfybwf bkb uheggf cnhfybw cgfvjv ('nj rfcftncz b 'ktrnhjyyjq gjxns), ljcnfnjxyj ce,]trnbdysq. Ífghbvth, djpmvtv ytcrjkmrj cfqnjd, ytjlyjrhfnyj ccskf.ob[cz yf cnhfybws lheu lheuf. Òfrbt ccskrb vjuen ghjcnj cdbltntkmcndjdfnm j c[jlyjq ntvfnbrt cfqnjd, bkb ,snm cjplfys cgtwbfkmyj lkz gjdsitybz hfy;bhjdfybz cnhfybw. Çfxfcne. ljcnfnjxyj ghj,ktvfnbxyj jghtltkbnm, rfrjq bp lde[ cwtyfhbtd ,sk bcgjkmpjdfy.  wtkjv, gjkmpjdfntkb kturj hfcgjpyf.n zdyst b ytghbrhsnst ghjzdktybz cgfvf. Ífghbvth, ,jkmibycndj cjukfcbncz, xnj tckb jcyjdyfz xfcnm ntrcnf yf cnhfybwt ytdblbvf gjkmpjdfntk. b yt cjjndtncndetn ntvfnbrt, nj, jxtdblyj, cnhfybwf ,skf lj,fdktyf c yfvthtybtv ddtcnb gjbcrjde. cbcntve d zdyjt pf,ke;ltybt. Òjxyj nfr ;t ltkj j,cnjbn, tckb yf cnhfybwt dcnhtxftncz juhjvyjt rjkbxtcndj URL, ccskf.ob[cz yf nfrbt [jcns rfr:
Ïhjwtcc fkujhbnvbxtcrjq bltynbabrfwbb cgfvf ckj;ty, gj'njve c[tvs, ghtlcnfdktyyst d lfyyjq hf,jnt yt ,elen jgthbhjdfnm ,tp dvtifntkmcndf cgtwbfkbcnf. Ïhtlkfuftvsq fkujhbnv hf,jnftn cktle.obv j,hfpjv: ckexfqyjq ds,jhrjq bp,bhf.ncz cnhfybws, rjnjhst ljk;ys ,snm bccktljdfys yf yfkbxbt cgfvf. Ýrcgthn bccktletn «ckexfqyst cnhfybws», b cjj,oftn fkujhbnve, ghbcencndetn kb yf yb[ cgfv. Âgjcktlcndbb fkujhbnv bltynbabwbhetn lheubt cnhfybws, rjnjhst, crjhtt dctuj, jrf;encz «[jhjibvb», ghb extnt b[ cdzpb c «[jhjibvb ckexfqysvb» cnhfybwfvb. Â 'njq hf,jnt:
2.1. bynthytn-vjltkm Ïhtlcnfdkztv vjltkm ctnb d dblt uhfaf ς = (ν,ε),cjcnjzotuj bp vyj;tcndf ν cnhfybw N b vyj;tcndf ε yfghfdktyys[ ccskjr, cjtlbyz.ob[ cnhfybws. Íf ghfrnbrt bynthytn-cnhfybwf p vj;tn cjlth;fnm vyjujxbcktyyst HMTL ubgthccskrb yf ytre. lheue. cnhfybwe q. Â 'njv ckexft vs ghtlcnfdkztv 'nb vyjujxbcktyyst ccskrb rfr tlbycndtyye. ccskre (p,q) º ε. Ìs nfr;t elfkztv dyenhtyybt ccskrb. Íf hbc.1 ghtlcnfdkty jxtym ghjcnjq Èynthytn uhfa, cjcnjzobq bp 4 cnhfybw b 4 ccskjr.
Ðbc.1 Ïhjcnjq Èynthytn uhfa
Êf;lfz cnhfybwf cjlth;bn d[jlzobt b bc[jlzobt ccskrb. Êjkbxtcndj d[jlzob[ ccskjr yf cnhfybwe p ghtlcnfdkztn cj,jq gjkecntgtym pf[jlf i(p). Êjkbxtcndj bc[jlzob[ ccskjr – gjkecntgtym bc[jlf w(p). Ífghbvth, gjkecntgtym pf[jlf cnhfybws 3 yf hbc.1 hfdyf tlbybwt, f gjkecntgtym bc[jlf – ldev. Ñnhfybws, rjnjhst yt cjlth;fn d[jlzobt ccskrb, yfpsdf.ncz cnhfybwfvb ,tp ccskjr. Ñnhfybws, rjnjhst yt cjlth;fn bc[jlzob[ ccskjr, yfpsdf.ncz yt ccskf.obvbcz cnhfybwfvb. Ñnhfybws, rjnjhst yt cjlth;fn yb d[jlzob[, yb bc[jlzob[ ccskjr, yfpsdf.ncz bpjkbhjdfyysvb. Ñnhfybwf 1 yf hbc.1 zdkztncz cnhfybwtq ,tp ccskjr, f cnhfybwf 4 – yt ccskf.otqcz.Ðfccvjnhbv 2 vfnhbws bynthytn-uhfajd, rjnjhst d lfkmytqitv ,elen bvtnm df;yjt pyfxtybt. Îlyf bp vfnhbw – vfnhbwf gtht[jlf Ò:
Ìfnhbwf gtht[jlf, cjjndtncnde.ofz uhfae yf hbc.1:
Ðfccvjnhb nfr;t j,hfnye. vfnhbwe gtht[jlf U:
Ítj,[jlbvj j,hfnbnm dybvfybt, xnj U≠TT . Ífghbvth, yf hbc.1 j,hfnyfz vfnhbwf gtht[jlf dsukzlbn nfr:
2.2. PageRank – fkujhbnv hfcxtnf fdnjhbntnyjcnb cnhfybws, f nfr;t cfv gjrfpfntkm d xbcktyyjv dshf;tybb. Òfr rfr ghtlkfuftvst fkujhbnvs jcyjdfys yf PagtRank, d lfyyjv hfpltkt ghtlkfuftncz tuj rjhjnrbq j,pjh. Page Rank cnhfybws ,eltn ljcnfnjxyj dscjrbv, tckb ytj,[jlbvjt rjkbxtcndj df;ys[ cnhfybw erfpsdf.n yf 'ne cnhfybwe. Page Rank jcyjdsdftncz yf dpfbvyjv dkbzybb cnhfybw. Ñnhfybwf yt njkmrj cfvf jrfpsdftn dkbzybt yf lheue. cnhfybwe, yj b bcgsnsdftn dkbzybt yf ct,t. Ïjrfpfntkb Page Rank r(p) cnhfybws p jghtltkz.ncz nfr:
ult α – rj'aabwbtyn hfcgflf1. Ðfdyjcbkmyj vfnhbxyjt ehfdytybt:
Òfrbv j,hfpjv, jwtyrf ytrjnjhjq cnhfybws p ghtlcnfdkztn cevve lde[ rjvgjytynjd. Îlyf xfcnm jwtyrb jnyjcbncz r cnhfybwfv, rjnjhst erfpsdf.n yf cnhfybwe p. Äheufz (cnfnbxtcrfz) xfcnm jwtyrb gjl[jlbn lkz dct[ dt,-cnhfybw.
Page Rank vj;tn dsxbckznmcz bnthfwbjyyj, yfghbvth, c gjvjom. vtnjlf Jacobi. Â cnhjuj vfntvfnbxtcrjv cvsckt bnthfwbz ljk;yf gtht[jlbnm d rjydthutywb.. Íf ghfrnbrt ghbyznj bcgjkmpjdfnm xtnrj pfabrcbhjdfyyjt xbckj bnthfwbq. Ñnfylfhnysq fkujhbnv PageRank ghbcdfbdftn cnfnbxtcre. jwtyre rf;ljq cnhfybwt, dthcbz Page Rank cj cvtotybtv aeyrwbjybhetn gj-lheujve. Â vfnhbxyjv ehfdytybb
dtrnjh d vj;tn ,snm bcgjkmpjdfy lkz ghbcdjtybz yektdjq cnfnbxtcrjq jwtyrb hzle cnhfybw. Îwtyrf nfrb[ cgtwbfkmys[ cnhfybw hfcghjcnhfyztncz dj dhtvz bnthfwbb yf erfpsdftvst cnhfybws. 3. ÎÖÅÍÊÀ ÑÒÅÏÅÍÈ ÄÎÂÅÐÈß
3.1. Ôeyrwbb ghjuyjpbhjdfybz b ljdthbz  hfpltkt 1 e;t ,skj crfpfyj, xnj hfcgjpyfdfybt cgfvf – pflfxf, nht,e.ofz dvtifntkmcndf xtkjdtrf b tuj ce,]trnbdyjq jwtyrb. Ñeotcndetn gjyznbt ghjdthrb cnhfybws yf cgfv c gjvjom. ldjbxyjq aeyrwbb ghjuyjpbhjdfybz (Î) dct[ cnhfybw p º ν:
Íf hbc.2 ghtlcnfdktys 7 bynthytn-cnhfybw. «Õjhjibt» cnhfybws ghtlcnfdktys yf ,tkjv ajyt, «gkj[bt» – yf xthyjv. Âspsdfz aeyrwb. ghjuyjpbhjdfybz lkz cnhfybw 1-4, ,eltn dslfyj pyfxtybt 1.
 Ðbc.2 Õjhjibt b gkj[bt epks ctnb
Ïhjwtlehf ghjuyjpbhjdfybz ljhjujcnjzofz b ljcnfnjxyj lkbntkmyfz. Ïj'njve ghbvtytybt gjlj,yjq aeyrwbb lkz dct[ cnhfybw yt ghbtvktvj. Ïhb ghjdtltybb fyfkbpf df;yj ghjltvjycnhbhjdfnm bp,bhfntkmyjcnm, gj'njve kjubxytt j,hfnbnmcz r 'rcgthne lkz fyfkbpf ytrjnjhs[ bynthytn-cnhfybw. Ïhb fyfkbpt «[jhjib[» cnhfybw vs gjkfufkbcm yf 'vgbhbxtcrjt yf,k.ltybt:«Õjhjibt» cnhfybws htlrj erfpsdf.n yf «gkj[bt». Äfyysq dsdjl jcyjdfy yf bynebwbb: «Ïkj[bt» cnhfybws cjplf.ncz c yfvthtymtv ddtcnb gjbcrjdst cbcntvs d pf,ke;ltybt, jyb lfktrb jn wtkb ghtljcnfdktybz gjktpyjq byajhvfwbb. Òfrbv j,hfpjv, e k.ltq, cjplf.ob[ «[jhjibt» cnhfybws, ytn yb vfktqituj jcyjdfybz ccskfnmcz yf «gkj[bt» cnhfybws. Îlyfrj cjplfntktq «[jhjib[» cnhfybw nj;t byjulf ddjlzn d pf,ke;ltybt. Ïj'njve d Èynthytnt vj;yj dcnhtnbnm ccskrb c «[jhjib[» cnhfybw yf «gkj[bt» (yf hbc.2 nfrfz ccskrf gjrfpfyf vt;le cnhfybwfvb 4 b 5 b gjvtxtyf pdtpljxrjq). Ðfccvjnhbv ghbvth. Âjpmvtv [jhjie., yj ytvjlthbhetve. ujcntde. rybue. Ñgfvths vjuen hfpvtcnbnm ccskre yf cdjb cgfv-cnhfybws, rfr xfcnm «ytdbyys[» cjj,otybq, hfpvtoftvs[ d 'njq «ujcntdjq».Èyjulf cgfvthcrbt cfqns ghtlcnfdkz.n bp ct,z n.y. «Honeypot» («ujhijxtr vtlf»): cfqns ghtlcnfdkz.n cj,jq yf,jh cnhfybw, rjnjhst cjlth;fn gjktpye. byajhvfwb. (yfghbvth, rjgbb ljrevtynfwbb Unix), d nj ;t dhtvz yf cnhfybwf[ cjlth;fncz crhsnst ccskrb yf cgfv-cnhfybws. «Honeypot», ghbdktrfz gjkmpjdfntktq ccskfnmcz yf yb[, edtkbxbdftn hfy;bhjdfybt cnhfybw, cjlth;fob[ cgfv. Ítj,[jlbvj gjlxthryenm, xnj, d cdj. jxthtlm, pfcgfvktyyst cnhfybws xfcnj ccskf.ncz yf «[jhjibt» cnhfybws. Ífghbvth, cjplfntkb pfcgfvktyys[ cnhfybw erfpsdf.n yf «[jhjibt» b df;yst cnhfybws, c wtkm. cjplfybz «Honeypot», kb,j d yflt;lt, xnj ,jkmijt rjkbxtcndj bc[jlzob[ ccskjr ,elen cgjcj,cndjdfnm gjdsityb. ytrjnjhs[ dbljd hfy;bhjdfybz. Äkz jwtyrb cnhfybw, yt ghb,tufz r gjrfpfntk. Î, ytj,[jlbvj jwtybnm, rfrjdf dthjznyjcnm njuj, xnj lfyyfz cnhfybwf Ð zdkztncz «[jhjitq». Âshf;fzcm yfexysv zpsrjv, jghtltkztncz aeyrwbz ljdthbz Ò bvt.ofz lbfgfpjy pyfxtybq jn 0 (gkj[fz cnhfybwf) lj 1 ([jhjifz cnhfybwf) Â bltfkt, lkz k.,jq cnhfybws h, Ò(h) ljk;yj gjrfpsdfnm dthjznyjcnm njuj, xnj cnhfybwf h – «[jhjifz».Èltfkmysq gjrfpfntkm aeyrwbb ljdthbz
T(p) = Pr[O(p) = 1] Äjgecnbv, bvttncz 100 cnhfybw, gjrfpfntkm ljdthbz rjnjhs[ cjcnfdkztn 0.7. Ïhtlgjkj;bv, xnj jwtyrf cnhfybw jceotcndkztncz c bcgjkmpjdfybtv aeyrwbb ghjuyjpbhjdfybz. Òjulf, tckb Ò chf,jnftn ye;ysv j,hfpjv, lkz 70 cnhfybw gjrfpfntkm ghjuyjpbhjdfybz cjcnfdbn 1, f lkz jcnfdib[cz 30 – 0. Åckb Ò yt vj;tn njxyj jghtltkbnm dthjznyjcnm njuj, xnj cnhfybwf «[jhjifz», nj lfyyfz aeyrwbz dct hfdyj jrf;tncz ytj,[jlbvjq ghb ltktybb cnhfybw yf «[jhjibt» b «gkj[bt», gjkfufzcm ghb 'njv yf ghb,kbpbntkmyst lfyyst. Ífghbvth, lfys ldt cnhfybws, p b q. Ïjrfpfntkm ljdthbz cnhfybws h yb;t gjrfpfntkz ljdthbz cnhfybws q. Èp 'njuj cktletn, xnj dthjznyjcnm njuj, xnj cnhfybwf h «[jhjifz» yb;t dthjznyjcnb njuj, xnj cnhfybwf q «[jhjifz». Ôeyrwbz ljdthbz Ò jrf;tncz gjktpyjq, gj rhfqytq vtht, ghb hfcghtltktybb htpekmnfnjd gjbcrf, rjulf ghtlgjxntybt jnlftncz cnhfybwfv, rjnjhst, dthjznytt dctuj, zdkz.ncz «[jhjibvb». Îlybv bp ghtlgjxnbntkmys[ cdjqcnd aeyrwbb ljdthbz zdkztncz «cdjqcndj egjhzljxtyyjcnb ljdthbz»
Îlby bp cgjcj,jd gjybpbnm nht,jdfybz r gjrfpfntk. ljdthbz – ddtcnb gjhjujde. dtkbxbye δ. Ïjhjujdsq gjrfpfntkm aeyrwbb ljdthbz
Åckb cnhfybwf p gjkexftn jwtyre dsit gjrfpfntkz δ 'nj cdbltntkmcndetn j njv, xnj cnhfybwf «[jhjifz». Â ghjnbdyjv ckexft, j cnhfybwt p ybxtuj ytkmpz ,eltn crfpfnm. Ôeyrwbz Ò ghtljcnfdkztn byajhvfwb., d cjjndtncndbb c rjnjhjq vj;yj jghtltkbnm, xnj cnhfybws, yf[jlzobtcz d ytrjnjhjv gjlvyj;tcndt b bvt.obt dscjrbq gjrfpfntkm ljdthbz zdkz.ncz [jhjibvb. Î,hfnbnt dybvfybt, xnj aeyrwbz Ò c gjhjujdsv gjrfpfntktv yt dctulf dkbztn yf cjhnbhjdre cnhfybw gj ghbywbge «[jhjibt»-«gkj[bt».
3.2. Ïjrfpfntkb jwtyrb  lfyyjv hfpltkt ghtlcnfdktys 3 gjrfpfntkz, rjnjhst gjvjuf.n jwtybdfnm [fhfrnthbcnbrb aeyrwbb Ò. Äjgecnbv, bvttncz χ ckexfqys[ bynthytn-cnhfybw, lkz rjnjhs[ vj;yj ghbdktxm aeyrwbb Ò b Î b jwtybnm, rfr hf,jnf.n nt bkb byst cdjqcndf lkz lfyyjuj vyj;tcndf. (d hfpltkt 6 ,eltn hfccrfpfyj, gj rfrjve ghbywbge ds,bhf.ncz cnhfybws, f gjrf vs cxbnftv, xnj χ – vyj;tcndj ckexfqys[ dt,-cnhfybw).Ïthdsq gjrfpfntkm ntcyj cdzpfy c pflfyysv gjrfpfntktv ljdthbz. Âdjlbncz ldjbxyfz aeyrwbz I(T, O, p, q), c gjvjom. rjnjhjq jghtltkztncz, xnj «gkj[bt» cnhfybws gjkexbkb gjrfpfntkm ljdthbz hfdysq bkb dsit «[jhjib[» cnhfybw
Çfntv bp ds,jhrb χ cnhfybw cjcnfdkz.ncz vyj;tcndf
Åckb pairord hfdty 1, nj d aeyrwbb ljdthbz jib,jr yt ,skj, tckb pairord hfdty 0, nj d aeyrwbb ljdthbz ytghfdbkmyfz lkz dct[ gfh.
Ïjlj,ysv j,hfpjv, vs jghtltkztv gjrfpfntkm Recall rfr jnyjitybt rjkbxtcndf [jhjib[ cnhfybw c erfpfyysv gjrfpfntktv ljdthbz r j,otve rjkbxtcnde [jhjib[ cnhfybw, ghbyflkt;fob[ χ.
4. Âsxbcktybt ljdthbz
 hfpltkt 4.3 ,eltn gjcnhjty fkujhbnv TrustRank. Ïht;lt ytj,[jlbvj ghjbpdtcnb gjlujnjdbntkmye. hf,jne. Ènfr, ghbcnegbv r dszdktyb. aeyrwbb ljdthbz. Ífxytv c cfvjuj ghjcnjuj. Ïhb eckjdbb, xnj rjk-dj L juhfybxtyj lkz dsxbcktybz aeyrwbb Î, yfxytv ytgjchtlcndtyyj c ds,jhrb vyj;tcndf S ckexfqys[ cnhfybw L b dspjdtv aeyrwb. ghjuyjpbhjdfybz lkz pflfyys[ 'ktvtynjd. ( hfpltkt 5 ,eltn hfccrfpfyj, rfr jgnbvfkmyj ds,hfnm ckexfqyst cnhfybws). Î,jpyfxbv gjlvyj;tcndf «[jhjib[» b «gkj[b[» cnhfybw S+ b S- cjjndtncndtyyj. Òfr rfr jcnfdibtcz cnhfybws yt ghjdthz.ncz 'rcgthnfvb, bv ghbcdfbdftncz gjrfpfntkm ljdthbz, hfdysq ½ bp-pf jncencndbz byajhvfwbb.Âdjlbncz gjyznbt gecnfz aeyrwbz ljdthbz T0 lkz k.,s[ p º ν:
Ífghbvth, ghbcdjbv L pyfxtybt 3 b ghbvtybv yfi vtnjl r ghbvthe yf hbc.2 Ñkexfqyj ds,hfyyjt vyj;tcndj S vj;tn bvtnm pyfxtybz {1, 3, 6}. Ïecnm o b t0 ,elen j,jpyfxfnm dtrnjhs ghjuyjpbhjdfybz b gjrfpfntktq ljdthbz lkz rf;ljq cnhfybws cjjndtncndtyyj. Òjulf:
Äkz jwtyrb gjdtltybz gecnjq aeyrwbb ljdthbz ghtlgjkj;bv, xnj yfif ds,jhrf X cjcnjbn bp 7 cnhfybw, b b vs hfccvfnhbdftv dct djpvj;yst 42 (7*6) gfhs. Òjulf gjrfpfntkm egjhzljxtyyjcnb gfhs cjcnfdbn 17/21. Äkz gjhjuf δ =½ gjrfpfntkm precision cjcnfdbn 1, f gjrfpfntkm recall – ½.
4.1. Ðfcghjcnhfytybt aeyrwbb ljdthbz Äkz lfkmytqituj gjlcxtnf gjrfpfntkz ljdthbz djcgjkmpetvcz ytcdzpyjcnm. «[jhjib[» cnhfybw.
Òf,kbwf1: gjdtltybt Ì-ifujdjq aeyrwbb ljdthbz ÒM, ghb M º {1, 2, 3} . Ì-ifujdfz aeyrwbz ljdthbz 
Ãlt q Ècgjkmpez ghbvth yf hbc.2 b ckexfqye. cjdjregyjcnm S = {1, 3, 6}, vj;yj ghtlcnfdbnm jwtyre ljdthbz lkz Ì c hfpysvb pyfxtybzvb: M=1: t1 = [1, 1, 1, ½, ½, 0, ½]  nf,kbwt1 gjrfpfyj, xnj ghb M = 1 b M = 2 pyfxtybz pairord b recall djphfcnf.n, f pyfxtybt precision hfdyo 1. Îlyfrj dct cjdctv yt nfr j,cnjbn ghb M = 3. Ñnhfybwf 5 gjkexftn jwtyre 1 ,kfujlfhz ccskrt c «[jhjitq» cnhfybws 4 yf «gkj[e.» cnhfybwe 5 (yf hbc. 2 jnvtxtyj pdtpljxrjq). Êfr gjrfpfk ghtlsleobq ghbvth, ghj,ktvf pfrk.xftncz d njv, xnj ghb gjrfpfntkt ljdthbz M-step ytn f,cjk.nyjq edthtyyjcnb d njv, xnj cnhfybws bp cjdjregyjcnb «[jhjib[» cnhfybw yf cfvjv ltkt zdkz.ncz «[jhjibvb». 4.2. Çfne[fybt gjrfpfntkz ljdthbz Íf,k.ltybz cdbltntkmcnde.n j njv, xnj vs gjyb;ftv gjrfpfntkm ljdthbz, gj vtht njuj, rfr dct lfkmit b lfkmit elfkztvcz jn «[jhjib[» ckexfqys[ cnhfybw. Ñeotcndetn vyjuj cgjcj,jd gj ljcnb;tyb. cyb;tybz gjrfpfntkz ljdthbz. Ðfccvjnhbv ldt djpvj;yst c[tvs. Íf hbc.3 ghtlkj;ty jlby bp cgjcj,jd, rjnjhsq yfpsdftncz trust dampening (gfltybt ljdthbz). Òfr rfr cnhfybwf 2 yf[jlbncz yf hfccnjzybb jlyjq ccskrb jn «[jhjitq» ckexfqyjq cnhfybws 1, nj tq vj;yj ghbcdjbnm pfyb;tyye. jwtyre ljdthbz β, ult β < 1. Òfr rfr cnhfybwf 3 cktletn pf cnhfybwtq 2, rjnjhjq ghbcdjty gjrfpfntkm β, nj tq ghbcdfbdftncz pfyb;tyyfz jwtyrf, hfdyfz β*β. Ítj,[jlbvj ds,hfnm cgjcj,, rfr ghbcdfbdfnm gjrfpfntkm ljdthbz cnhfybwfv, rjnjhst cjlth;fn vyjujxbcktyyst d[jlzobt ccskrb. Ífghbvth, yf hbc.3 cnh.1 nfr;t ccskftncz yf cnh. 3.  'njv ckexft, bvttn cvsck ghbcdjbnm cnh.3 vfrcbvfkmyjt pyfxtybt gjrfpfntkz ljdthbz, d lfyyjv ckexft β, bkb chtlytt pyfxtybt, d lfyyjv ckexft: (β+β*β)/2 Ðbc.3 Trust dampening  Ðbc.4 Trust splitting Ânjhjq cgjcj, lkz cyb;tybz gjrfpfntkz ljdthbz, rjnjhsq yfpsdftncz trust splitting (hfpltktybt ljdthbz) jcyjdfy yf cktle.otv yf,k.ltybb: jcnjhj;yjcnm, c rjnjhjq gjkmpjdfntkb lj,fdkz.n ccskrb yf cdjb cnhfybws, j,hfnyj ghjgjhwbjyfkmyf rjkbxtcnde ccskjr yf cnhfybwt. Äheubvb ckjdfvb, tckb «[jhjifz» cnhfybwf cjlth;bn dctuj ytcrjkmrj bc[jlzob[ ccskjr, nj, crjhtt dctuj, cnhfybws, yf rjnjhst dtlen 'nb ccskrb, «[jhjibt». Îlyfrj tckb «[jhjifz» cnhfybwf cjlth;bn cjnyb bc[jlzob[ ccskjr, nj dtkbrf dthjznyjcnm njuj, xnj cnhfybws, yf rjnjhst dtlen 'nb ccskrb, jrf;encz «gkj[bvb». Äfyyjt yf,k.ltybt ghbdjlbn yfc r «hfpltktyb. ljdthbz», nfr rfr lfyyjt yf,k.ltybt hfcghjcnhfyztncz b yf lheubt cnhfybws: tckb cnhfybwf h bvttn gjrfpfntkm ljdthbz Ò(h) b erfpsdftn yf !(h) cnhfybw, nj jwtyrf lkz rf;ljq bp !(h) cnhfybw ,eltn hfdyf jnyjityb. T(p)/!(p).  'njv ckexft, htfkmyfz jwtyrf cnhfybws ,eltn ghtlcnfdkznm cj,jq cevve jwtyjr, hfccxbnfyys[ c gjvjom. d[jlzob[ ccskjr. Ífukzlyj, xtv ,jkmit ljdthbz gjkexftn cnhfybwf c lheub[ cnhfybw, ntv ,jkmit dthjznyjcnm njuj, xnj lfyyfz cnhfybwf «[jhjifz». Ðbc.4 c[tvfnbxyj ghtlcnfdkztn vtnjl trust splitting. «Õjhjifz» ckexfqyfz cnhfybwf 1 cjlth;bn 2 bc[jlzobt ccskrb, nfrbv j,hfpjv, jyf hfcghtltkztn gjkjdbye jwtyrb, hfdyjq 1, vt;le cnhfybwfvb, yf rjnjhst jyf erfpsdftn. Òjxyj nfr ;t, «[jhjifz» ckexfqyfz cnhfybwf 2 cjlth;bn nhb bc[jlzob[ ccskrb, cjjndtncndtyyj, rf;lfz cnhfybwf, yf rjnjhe. erfpsdftn cnhfybwf 2, gjkexftn jlye nhtnm jn tt jwtyrb. Òjulf jwtyrf cnhfybws 3 ,eltn crkflsdfnmcz cktle.obv j,hfpjv: 1/2 + 1/3 = 5/6. Ítj,[jlbvj jnvtnbnm, xnj djpvj;yj cjdvtotybt lde[ cgjcj,jd cyb;tybz gjrfpfntkz ljdthbz. Íf hbc.4, yfghbvth, cnh.3 vj;tn ,snm ghbcdjtyf jwtyrf, rjnjhfz hfccxbnsdftncz cktle.obv j,hfpjv: β*(1/2 + 1/3) . lfkmytqitv ,eltn ljrfpfyj, xnj ghb dsxbcktybb jwtyrb ljdthbz wtktcjj,hfpyj gjkfufnmcz yf fkujhbnv Page Rank. 4.3 Àkujhbnv TrustRank Ôeyrwbz TrustRank, bpj,hf;tyyfz yf hbc. 5, ytj,[jlbvf ghb gjlcxtnt jwtyrb ljdthbz lkz bynthytn-uhfaf. Àkujhbnv hf,jns j,]zcyztncz c gjvjom. hbc.2. Àkujhbnv TrustRank ghtlcnfdkztn cj,jq uhfa (gtht[jlyfz vfnhbwf Ò b N bynthytn-cnhfybw). Ècgjkmpe.ncz gfhfvtnhs, rjnjhst rjynhjkbhe.n hf,jne fkujhbnvf (L, MB, αB cv. yb;t).  Ðbc.5 Àkujhbnv TrustRank Øfu1: fkujhbnv dspsdftn aeyrwb. SelectSeed, rjnjhfz djpdhfoftn dtrnjh s. Ñjcnfdkz.obt dtrnjhf s(p) jghtltkz.n «ghtlgjxntybt» cnhfybws p rfr ckexfqyjq cnhfybws (gjlhj,yjcnb vj;yj yfqnb d hfpltkt 5). Êfr gjrfpfyj d hfpltkt 5.1, jlyf dthcbz SelectSeed djpdhfoftn cktle.obq dtrnjh r ghbvthe yf Ðbc.2: s = [0,08, 0,13, 0,08, 0,10, 0,09, 0,06. 0,02].Øfu 2: aeyrwbz Rank(x,s) jceotcndkztn ghtj,hfpjdfybz dtrnjhf [ d [", c 'ktvtynfvb ["(i) d gjhzlrt e,sdfybz pyfxtybz s(x’(i)). Ífghbvth, σ = [2, 4, 5, 1, 3, 6, 7]. cjjndtncndbb c ghbdtltyysv ghbvthjv, cnhfybwf 2 cfvfz ghtlgjxnbntkmyfz ckexfqyj ds,hfyyfz cnhfybwf, cktle.ofz 4 b n.l. Øfu 3: frnbdbpbhetncz aeyrwbz Oracle lkz L, yfb,jktt ghtlgjxnbntkmys[ cnhfybw. Ñjcnfdkz.obt cnfnbxtcrjuj dtrnjhf hfcghtltktybz d, cjjndtncnde.obt [jhjibv cnhfybwfv, ecnfyfdkbdf.ncz hfdysvb 1.Øfu 4: yjhvfkbpetncz dtrnjh d, nfr, xnj,s cevvf tuj cjcnfdkz.ob[ hjdyzkfcm 1. Äjgecrfz, xnj L=3, vyj;tcndj ckexfqys[ cnhfybw {2, 4, 5}. 2 b 4 zdkz.ncz [jhjibvb ckexfqyj ds,hfyysvb cnhfybwfvb, vs gjkexftv cktle.obq dtrnjh hfcghtltktybz cnfnbxtcrb[ jwtyjr lkz yfituj ghbvthf, d = [0, ½, 0, ½, 0, 0, 0].Øfu 5: pfrk.xbntkmysq 'nfg, gjlcxbnsdftncz TrustRank c bcgjkmpjdfybtv cvtotyys[ dsxbcktybq PageRank, ult d pfvtyztn hfdyjvthyjt hfcghtltktybt. Çfvtnmnt, xnj ifu 5 ghtlcnfdkztn jghtltktyye. vjltkm, rjulf ljdthbt cyb;ftncz b hfpltkztncz: d rf;ljq bnthfwbb gjrfpfntkm ljdthbz dthibys hfcghtltkztncz vt;le cjctlcnde.obvb b cyb;ftncz gj ghbxbyt rj'aabwbtynf pfne[fybz αÂ. t* = [0, 0,18, 0,12, 0,15, 0,13, 0.,05, 0,05] Î,hfnbnt dybvfybt, xnj cgjcj, bnthfwbjyyjuj jghtltktybz gjrfpfntkz ljdthbz dkbztn yf nj, xnj [jhjibt, ckexfqyj ds,hfyyst cnhfybws (2 b 4), yt bvt.n ,jkmit gjrfpfntkz, hfdyjuj 1.Îlyfrj, e yb[ gj-ght;ytve cfvst dscjrbt gjrfpfntkb. Òfr;t cktletn jnvtnbnm, xnj cnhfybwf 4 bvttn ,jktt ybprbq gjrfpfntkm, xtv cnhfybwf 2. Ýnj cdzpfyyj cj cnhernehjq ccskjr d lfyyjv ghbvtht: ccskrb yf cnhfybwe 2 cltkfys cj cnhfybws c dscjrbv gjrfpfntktv (cnhfybwf 3), f yf cnhfybwe 4 ytn. Òfrbv j,hfpjv, fkujhbnv TrustRank «rjhhtrnbhetn» gthdjyfxfkmyst gjrfpfntkb, ghtlcnfdktyyst aeyrwbtq ghjuyjpbhjdfybz Oracle, ghtlcnfdkzz ,jkmit ljrfpfntkmcnd njuj, xnj gj chfdytyb. cj cnhfybwtq 4, cnhfybwf 2 – [jhjifz. Åckb gjkexbncz, vj;yj yjhvfkbpjdfnm cevvfhysq dtrnjh, hfpltkbd dct gjrfpfntkb yf cfvsq dscjrbq (ltkfz gjrfpfntkm cnhfybws 2 hfdysv 1), nj lfyyjt ltqcndbt yt ghbdytctn rfhlbyfkmys[ bpvtytybq d gjhzljr cnhfybw. Èp lfyyjuj ghbvthf dblyj, xnj fkujhbnv TrustRank ghbcdfbdftn [jhjibv cnhfybwfv ,jktt dscjrbq gjrfpfntkm.  xfcnyjcnb, nhb bp xtnsht[ [jhjib[ cnhfybw (2, 3 b 4) gjkexbkb dscjrbq gjrfpfntkm, f ldt bp nht[ gkj[b[ cnhfybw (cnhfybws 6 b 7) gjkexbkb ybprbq gjrfpfntkm. Îlyfrj, gjrfpfntkb cnhfybw 1 b 5 ,skb jghtltktys fkujhbnvjv yt fltrdfnyj. Ñnhfybwf 1 yt ,skf chtlb ckexfqyj ds,hfyys[ b yt bvtkf ljcnfnjxyjuj rjkbxtcndf ccskjr c cfqnjd c dscjrbvb gjrfpfntkzvb, yj tt gjrfpfntkm jcnfkcz hfdysv 0. Ñj dctvb [jhjibvb cnhfybwfvb, yt bvt.obvb ccskjr, ghjbc[jlbn nj;t cfvjt, tckb njkmrj jyb yt ckexfqyj ds,hfyyst. Ïkj[fz cnhfybwf 5 gjkexbkf dscjrbq gjrfpfntkm, n.r. yf 'njq cnhfybwt erfpfyf jlyf bp htlrb[ good-to-bad ccskjr. Êfr ,eltn dblyj bp hfpltkf 6, ytcvjnhz yf gjlj,yst jib,rb, yf htfkmyjv dt,-uhfat fkujhbnv TrustRank ghfdbkmyj jghtltkztn ,jkmibycndj gjl[jlzob[ cnhfybw. 5. Âs,jh ckexfqys[ cnhfybw
Çflfxf aeyrwbb SelectSeed jghtltkbnm ghtlgjxnbntkmyst cnhfybws, rjnjhst djqlen d ckexfqyj ds,hfyyst. Ætkfntkmyj yfqnb cnhfybws, rjnjhst ,elen yfb,jktt ghbujlysvb lkz jghtltktybz ljgjkybntkmys[ gjl[jlzob[ cnhfybw.  nj ;t dhtvz ;tkfntkmyj yt edtkbxbdfnm rjkbxtcndj ckexfqyj ds,hfyys[ cnhfybw c wtkm. juhfybxtybz bcgjkmpjdfybz aeyrwbb Oracle.  lfyyjv hfpltkt ,elen hfccvjnhtys ldt cnhfntubb lkz aeyrwbb SelectSeed, rfr ljgjkytybt r hfytt egjvzyenjq cnhfntubb ckexfqyjuj ds,jhf. 5.1. Èydthcysq (j,hfnysq) PageRankÒ.r. gjrfpfntkm ljdthbz dj vyjujv jghtltkztncz [jhjibvb ckexfqysvb cnhfybwfvb, jlybv bp gjl[jljd vj;tn ,snm ds,jh cnhfybw, c gjvjom. rjnjhs[ ,eltn djpvj;yj gjkexbnm lheubt.  jcj,tyyjcnb, ds,jh ckexfqys[ cnhfybw, ghbybvfz dj dybvfybt bc[jlzobt ccskrb. Ífghbvth, yf Ðbc.2, ult cjjndtncnde.ott vyj;tcndj ckexfqys[ cnhfybw L=2, n.r. S = {2, 5}, e cnhfybw 2 b 5 cfvjt ,jkmijt xbckj bc[jlzob[ ccskjr.  Ðbc. 6: Àkujhbnv bydthcyjuj PageRank  lfkmytqitv, vj;yj edtkbxbnm gjrhsdf.oe. cgjcj,yjcnm. Íf,jh ckexfqys[ cnhfybw vjuen cjcnfdbnm nt cnhfybws, rjnjhst erfpfkb ,jkmitt rjkbxtcndj cnhfybw, d cdj. jxthtlm, erfpfdib[ yf lheubt cnhfybws b n.l. Èynthtcyj, xnj lfyysq gjl[jl ,kbpjr c[tvt, gj rjnjhjq hf,jnftn PageRank, hfpybwf d njv, xnj d yfitv ckexft df;yjcnm cnhfybws pfdbcbn jn tt bc[jlzob[ ccskjr, f yt jn d[jlzob[. Òfrbv j,hfpjv, xnj,s hfccxbnfnm ghtlgjxnbntkmyjcnm cnhfybws, ghjbpdtltv dsxbcktybz PageRank yf uhfat ς׳ = (ν,ε׳), ult 
Àkujhbnv yfpsdftncz bydthcysv, n.r. vs bydthnbhjdfkb ccskrb. Íf hbc.6 gjrfpfy fkujhbnv dsxbcktybq bydthcyjuj PageRank. Çfvtnmnt, xnj rj'aabwbtyn pfne[fybz αI b xbckj bnthfwbq (gtht[jljd) MI vjuen jnkbxfnmcz jn αB b ÌB, bcgjkmpjdfyys[ d fkujhbnvt TrustRank. Âsxbcktybz bltynbxys cltkfyysv gj nhflbwbjyyjve fkujhbnve PageRank (Ðfpltk 2.2), pf bcrk.xtybtv bydthcyjq gtht[jlyjq vfnhbws U, bcgjkmpjdfyyjq dvtcnj j,sxyjq gtht[jlyjq vfnhbws Ò. s = [0,08, 0,13, 0,08, 0,10, 0,09, 0,06, 0,02]
Äkz xbckjdjuj pyfxtybz L = 3, ckexfqysq yf,jh S = {2, 4, 5}. Ñjjndtncndtyyj, gjl[jlzott ckexfqyjt vyj;tcndj S+ = {2, 4}, n.j. cnhfybws 2 b 4 zdkz.ncz jnghfdyjq njxrjq lkz hfcxtnf hfcghtltktybz. rjnjhsq dtltn r ckexfqyjve vyj;tcnde S = {1, 2}.  Ðbc.7: Ãhfa, lkz rjnjhjuj bydthcysq PageRank yt ghtlcnfdkztn vfrcbvfkmysq j[dfn. Âj-dnjhs[, edtkbxtybt j[dfnf yt dctulf zdkztncz yfbkexitq cnhfntubtq. Ïhjbkk.cnhbhetv 'nj, hfcghjcnhfyzz gjrfpfntkm ljdthbz gjchtlcndjv hfpltktybz, ,tp extnf rfrb[-kb,j tuj cjrhfotybq. Âjpdhfofzcm r Ðbc.7, ds,bhftv cnhfybwe 2 rfr ckexfqye., jyf jrfpsdftncz [jhjitq. Çfntv cnhfybws 4, 5 b 6, rf;lfz gjkexftn gjrfpfntkm 1/3. Ïhtlgjkj;bv, xnj ckexfqyj ds,hfyyfz cnhfybwf 3 nfr;t ,eltn [jhjitq. Ñnhfybwf 7 gjkexftn gjrfpfntkm 1. Â pfdbcbvjcnb jn rjytxyjq wtkb, ghtlgjxnbntkmysv vj;tn ,snm bcgjkmpjdfybt cnhfybws 3, n.r. vj;yj njxyj ghtlgjkj;bnm rfrbt cnhfybws jyf jghtltkbn, ytcvjnhz yf nj, xnj b[ vj;tn ,snm ytvyjuj. Îlyfrj tckb bcgjkmpjdfnm gjrfpfntkm ljdthbz kbim lkz chfdytybz c lheubv gjrfpfntktv, cktletn hfccvjnhtnm ,jkmitt rjkbxtcndj cnhfybw gecnm c vtymitq njxyjcnm.. 5.2. Âscjrbq PageRank Äjgecnbv, xnj cntgtym bltynbabrfwbb cnhfybw, rfr [jhjib[ bkb gkj[b[, ,eltn jlbyfrjdjq lkz dct[ dt,-cnhfybw. Ájktt df;ysv vj;tn jrfpfnmcz ljrfpfntkmcndj njuj, xnj cnhfybwf, bvt.ofz dscjre. jwtyre chtlb htpekmnfnjd gjbcrf, ltqcndbntkmyj zdkztncz [jhjitq. Ífghbvth, rjyntyns cnhfybw p, q, r b s fltrdfnyj b d hfdyjq cntgtyb jndtxf.n ddtltyyjve pfghjce. Åckb gjbcrjdfz cbcntvf bcgjkmpetn PageRank lkz egjhzljxbdfybz htpekmnfnjd, nj cnhfybwf c cfvsv dscjrbv PageRank yfghbvth, p, ,eltn ghtlcnfdktyf gthdjq, pfntv cnhfybwf c vtymibv PageRank – q b n.l. d gjhzlrt e,sdfybz. Âthjznytt, xnj gjkmpjdfntkz pfbynthtce.n cnhfybws p b q, f yt r b s, gj'njve d gthde. jxthtlm ytj,[jlbvj jghtltkbnm gjrfpfntkm ljdthbz lkz cnhfybw p b q. Ífghbvth, tckb cnhfybwf p jrf;tncz cgfvthcrjq, nj gjkmpjdfntkm vj;tn djcgjkmpjdfnmcz cnhfybwtq q. Òfrbv j,hfpjv, dnjhjt gjlndth;ltybt 'dhbcnbxyjcnb PageRank d ds,jht ckexfqyjuj yf,jhf cnhfybw pfcnfdbn jnlfnm ghtlgjxntybt cnhfybwfv c dscjrbv PageRank, nfr rfr nfrbt cnhfybws erf;en yf ljcnjqyst b[ cnhfybws. Ñktljdfntkmyj, vj;yj ,eltn jghtltkbnm cjjndtncnde.obt gjrfpfntkb ljdthbz cnhfybw, pfybvf.ob[ gthdst cnhjrb d htpekmnfnf[ gjbcrf. Âs,jh ckexfqys[ cnhfybw cjukfcyj PageRank ghtljcnfdbn djpvj;yjcnm jghtltkbnm, yfcrjkmrj gjl[jlzotq zdkztncz cnhfybwf (gj chfdytyb. c bydthcysv PageRank). Íj 'nb cnhfybws gjnht,e.n ,jktt nofntkmyjuj hfccvjnhtybz. 6. ÝÊÑÏÅÐÈÌÅÍÒÛ
6.1. Êjvgktrn lfyys[ Ñ wtkm. dsxbcktybz fkujhbnvjd ,skb ghjdtltys 'rcgthbvtyns (fduecn 2003) c bcgjkmpjdfybtv gjkyjuj vyj;tcndf cnhfybw, yfqltyys[ b ghjbyltrcbhjdfyys[ gjbcrjdjq cbcntvjq Alta Vista. Äkz lfyys[ dsxbcktybq, jlby bp fdnjhjd 'njq hf,jns csuhfk hjkm jhfrekf, bccktlez cnhfybws hfpkbxys[ cfqnjd, ghjdthzz b[ yf cgfv b ghtlkfufz ljgjkybntkmye. rkfccbabrfwb., rjnjhfz ,eltn ghtlcnfdktyf lfktt. Íj bcgjkmpjdfybt fkujhbnvf jwtyrb fdnjhf, vj;tn cnfnm ghbxbyjq ytj,]trnbdys[ htpekmnfnjd. Ðexyjt dsxbcktybt gjrfpfntkz ljdthbz pfyzkj ytltkb: ghjdthrf cfqnf cjcnjzkf bp ghjcvjnhf ,jkmituj rjkbxtcndf cnhfybw c wtkm. dszdktybz yfvthtybz j,vfyenm gjbcrjde. cbcntve. Ñktle.otq nhelyjdsgjkybvjq pflfxtq ,skj yfqnb cgtwbfkbcnjd d j,kfcnb gjbcrjds[ cbcntv, rjnjhst cvjukb ,s dsgjkybnm lfyyjt pflfybt. Âvtcnj 'njuj, fdnjh yf,k.lfk pf hf,jnjq cgtwbfkbcnjd, bpexfz nt[ybre jghtltktybz cgfvthcrb[ cfqnjd. Â lfkmytqitv, bv ,skb ghtlghbyzns gjgsnrb bcgjkmpjdfybz lfyys[ vtnjljd c gjcktle.obv ghtlcnfdktybtv vfrcbvfkmyj j,]trnbdys[ htpekmnfnjd. 6.2. Ìyj;tcndj ckexfqyj ds,hfyys[ cnhfybw Ïthdsq 'nfg ,sk ghtlcnfdkty 'rcgthbvtynfvb gj chfdytyb. bydthcyjuj PageRank b dscjrjuj PageRank (Ðfpltk 5.1 b 5.2). Äkz crjhtqituj ghtlcnfdktybz htpekmnfnjd, lkz ghjdtltybz 'rcgthbvtynjd ,skb bcgjkmpjdfys rjvgktrcyst dt,-uhfas, ghtlcnfdkz.obt jcyjdyst [fhfrnthbcnbrb ctntdjuj cgfvf. Ïhbybvfz dj dybvfybt juhfybxtybz d j,]tvt cnfnmb, jgbcfybt 'rcgthbvtynjd yt ,eltn ghtlcnfdktyj gjkyjcnm.. Ñktletn jnvtnbnm kbim nj, xnj bcgjkmpjdfybt bydthcyjuj PageRank lkz jghtltktybz vyj;tcndf ckexfqyj ds,hfyys[ cnhfybw, ghtlcnfdkztncz kexibv. Ïj'njve, dct lfkmytqibt 'rcgthbvtyns ,elen ghjdtltys c bcgjkmpjdfybtv lfyyjuj vtnjlf.Ìtnjl bydthcyjuj PageRank gjpdjkbk dscnhjbnm dtcm ghjwtcc nfrbv j,hfpjv, xnj,s lfnm ghfdbkmye. jwtyre ghjuyjpbhjdfybz. Â gthde. jxthtlm ,skb ghtlcnfdktys gjkyst dsxbcktybz bydthcyjuj PageRank c gjvjom. dt,-uhfaf yf ehjdyt cfqnjd, cj cktle.obvb gfhfvtnhfvb αI = 0,85 b ÌI = 20. (Êj'aabwbtyn pfne[fybz, hfdysq 0,85, dgthdst ,sk pfzdkty d b c nt[ gjh cxbnftncz cnfylfhnyjq dtkbxbyjq d PageRank kbnthfneht. Òtcns gjrfpsdf.n, xnj 20 bnthfwbq ,skj ljcnfnjxyj, xnj,s ljcnbuyenm rjydthutywbb yf jnyjcbntkmyjq egjhzljxtyyjcnb cfqnjd.) Ïjckt egjhzljxbdfybz cfqnjd yf jcyjdfybb pyfxtybz b[ bydthcyjuj PageRank (ifu(2) yf Ðbc.5), jcyjdyjt dybvfybt ,skj eltktyj gthdsv 25 000. Âvtcnj gjkyjuj dsxbcktybz ghjuyjpf lkz lfyys[ cfqnjd, cyfxfkf ,skf ghjbpdtltyf ,tukfz jwtyrf, lkz elfktybz ytrjnjhst cjvybntkmys[ cfqnjd. Â xfcnyjcnb, ,skj pfvtxtyj, xnj cfqns c dscjrbv gjrfpfntktv bydthcyjuj PageRank ltvjycnhbhe.n ,jkmie. ghtlhfcgjkj;tyyjcnm r cgfve, ukfdysv j,hfpjv bp-pf rkjyjd jnrhsns[ rfnfkjujd: ytrjnjhst cgfvths ltkf.n njxyst rjgbb dctuj rjyntynf jnrhsnjuj rfnfkjuf DMOZ, d yflt;lt ekexibnm jcyjdyst gjrfpfntkb bkb c yfvthtybtv cjplfnm «Honeypot», j rjnjhs[ ikf htxm d hfpltkt 3.1. ×nj,s ,scnhj bp,fdbnmcz jn cgfvf, bp cgbcrf 25 000 cfqnjd ,skb elfktys nt, rjnjhst yt pyfxbkbcm d rhegytqib[ dt,-rfnfkjuf[, cjrhfnbd gthdjyfxfkmysq yf,jh lj 7 900 cfqnjd. Âs,jhjxyfz ghjdthrf jnabkmnhjdfyys[ cfqnjd gjrfpfkf, xnj ,skb elfktys ytrjnjhst [jhjibt cfqns. Ðbc. 8: Äbfuhfvvf ghbvthyjq jwtyrb cfqnjd. Èp jcnfdib[cz 7 900 cfqnjd, jwtyrt ,skb gjldthuyens gthdst 1 250 (vyj;tcndj ckexfqyj ds,hfyys[ cfqnjd S), bp rjnjhs[ gjl[jlzobvb ,skb ghbpyfyys 178. Äfyysq ghjwtcc ghtlcnfdkty yf Ðbc.5, ifu (3). Înyjcbntkmyj yt,jkmijt rjkbxtcndj cfqnjd, cjcnfdkz.ob[ ckexfqyjt vyj;tcndj S+, cnfkj htpekmnfnjv ;tcnrjuj rhbnthbz jn,jhf: cfqns yt njkmrj ghjdthzkbcm yf cgfvthcrbt, gj jnyjityb. r ybv, nfr;t, ,sk bcgjkmpjdfy dnjhjq abkmnh. Â cjjndtncndbb c ybv, jn,bhfkbcm cfqns njkmrj c xtnrj hfcgjpyfdftvsv dkfltkmwtv (nfrbt rfr ghfdbntkmcndtyyst bkb j,hfpjdfntkmysq exht;ltybz b rjvgfybb), jceotcndkz.obv rjynhjkm pf rjyntynjv cfqnf. Äjgjkybntkmysq abkmnh ufhfynbhjdfk ghjljk;bntkmye. b rfxtcndtyye. hf,jne ckexfqyj ds,hfyyjuj vyj;tcndf cfqnjd. 6.3. Ïhbvthyfz jwtyrf ×nj,s jghtltkbnm gjrfpfntkb, ghtlcnfdktyyst d Ðfpltkt 3.2, ytj,[jlbvj vyj;tcndj χ cfqnjd c bpdtcnysvb gjrfpfntkzvb ghjuyjpbhjdfybz. Áskj ds,hfyj 1000 cfqnjd, lfyyjt rjkbxtcndj cvj;tn ghtljcnfdbnm ye;yst lfyyst b d ljcnfnjxyj rjhjnrbq chjr. Áskj htityj yt ds,bhfnm cfqns ckexfqyj. Ò.r. vyjubt cfqns vjukb jrfpfnmcz yt,jkmibvb, cjlth;fnm kbim ytcrjkmrj cnhfybw b/bkb bvtnm jxtym ybprbq PageRank. Èpdtcnyj, xnj yt,jkmibt cfqns b cfqns c ybprbv PageRank cktle.n hfcghtltktyb. gj cntgtyyjq pfdbcbvjcnb, pfxfcne. jrfpsdfzcm jlybvb bp gjcktlyb[. Â cjjndtncndbb c hfpltkjv 5.2, ,jktt df;ysv ghtlcnfdkztncz jghtltktybt cgfvf yf cfqnf[ c dscjrbv PageRank, n.r. bvtyyj jyb xfot lheub[ abuehbhe.n d htpekmnfnf[ pfghjcf. Ê njve ;t, ghtlcnfdbnm njxye. jwtyre yt,jkmijve cfqne ckj;ytt bp-pf ytljcnfnrf lfyys[ j ytv.×nj,s j,tcgtxbnm htghtptynfnbdyjcnm, ,sk bcgjkmpjdfy cktle.obq vtnjl. Ñfqns ,skb hfcgjkj;tys d e,sdf.obv gjhzlrt, cjukfcyj pyfxtyb. b[ PageRank, dtcm cgbcjr ,sk hfpltkty yf 20 ,kjrjd, rf;lsq bp rjnjhs[ drk.xfk hfpyjt rjkbxtcndj cfqnjd, yj c gjrfpfntkzv PageRank d cevvt hfdyjv 5%, jn j,otuj gjrfpfntkz PageRank. Òfrbv j,hfpjv gthdsq ,kjr drk.xfk 86 cfqnjd c cfvsvb dscjrbvb gjrfpfntkzvb, dj dnjhjv ,kjrt ,skj 665, njulf rfr 20-sq cjcnjzk bp 5 vky. cfqnjd c cfvsvb ybprbvb gjrfpfntkzvb. Ïhbvthysq yf,jh bp 1000 cfqnjd ,sk cjcnfdkty gentv ckexfqyjq ds,jhrb bp rf;ljuj ,kjrf. Äfktt ,skf ghjdtltyf gjdthrf cfqnjd c wtkm. jghtltktybz cgfvthcrb[. Ðtpekmnfns ghtlcnfdktys yf Ðbc.8 – lbfuhfvvf, ghtlcnfdkz.ofz hfpkbxyst dbls cfqnjd. Òfrbv j,hfpjv, ,skj jghtltktyj, xnj kbim 748 cfqnjd ,elen bcgjkmpjdfys lkz jghtltktybz gjrfpfntkz TrustRank.
Ýnb 748 cfqnjd j,hfpe.n vyj;tcndj χ. Îcnfdibtcz 252 ,skb ghbpyfys yt ghbujlysvb lkz lfkmytqib[ dsxbcktybq gj hfpysv ghbxbyfv:
6.4. Ðtpekmnfns  Ðfpltkt 4 ,skb jgbcfys cgjcj,s gthtlfxb gjrfpfntkz ljdthbz lkz vyj;tcndf ckexfqyj ds,hfyys[ cnhfybw.  'njv hfpltkt ,elen hfccvjnhtys nhb fkmnthyfnbdys[ dfhbfynf TrustRank b ldt jcyjdyst cnhfntubb, b jwtytyf b[ 'aatrnbdyjcnm c gjvjom. ds,jhrb χ:
 Ðbc. 9: Õjhjibt cfqns d ,kjrf[ PageRank b TrustRank.  Ðbc.10: Ïkj[bt cfqns d ,kjrf[ PageRank b TrustRank. 6.4.1. PageRank ghjnbd TrustRank  gthde. jxthtlm cktletn ghtlcnfdbnm hfpybwe vt;le PageRank b TrustRank. Àkujhbnv PageRank yt exbnsdftn rfxtcndj cfqnf, f djpvj;yst yfrfpfybz cfqnf pf yt rfxtcndtyyjcnm njxyj yt jghtltktys. Íthtlrj cfqns, cjplfyyst evtksvb cgfvthfvb, gjkexf.n dscjrbq gjrfpfntkm PageRank. Òjulf rfr TrustRank ghbpdfy hfpkbxfnm [jhjibt b gkj[bt cfqns: 'nj lftn yflt;le yf nj, xnj cgfvthcrbt cfqns yt gjkexfn dscjrb[ gjrfpfntktq. Íf hbc.9 b hbc.10 ghtlcnfdktyj chfdytybt PageRank b TrustRank c extnjv gkj[b[ b [jhjib[ cfqnjd d rf;ljv ,kjrt. Ákjrb PageRank ,skb ghtlcnfdktys d hfpltkt 6.3; ,skj jghtltktyj, xnj ,kjrb TrustRank drk.xf.n nfrjt ;t xbckj cfqnjd, xnj b ,kjrb PageRank. Ákjrb c 17 gj 20 ,skb j,]tlbytys b lkz PageRank, b lkz TrustRank. (Ýnb gjcktlybt 4 ,kjrf drk.xf.n ,jktt xtv 13 vky. cfqnjd, yt bvt.ob[ ccskjr. Âct nfrbt cfqns gjkexbkb vbybvfkmysq cnfnbxtcrbq gjrfpfntkm PageRank b gjrfpfntkm yektdjuj TrustRank, ghtljcnfdkzz djpvj;yjcnm egjhzljxbnm b[). Ãjhbpjynfkmyst jcb yf hbc.9 b 10 jnvtxf.n xbckj ,kjrjd PageRank b TrustRank. Âthnbrfkmyst jcb yf gthdjv hbceyrt cjjndtncnde.n ghjwtynyjve cjjnyjityb. [jhjib[ cfqnjd d rf;ljv ,kjrt, xbckj [jhjib[ cfqnjd ltktyyjt yf j,ott xbckj cfqnjd d ,kjrt. Ðbc.11: Ïjyb;tybt gjrfpfntkz TrustRank d ,kjrf[. Ñktletn gjvybnm, xnj ljcnjqyst cfqns, cfqns dt,-cbcntv, htrkfvf hfccvfnhbdf.ncz rfr [jhjibt; jnyjcbntkmyjt edtkbxtybt jnvtxtyf ,tksv, cdtnkj-cthsv b ntvyj-cthsv cjjndtncndtyyj. Âthnbrfkmyst jcb dnjhjuj hbceyrf cjjndtncnde.n ghjwtynyjve cjjnyjityb. gkj[b[ cfqnjd d jghtltktyyjv ,kjrt. Ífghbvth, cjukfcyj hbc.10, 31% ghbtvktvs[ cfqnjd d ,kjrt TrustRank zdkztncz gkj[bv. Íf lfyyjv hbceyrt dblyj, xnj TrustRank zdkztncz ghbtvktvsv chtlcndjv lkz dszdktybz cgfvf. Çfvtnmnt, xnj d gthds[ gznb ,kjrf[ TrustRank ytn cgfvf, njulf rfr d ,kjrf[, hfcgjkj;tyys[ yb;t jnvtxtyj dscjrjt cjlth;fybt cgfvf.  nj ;t dhtvz, elbdbntkmyj, xnj dnjhjq ,kjr PageRank gjxnb yf 20% cxbnftncz gkj[bv. Äkz PageRank, cjjnyjitybt gkj[b[ cfqnjd ljcnbukj htrjhlyjuj ehjdyz d ,kjrf[ 9 b 10 (50% cgfvf). Ðbc.11 ghtlkfuftn lheujq dpukzl yf jnyjitybz PageRank b TrustRank. Çltcm ddjlbncz gjyznbt gjyb;tybt(demotion), zdktybt, rjulf cfqn bp ,kjrf c ,jktt dscjrbv PageRank, gjzdkztncz d ,kjrt c ,jktt ybprbv TrustRank. Înhbwfntkmyjt gjyb;tybt 'nj gjdsitybt(promotion), ghtlgjkfuf.ott j,hfnysq gjhzljr ltqcndbq: cfqn bp ,kjrf c ybprbv PageRank gjzdkztncz d ,kjrt c ,jktt dscjrbv TrustRank. Ñhtlytt gjyb;tybt gkj[b[ cfqnjd – df;ysq 'ktvtyn dsxbcktybz TrustRank. Ãjhbpjynfkmyst jcb yf hbc.11 cjjndtncnde.n ,kjrfv PageRank. Âthnbrfkmyst j,jpyfxf.n rjkbxtcndj ,kjrjd, cfqns rjnjhs[ bp PageRank gthtvtofkbcm (gjyb;fkbcm) d TrustRank. Átksq wdtn cjjndtncndetn ljcnjqysv cfqnfv, xthysq – cgfve. Íf hbc.11 dblyj, xnj chtlb cfqnjd, pfybvf.ob[ dscjrbt gjpbwbb, ytn cgfvf, 'nj cdbltntkmcndetn j 'aatrnbdyjcnb TrustRank. Äfyysq gjrfpfntkm ltvjycnhbhetn b nj, xnj [jhjibt cfqns, d ,jkmibycndt ckexftd, jcnfdfkbcm d njv ;t ,kjrt, relf gjgfkb bpyfxfkmyj. Ñktljdfntkmyj, vj;yj rjycnfnbhjdfnm, xnj TrustRank (d jnkbxbt PageRank), ufhfynbhetn, xnj gthdst gjpbwbb ,elen pfybvfnm njkmrj [jhjibt cfqns. Ê cj;fktyb., bp-pf ytljcnfnrf byajhvfwbb (dyenhtyybt ccskrb) j cfqnt, TrustRank yt vj;tn jnkbxbnm [jhjibq cfqn c ybprbv gjrfpfntktv jn gkj[juj. Ðbc.12: Pairwise orderedness (gjgfhyfz egjhzljxtyyjcnm). 6.4.2. Pairwise orderedness (PO) Äfyyst PO, ghtlcnfdktyyst d hfpltkt 3.2, nfr;t bcgjkmpe.ncz lkz dsxbcktybz gjrfpfntkz TrustRank. Äkz ghjdtltybz 'njuj 'rcgthbvtynf ,sk cjcnfdktyj vyj;tcndj Ðtpekmnfns 'rcgthbvtynf gjrfpfys yf hbc.12. Ãjhbpjynfkmyst jcb erfpsdf.n xbckj cfqnjd, bcgjkmpjdfyys[ lkz hfcxtnf, njulf rfr dthnbrfkmyst jcb ghtlcnfdkz.n gjrfpfntkb PO lkz jghtltktyys[ cfqnjd. Ífghbvth, lkz 500 cfqnjd c dscjrbv PageRank, gjrfpfntkm PO lkz TrustRank ,eltn hfdty ghb,kbpbntkmyj 0,95. Íf hbc.12 nfr;t bpj,hf;tys gjrfpfntkb PO lkz aeyrwbb gecnjuj Trust b PageRank. Ñjdvtotybt vyj;tcnd ckexfqys[ ds,jhjr S b χ ghjbpjikj yf 5 [jhjib[ cfqnf[, jn aeyrwbb gecnjuj Trust'nb cfqns gjkexbkb gjrfpfntkb hfdyst ½. Ïjrfpfntkb PO lkz gecnjq aeyrwbb bcgjkmpe.ncz d njv ckexft, rjulf byajhvfwbb j rfxtcndt cfqnf vbybvfkmyf. Òfr;t b lkz PageRank, gjrfpfntkb PO erfpsdf.n, crjkmrj bvttncz ye;yjq byajhvfwbb lkz jghtltktybz rfxtcnd cfqnf. Èp lfyyjuj ghbvthf dblyj, xnj TrustRank ghtdjc[jlbn b gecne. aeyrwb. b PageRank. 6.4.3. Ïjrfpfntkb njxyjcnm (Precision) b djcghjbpdtltybt (Recall)Ïjcktlybt htpekmnfns 'rcgthbvtynf (hbc.13) ghtlcnfdkz.n jghtltktybt TrustRank c extnjv gjrfpfntktq Precision b Recall. Ïjuhfybxyst gjrfpfntkb TrustRank, jnltkz.obt 17 ,kjrjd TrustRank, bcgjkmpe.ncz rfr gjhjujdst pyfxtybz δ, j rjnjhs[ ujdjhbkjcm d hfpltkt 6.4.1. Ïjcktlybt ,kjrb, cjjndtncnde.obt rf;ljve gjhjujdjve pyfxtyb., ghtlcnfdktys yf ujhbpjynfkmys[ jcz[, yf dthnbrfkmys[ gjrfpfys gjrfpfntkb Precision b Recall.  Ðbc.13: Precision and recall. Ó [jhjib[ cfqnjd, cjukfcyj TrustRank, dscjrbt gjrfpfntkb, cjjndtncndtyyj, xtv yb;t gjrfpfntkm, ntvb [e;t cfqn. Òfrbv j,hfpjv, gjrfpfntkb Precision b Recall ltvjycnhbhe.n kbytqyjt gjyb;tybt b gjdsitybt. Î,hfnbnt dybvfybt yf dscjrbq gjrfpfntkm Precision (0,82) lkz dctuj ghbvthyjuj vyj;tcndf: gjlj,yjt pyfxtybt yt vj;tn ,snm j,obv lkz ghj,ktv nhflbwbjyyjuj gjbcrf byajhvfwbb, j,sxyj cjcnjzob[ bp ,jkmijuj j,]tvf ljrevtynjd, ult kbim xfcnm zdkztncz gjl[jlzotq jghtltktyyjve pfghjce.  jnkbxbt jn 'njuj, yfit ghbvthyjt vyj;tcndj cjcnjbn, ukfdysv j,hfpjv, bp [jhjib[ ljrevtynjd, dct bp rjnjhs[ gjl[jlzobt. Âjn gjxtve ,fpjdsq gjrfpfntkm Precision lkz vyj;tcndf χ nfrjq 613/(613+135) = 0,82. 7. Çfrk.xtybtÑ edtkbxtybtv hfpvthjd b pyfxtybz ctnb, hjkm gjbcrjds[ cbcntv cnfyjdbncz dct ,jktt pyfxbntkmyjq. Îlyfrj ctqxfc cthmtpyjq euhjpjq lkz gjbcrjds[ cbcntv cnfk ctntdjq cgfv, bp-pf rjnjhjuj e[eliftncz aeyrwbjybhjdfybt hfpkbxys[ cthdbcjd. Äkz ,jhm,s cj cgfvjv, gjbcrjdst cbcntvs bcgjkmpe.n hfpkbxyst vtnjls. Ïhjdtltyyjt d lfyyjq cnfnmt bccktljdfybt cnfkj jlyjq bp gjgsnjr ajhvfkbpjdfnm ghj,ktve b ghtlcnfdbnm tt rjvgktrcyjt htitybt. Ñjukfcyj htpekmnfnfv 'rcgthbvtynf, djpvj;yj njxyj jghtltkznm dscjrjrfxtcndtyyst [jhjibt cnhfybws, yt zdkz.obtcz cgfvjv. Ítcvjnhz yf ghjltkfyysq j,]tv hf,jns, geyrnjd, ljcnjqys[ ,jktt dybvfntkmyjuj hfccvjnhtybz, jcnfkjcm ljcnfnjxyj.  ljgjkytybt rj dctve dsitcrfpfyyjve, cktletn jnvtnbnm, xnj bcgjkmpjdfyyst vtnjls vjuen ,snm ekexitys. Ífghbvth, dvtcnj ds,jhf dctuj ckexfqyjuj vyj;tcndf chfpe, cktletn hfccvjnhtnm bcgjkmpjdfybt gjifujdjuj ghjwtccf. Ýnj vj;tn cnfnm ntvjq ,eleob[ bccktljdfybq.Î,hfnbnt dybvfybt, xnj ceotcndetn ytcrjkmrj 'rdbdfktynys[ jghtltktybq gjyznbz PageRank, rjnjhst vjuen ytceotcndtyyj jnkbxfnmcz vfntvfnbxtcrjq ajhvekbhjdrjq b xbckjdsvb pyfxtybzvb, yj ghtlcnfdkznm jnyjcbntkmyj jlbyfrjde. egjhzljxtyyjcnm vt;le levz dt,-cnhfybwfvb. Ïhj,ktvf jghtltktybz vbybvfkmyjuj yf,jhf cnhfybw, ghtlcnfdkz.ob[ vfrcbvfkmye. gjrhsdf.oe. cgjcj,yjcnm, gjlj,yf ghj,ktvt ytpfdbcbvjuj yf,jhf yf yfghfdktyyjv uhfat, rfr gjrfpfyj lfktt. Ât,- uhfas vjuen ,snm nhfycajhvbhjdfys d yfghfdktyyst uhfas ς" = (ν,ε"), ult ht,hj uhfaf (p,q) º ε" gjrfpsdftn, xnj yf cnhfybwe q vj;yj gjgfcnm cj cnhfybws p. Ñgjhyj, xnj nfrfz byajhvfwbz yt dytc¸n ybrfrb[ bpvtytybq d dtcm fkujhbnv, nfr rfr jy drk.xftn j,ibhysq gjbcr c gjkbyjvbyfkmysv dhtvtytv bcgjkytybz. Çfntv, yf[j;ltybt vbybvfkmyjuj vyj;tcndf j,tcgtxbdftn vfrcbvfkmysq j[dfn, rjnjhsq c[jlty c vfrcbvfkmysv ytpfdbcbvsv vyj;tcndjv lkz ς", rjnjhjt zdkztncz ghj,ktvjq NP-gjkyjns. Äjvtyyjt bvz– 'nj xfcnm URL, hfcgjkj;tyyfz vt;le ghtabrcjv http://, rjnjhsq yfpsdftncz c[tvf b gthdsv ck'ijv, rjnjhsq cktletn pf dscjrjehjdytdsv ljvtyjv, yfghbvth, .com bkb TCP yjvthjv gjhnf cthdthf. Ífghbvth, ljvtyyjt bvz URL http://www.romver.ru/my/index.php – 'nj www.romver.ru. www.vldb.orgÇjknfy Ãmtyub (Zoltan Gyongyi), Ãtrnjh Ãfhcbf-Ìjkbyf (Hector Garcia-Molina), ßy Ïtlthcty (Jan Pedersen)/Ïthtdjl gjl htl. Àyys Ìfrfhjdjq b Åktys Ïjgjdjq |
gfh cnhfybw (p,q), p ≠ q, pfntv dsxbckztncz, c rfrbvb gfhfvb cnhfybw aeyrwbz ljdthbz yt ljgecrftn jib,jr:
M p cdbltntkmcndetn j ceotcndjdfybb genb vfrcbvfkmyjq lkbys Ì cj cnhfybws q yf cnhfybwe p. Òfrjq genm yt ljk;ty cjlth;fnm «gkj[b[» cnhfybw.