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Ukuhlehla komugqa kungenye ye-algorithms eyisisekelo yezindawo eziningi ezihlobene nokuhlaziywa kwedatha. Isizathu salokhu sisobala. Lena i-algorithm elula kakhulu futhi eqondakalayo, eye yaba nomthelela ekusetshenzisweni kwayo kabanzi amashumi amaningi, uma kungengamakhulu eminyaka. Umqondo uwukuthi sithatha ukuncika komugqa kokuhlukile okukodwa kusethi yokunye okuguquguqukayo, bese sizama ukubuyisela lokhu kuncika.
Kodwa lesi sihloko asikona ukusebenzisa ukuhlehla komugqa ukuxazulula izinkinga ezingokoqobo. Lapha sizocubungula izici ezithakazelisayo zokusetshenziswa kwama-algorithms asabalalisiwe ukuze ilulame, esihlangabezane nayo lapho sibhala imojula yokufunda yomshini . Izibalo ezincane eziyisisekelo, ukufunda komshini, kanye nekhompuyutha esabalalisiwe kungakusiza ukuthi uthole ukuthi ungenza kanjani ukuhlehla komugqa nanoma idatha yakho isatshalaliswa ezinkulungwaneni zamanodi.
Sikhuluma ngani?
Sibhekene nomsebenzi wokubuyisela ukuncika komugqa. Njengedatha yokufaka, isethi yamavektha ezinto eziguquguqukayo okuthiwa zizimele zinikezwa, ngayinye yazo ehlotshaniswa nenani elithile lokuhluka okuncikile. Le datha ingamelwa ngendlela yamatrices amabili:
Manje, njengoba ukuncika kucatshangwa, futhi, ngaphezu kwalokho, okuqondile, sizobhala ukucabanga kwethu ngendlela yomkhiqizo wamatrices (ukwenza kube lula ukurekhoda, lapha nangaphansi kucatshangwa ukuthi isikhathi samahhala se-equation sifihliwe ngemuva. , kanye nekholomu yokugcina ye-matrix iqukethe amayunithi):
Kuzwakala kufana nesistimu yezibalo zomugqa, akunjalo? Kubonakala sengathi, kodwa cishe ngeke kube nezixazululo ohlelweni olunjalo lwezibalo. Isizathu salokhu umsindo, okhona cishe kunoma iyiphi idatha yangempela. Esinye isizathu kungase kube ukuntuleka kokuncika komugqa kanjalo, okunganqandwa ngokwethula okuguquguqukayo okwengeziwe okuncike ngokungaqondile kokwangempela. Cabangela isibonelo esilandelayo:
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Lesi isibonelo esilula sokuhlehla komugqa esibonisa ubudlelwano bokuguquguquka okukodwa (kuhambisana ne-eksisi ) kokunye okuguquguqukayo (kuhambisana ne-eksisi ). Ukuze uhlelo lwezibalo zomugqa oluhambisana nalesi sibonelo lube nesixazululo, wonke amaphuzu kufanele alale ncamashi emugqeni ofanayo oqondile. Kodwa lokho akulona iqiniso. Kodwa awaqambi amanga emugqeni ofanayo oqondile ngenxa yomsindo (noma ngenxa yokuthi ukuqagela kobudlelwano bomugqa bekunephutha). Ngakho-ke, ukuze ubuyisele ubudlelwano bomugqa kusuka kudatha yangempela, ngokuvamile kuyadingeka ukwethula omunye umcabango: idatha yokufaka iqukethe umsindo futhi lo msindo . Ungenza ukucabangela mayelana nezinye izinhlobo zokusabalalisa umsindo, kodwa ezimweni eziningi ukusabalalisa okuvamile okucatshangelwayo, okuzoxoxwa ngakho.
Indlela enkulu yokuba nokwenzeka
Ngakho-ke, sicabangele ukuba khona komsindo osakazwa ngokungahleliwe. Yini okufanele uyenze esimweni esinjalo? Kulokhu kwizibalo kukhona futhi isetshenziswa kabanzi . Kafushane, ingqikithi yayo ilele ekukhetheni kanye nokukhulisa kwayo okwalandela.
Sibuyela ekubuyiseleni ubudlelwano bomugqa kusuka kudatha enomsindo ojwayelekile. Qaphela ukuthi ubudlelwano bomugqa ocatshangwayo buwukulindela kwezibalo ukusatshalaliswa okujwayelekile okukhona. Ngesikhathi esifanayo, amathuba okuthi ithatha inani elilodwa noma elinye, kuncike ekubeni khona kwezinto ezibonakalayo , Ngokulandelayo:
Manje ake sishintshe esikhundleni ΠΈ Okuguquguqukayo esikudingayo yilawa:
Okusele ukuthola i-vector , lapho la mathuba aphezulu khona. Ukwandisa umsebenzi onjalo, kulula ukuthatha i-logarithm yayo kuqala (i-logarithm yomsebenzi izofinyelela ubuningi endaweni efanayo nomsebenzi ngokwawo):
Okuyikhona, okufika phansi ekunciphiseni umsebenzi olandelayo:
Ngendlela, lokhu kubizwa ngokuthi indlela . Ngokuvamile konke okucatshangelwayo okungenhla kuyashiywa futhi le ndlela imane isetshenziswe.
Ukwahlukaniswa kwe-QR
Ubuncane bomsebenzi ongenhla bungatholwa ngokuthola iphoyinti lapho ukugreda kwalo msebenzi kunguziro. Futhi i-gradient izobhalwa kanje:
iyindlela ye-matrix yokuxazulula inkinga yokunciphisa esetshenziswa endleleni yezikwele ezincane. Mayelana nalokhu, sibhala kabusha isibalo ngendlela ye-matrix:
Ngakho sibolisa i-matrix kumatikuletsheni ΠΈ futhi wenze uchungechunge lwezinguquko (i-algorithm yokuwohloka kwe-QR ngokwayo ngeke icatshangelwe lapha, ukusetshenziswa kwayo kuphela maqondana nomsebenzi owenziwayo):
Matrix i-orthogonal. Lokhu kusivumela ukuthi sisuse umsebenzi :
Futhi uma esikhundleni on , khona-ke kuzolunga . Uma ucabangela lokho iyi-matrix engunxantathu ephezulu, ibonakala kanje:
Lokhu kungaxazululwa ngokusebenzisa indlela yokufaka esikhundleni. Isici itholakala njenge , isici sangaphambilini itholakala njenge nokunye.
Kuyaphawuleka lapha ukuthi inkimbinkimbi ye-algorithm ewumphumela ngenxa yokusetshenziswa kokubola kwe-QR ilingana . Ngaphezu kwalokho, naphezu kweqiniso lokuthi ukusebenza kokuphindaphinda kwe-matrix kuhambisana kahle, akunakwenzeka ukubhala inguqulo ephumelelayo esabalalisiwe yale algorithm.
Ukwehla kweGradient
Uma ukhuluma ngokunciphisa umsebenzi, kufanelekile ukukhumbula indlela yokwehla kwe-gradient (stochastic). Lena indlela elula nesebenzayo yokunciphisa esekelwe ekubaleni ngokuphindaphindiwe ukuthambekela komsebenzi endaweni ethile bese uwususa uqonde endaweni ephambene negradient. Isinyathelo ngasinye esinjalo siletha ikhambi eduze kokuncane. I-gradient isabukeka ifana:
Le ndlela iphinde ifaniswe kahle futhi isatshalaliswe ngenxa yezakhiwo zomugqa zomqhubi we-gradient. Qaphela ukuthi kule fomula engenhla, ngaphansi kophawu lwesamba kukhona imigomo ezimele. Ngamanye amazwi, singakwazi ukubala i-gradient ngokuzimela kuzo zonke izinkomba kusukela ekuqaleni kuya , ngokuhambisana nalokhu, bala ukuthambekela kwezinkomba nge ukuze . Bese wengeza ama-gradients avelayo. Umphumela wokwengeza uzofana nokuthi sibale ngokushesha i-gradient yezinkomba ukusuka kweyokuqala ukuya . Ngakho, uma idatha isatshalaliswa phakathi kwezingcezu ezimbalwa zedatha, i-gradient ingabalwa ngokuzimela esiqeshini ngasinye, bese imiphumela yalezi zibalo ingafingqwa ukuze kutholwe umphumela wokugcina:
Ngokombono wokusebenzisa, lokhu kuhambisana nepharadigm . Esinyathelweni ngasinye sokwehla kwegradient, umsebenzi uthunyelwa endaweni ngayinye yedatha ukuze kubalwe ukuthambeka, bese amagradient abaliwe aqoqwa ndawonye, ββbese umphumela wesamba sawo usetshenziselwa ukuthuthukisa umphumela.
Ngaphandle kokusebenziseka kalula kanye nekhono lokuqalisa ku-paradigm ye-MapReduce, ukwehla kwe-gradient nakho kunezihibe zako. Ikakhulukazi, inani lezinyathelo ezidingekayo ukuze kufinyelelwe ekuhlanganeni liphezulu kakhulu uma liqhathaniswa nezinye izindlela ezikhethekile.
I-LSQR
kungenye indlela yokuxazulula inkinga, efanele kokubili ukubuyisela ukuhlehla komugqa kanye nokuxazulula amasistimu wezibalo zomugqa. Isici sayo esiyinhloko ukuthi sihlanganisa izinzuzo zezindlela ze-matrix kanye nendlela yokuphindaphinda. Ukusetshenziswa kwale ndlela kungatholakala kuyo yomibili imitapo yolwazi , futhi . Incazelo yale ndlela ngeke inikezwe lapha (itholakala esihlokweni ). Esikhundleni salokho, kuzoboniswa indlela yokuvumelanisa i-LSQR ukuze isetshenziswe endaweni esabalalisiwe.
Indlela ye-LSQR isuselwe ku . Lena inqubo ephindaphindayo, ukuphindaphinda ngakunye okuhlanganisa izinyathelo ezilandelayo:
Kodwa uma sicabanga ukuthi matrix ihlukaniswe ngokuvundlile, bese ukuphindaphinda ngakunye kungamelwa njengezinyathelo ezimbili Zokunciphisa Imephu. Ngale ndlela, kungenzeka ukunciphisa ukudluliswa kwedatha ngesikhathi sokuphindaphinda ngakunye (kuphela ama-vector anobude obulingana nenani lokungaziwa):
Yile ndlela esetshenziswayo uma kusetshenziswa ukuhlehla komugqa ku .
isiphetho
Kunama-algorithms amaningi wokubuyisela ukuhlehla komugqa, kodwa akuwona wonke angasetshenziswa kuzo zonke izimo. Ngakho-ke ukubola kwe-QR kuhle kakhulu ngesixazululo esinembile kumasethi amancane wedatha. Ukwehla kwe-Gradient kulula ukuyisebenzisa futhi kukuvumela ukuthi uthole ngokushesha isixazululo esiseduze. Futhi i-LSQR ihlanganisa izakhiwo ezinhle kakhulu zama-algorithms amabili adlule, njengoba ingasatshalaliswa, ihlangana ngokushesha uma iqhathaniswa nokwehla kwe-gradient, futhi ivumela nokumiswa kwangaphambi kwesikhathi kwe-algorithm, ngokungafani nokubola kwe-QR, ukuthola isisombululo esiseduze.
Source: www.habr.com