mahitee adthala paddhat

mahitee adthala paddhat heey naftali tishby, fernando see yanni sadar kelele mahitee siddhantatil eka tantra aahe. pereira aanee william biyalek. saransh detana achookata aanee guntagunt (sampidan) yanchyatil sarvottam vinimay shodhanyasathi tyachi rachana kelee gelee aahe (udaa.jee. clustering) eka yadruchchik chull x, jeey x aanee nirikshan kelelya sambandhit chull y darmyan sanyukt sambhavyata vitaran p (x, y) dile jaate-aanee "signal processing aanee shikanyachya vividh samasyanvar charcha karnyasathi eka aashcharyakarak samruddha chaukat" pradan karate asey swayam-varnan kele jaate.
anuprayoganmadhye vitaranatmak samooh aanee pariman qamee karane samavisht aahe aanee agadi alikade too sakhol shikshanasathi saiddhantik paya mhanoon suchavala gela aahe. tyane parimaniy aakadevaripasun teey aniyantrit vitaranaparyantchya kiman puresha aakadevarichya shastriy kalpaneche samanyikaran kele, ghatankiy swarupachi nahee. paraspar mahiticha kahee bhag sambandhit chull y saha midvinyasathi pureshi aut shithil karoon teey asey karate.
mahititil adthalyakade darr vikrutee samasya mhanoon dekhil pahile jaau shakate, jyamadhye vikrutee karya asate jeey x pasoon tyachya thet andajachya tulanet sankuchit pratinidhitva t pasoon y chaa andaj kitee changla aahe heey mojate. haah arth lavane mahitichya adthalyache nirakaran karnyasathi aanee vitaran pii (ex, vaay) madhoon mahitichya vakratechi ganana karnyasathi eka samanya punaravrutti algoridam pradan karate.
sankuchit pratinidhitva yadruchchik chull sootra _ 1 dware dile jaau dya. algoridam sashart vitaran sootra _ 2 chya sandarbhat khaleel karyatmakata qamee karateh
jethe sootra _ 4 aanee sootra _ 5 hii sootra _ 6 aanee sootra _ 1 chee paraspar mahitee aahe aanee sootra _ 1 aanee sootra _ 9 chee anukrame mahitee aahe aanee sootra _ 10 haah eka lagrange gunak aahe.
sakhol shikshanasathi shikanyacha siddhant.
heey ganitiyadrushtya siddha jhaale aahe qee mahitichya adthalyanvar niyantran thevane haah sakhol shikshanatil samanyikaran truti niyantrit karnyacha eka marg aahe. mhanjech, samanyikaran truti sootra 11 mhanoon pramanit kelee jaate, jethe sootra 12 hii prashikshan namunyanchi sankhya aahe, sootra 6 heey sakhol majjatantu jaalyasathiche input aahe aanee sootra 1 heey lapalelya tharache output aahe. heey samanyikaran baddh praman mahitichya adthalyachya pramanasah, itar samanyikaran maryadanpeksha vegale aahe jeey mapdandanchi sankhya, vhee. see. pariman, redmaker jatilata, sthirata kinwa drudhatesah mojale jaate.
sakhol shikshanacha mahitee siddhant.
mahitichya adthalyacha siddhant alikadech deep neural networkcha (dii. aine. aine.) abhyas karnyasathi vaparla jaato.
sootra _ 15 aanee sootra _ 16 heey anukrame dii. aine. aine. chey input aanee output thurr mhanoon vicharat ghya aanee sootra _ 17 haah jaalyacha konatahi lapalela thurr asoo dya. 
schwartz-zive aanee tishby yanni paraspar mahitee mapan sootra _ 18 aanee sootra _ 19 yanchyatil paraspar vinimay vyakt karnari mahitee adthala prastavit kelee. yaa prakaranat, sootra _ 18 aanee sootra _ 21 anukrame lapalelya tharamadhye input aanee outputbaddal asalelya mahitichya pramanache praman tharavatat.
tyanni assa andaj lavala qee dii. aine. aine. chya prashikshan prakriyet done vegvegale tappe asatat; 1) prarambhik fitting tappa jyamadhye sootra _ 19 vadhate aanee 2) tyanantarcha sampidan tappa jyamadhye sootra _ 18 qamee hote. sacks aanee itar. schwartz-zive aanee tishbeechya davyacha pratikar kartana, dii. aine. aine. madheel hii sampidan ghatana sarvasamaveshak nahee aanee tee vishisht sakriyakaran karyavar avalambun aahe asey namood kele. visheshtah, tyanni assa dawa keela qee rile sakriyan karyansah sankochan hott nahee. schwartz-zive aanee tishby yanni yaa davyanvar aakshep ghetala aanee assa yuktivad keela qee paraspar mahitichya kamkuvat andajanmule sacks aanee itaranni sankochan pahile navhate. alikade, noshad aanee itar. yaa vadacha shodh ghenyasathi paraspar mahitichya darr-ishtatam andajakacha vapar keela, heey nirikshan karat qee ishtatam hash-aadharit andajak heey rile aanee maxpooling sakriyatesah networkchya vistrut shrenimadhye sampidan ghatana prakat karato. dusarikade, alikade goldfeld aanee itar. nirikshan kelele sampidan heey bhaumitik parinam aahe, mahitee-saiddhantik ghatananche nahee, assa yuktivad keela aahe, jyaa drushtikonat dekhil samayik kele gele aahe.
gossian adthala.
gausian adthale mhanje, gausian chalanna mahitee adthala drushtikon lagoo kelyane, canonical sahsambandh vishleshanashi sambandhit upay hotat. asey gruheet dhara qee sootra _ 24 heey sanyuktapane bahuparivartan shoonya sarasari samanya vahak aahet, jyamadhye sahparivartan sootra _ 25 aahe aanee sootra _ 26 hii sootra _ 27 chee sankuchit aavrutti aahe, jee sootra _ 28 saha paraspar mahitiche dilele moolya rakhane aavashyak aahe. heey darshavile jaau shakate qee ishtatam sootra _ 26 heey eka samanya vahak aahe jyamadhye sootra _ 30 chya ghatakanchya resheey sanyojanancha samavesh aahe, jethe matricks sootra _ 31 madhye orthogonal pankti aahet. 
prakshepan matricks sootra _ 32 madhye pratyakshat matrixchya ekvachan moolya vighatan (samanyatah asamamiteey) chya bharit davya eigenvectorsmadhun nivadalelya sootra _ 33 pankti asatat.
ekvachan moolya vighatan paribhashit qaraa
aanee gambhir moolye
mug prakshepanatil sakriy igenvectors sootra _ 37, kinwa andajacha kram, asey dile jaateh
aanee shevati aamhala
jyamadhye vajan dile jaate
jethe sootra _ 41
velechya malikesathi (prakriya) gossian mahiticha adthala lagoo kelyane, ishtatam bhavishyasuchak kodingshi sambandhit upay midatat. hii prakriya aupcharikpane resheey santh vaishishtyanchya vishleshanachya samatulya aahe.
resheey gatishil pranalinmadhil ishtatam tatpuratya sanrachana tathakathit bhootkalatil bhavishyatil mahitichya adthalyat ughad kelya jaau shakatat, jee gair-gossian namunedar detavar adthalyachya paddhaticha vapar aahe. hii sankalpana, cretzig, tishby aanee itaranni hatalali aahe., heey guntaguntishivay nahee kaaran done swatantra tappe vyayamat tayar hotatah pratham adnyat mool sambhavyatechya ghanatecha andaj jyatoon detache namune kadhale jaatat aanee dusare mhanje adthalyachya mahitee saiddhantik chaukatit yaa ghanatecha vapar.
ghanatecha andaj.
adthalyachi paddhat sankhyikeey atinaivaji sambhavyatechya drushtine tayar kelee jaat asalyane, namuna bindu sootra _ 42 madheel antarnihit sambhavyatechi ghanata andajit kelee jaane aavashyak aahe. silvermanne varnan kelelya anek upayansah hii eka suprasiddha samasya aahe. sadhyachya paddhatimadhye, markov sankraman matricks paddhaticha vapar karoon sanyukt namuna sambhavyata aadhaltat aanee yaat adthale aananyachya paddhatishich kahee ganiteey samanvay aahe.
serve namuna jodya aanee antar matrixmadhil aniyantritpane vadhanare antar metrik sootra _ 43 heey sootra _ 44 aahe. mug kahee sutrasathi namuna jodyanmadhil sankraman sambhavyata sootra _ 45 mojali jaane aavashyak aahe. namune sthitee mhanoon aanee formula 47 chee samanyikrut aavrutti markov sthitee sankraman sambhavyata matricks mhanoon, formula 49 nantarchya 'avasthanchya' sambhavyatecha vector, prarambhik sthitee sootra 49 varr aut ghatali aahe, teey formula 50 aahe. samtol sambhavyata vector sootra 51, nehmipramane, matricks formula 47 chya pramukh eigenvectordware dile jaate, jeey prarambhik vector formula 49 pasoon swatantra aahe. hii markov sankraman paddhat namuna bindunvar sambhavyata sthapit karate jee tethil sambhavyatechya ghanatechya pramananusar asalyacha dawa keela jaato.
durastha matricks sootra _ 54 chya eigenvalueschya vaparachya itar vyakhyanchi charcha silvermanchya "sankhyiki aanee deta vishleshanasathi ghanata andaj" madhye kelee aahe.
samooh.
pudhil soft clustering udaharanamadhye, sandarbh vector sootra _ 55 madhye namuna shreni aahet aanee sanyukt sambhavyata sootra _ 56 dnyat aahe asey gruheet dharale jaate. soft cluster sootra _ 57 heey deta sample sootra _ 58. tishby aanee itaranvar tyachya sambhavyatechya vitaranadvare paribhashit kele jaate. samooh nishchit karnyasathi khaleel punaravrutti samikarane sadar kelee jee shevati darr vikrutee siddhantat vikasit kelelya blahoot-erimoto algoridamche samanyikaran aahe. neural networkmadhye yaa prakarchya algoridamcha vapar nirdharak anilingmadhye gibbs vitarananchya vaparat vaparat entropy yuktivadanmadhye udbhavalyache disate.
punaravruttichya pratyek oliche karya asey vistarte
ola 1: haah sashart sambhavyatecha mulyavardhit sanch aahe
namuna deta sootra _ 63 dware tayar kelelya sootra _ 55 vector aanee tyachya qamee kelelya mahitee proxy sootra _ 64 dware tayar jhalelya sutranmadhil coolback-leabler vichalan sootra _ 61 moolbhut adthalyachya samikarananusar sandarbh (kinwa shrenibaddha) deta sootra _ 55 chya sandarbhat sankuchit vectorchya vishvasarhateche moolyankan karnyasathi lagoo kele jaate. sootra _ 66 heey vitaran sootra _ 67 madheel coolback-leabler vichalan aahe.
aanee sootra _ 69 heey scalar normalisation aahe. antarachya nakaratmak ghatankachya vajanacha arth assa aahe qee jevha coolback-leabler vichalan mothe asate tevha pahilya olimadhye purvichya samooh sambhavyateche vajan qamee kele jaate, asha prakare yashasvi samooh sambhavyatet vadhatat aanee ayashasvi samooh kshay hotat.
ola 2: sashart sambhavyatecha dusra matricks-moolya sanch. vyakhyenusar
jethe beyas identity sootra _ 71 vaparale jaate.
ola 3: yaa reshela samooh sootra _ 64 chey kirkol vitaran aadhalate
haah eka manak parinam aahe.
algoridammadhe pudhil input mhanje seemant namuna vitaran sootra _ 74 jeey aadhich sootra _ 47 chya pramukh eigenvectordware aanee matricks moolya asalelya coolback-leabler diversions functiondware nirdharit kele gele aahe.
namuna antar aanee sankraman sambhavyatepasun vyutpann.
matricks sootra _ 77 yadruchchikpane kinwa vajvi andajasah suru kele jaau shakate, tarr matricks sootra _ 78 laa purv mulyanchi aavashyakta nahee. jaree algoridam ekatra yet asala taree, anek minima astitvat asoo shakatat jyanche nirakaran karane aavashyak aahe.
nirnayachi ruparesha paribhashit karane.
prashikshan sanch sootra 80 chya bahereel naveen namuna sootra 79 chey vargikaran karnyasathi, mageel antar metrik sootra 79 aanee serve namunyanmadhil sankraman sambhavyata sootra 82, sootra 83 madhye sootra 84 aii normalisations shodhate. dusare mhanje samooh aanee sashart shreni sambhavyata midvinyasathi 3-ola algoridamchya shevatchya done olee lagoo qaraa.
shevati
mapdand sootra _ 87 heey barkaine nirikshanakhali thewale jaane aavashyak aahe, kaaran teey shunyapasoon vadhavalyamule, vaishishtyanchi sankhya vadhat asatana, sambhavyatechya shrenitil jaaget, vishisht gambhir maryadanvar laksh kendrit kele jaate.
eka udaharan.
khaleel prakaran yadruchchik input sootra _ 88 aanee formula _ 90 dware tayar kelelya outputchya done shreneensah chaar chaturthansh gunakamadhye clusterchi tapasani karate. yaa karyat pratyek shrenisathi done sthanikaritya vegale kelele samooh aahet aanee tyamule hii paddhat asha vitarananna hatalu shakate heey darshavate.
20 namune ghetale jaatat, jeey _ 91 yaa varg sutravar eksamanpane vitarit kele jaatat. varganchya sankhyechya palikade vaparlya jaanarya samoohanchya sankhyecha, yaa prakaranat done, kamgirivar farsa parinam hott nahee aanee sootra _ 92 chaa vapar karoon done samoohansathi parinam darshavile jaatat.
antarache karya sootra 93 aahe jethe sootra 94 tarr sashart vitaran sootra 95 heey 2 × 20 matricks aahe.
aanee itaratra shoonya.
shoonya olitil bereejmadhye + 1 kinwa-1 chya prashikshan mulyanche pratinidhitva karnari keval done moolye samavisht aahet, parantu tarihi tee changli karya karate. aakruti vees namunyanchi thikane darshavate jyat '0' heey 'y' = 1 darshavate aanee 'x' heey 'y' = −1 darshavate. ektechya sambhavyatechya gunottar patalivaril samocch darshavile aahe,
naveen namuna sootra mhanoon _ 98 heey chaurasavar scan kele aahe. saiddhantikdrushtya samochchane sootra 99 aanee sootra 100 nirdeshankanshi sanrekhit kele pahije parantu asha lahan namuna sankhyansathi tyanni tyaeivaji namuna bindunchya banavat samoohanche anusaran kele aahe.
neural network/fuzzy logic sadrushya.
haah algoridam kahisa ekach lapalela thurr asalelya majjatantu jaalyashi samaan aahe. antargat nodes samooh sootra _ 101 dware darshavile jaatat aanee jaale vajanache pahile aanee dusare thurr anukrame sashart sambhavyata sootra _ 102 aanee sootra _ 103 aahet. tathapi, manak neural networkchya ulat, algoridam purnapane sambhavyatevar avalambun asate, namuna mulyanaivaji input mhanoon, tarr antargat aanee utpadan moolye hii serve sashart sambhavyata ghanata vitaran aahet. nonlinear functions heey durchya metrik sutramadhye _ 104 (kinwa 'prabhav functions/radial besis functions') aanee sigmoid functionsaivaji sankraman sambhavyatemadhye samavisht kele jaatat.
blahoot-arimoto teen-reshancha algoridam vegane ekatra yeto, anekada dahapat punaravruttimadhye aanee _ 87, sootra _ 106 aanee sootra _ 43 aanee samoohanchya mukhyatenusar, vaishishtyanvar laksh kendrit karnyachya vividh staranvar sadhya kele jaau shakate.
sankhyikeey soft clustering vyakhya sootra _ 78 madhye aspasht tarkshastrachya maukhik aspasht sadasyatva sankalpaneshi kahee pramanat parasparsambandhit aahe.
vistar.
eka manoranjak vistar mhanje bajuchya mahitisah mahititil adthalyache prakaran. yethe eka lakshya chalabaddal mahitee jastit jaast kelee jaate aanee aanee qamee kelee jaate, detachya nivadalelya pailumbaddal mahitipurn pratinidhitva shikane. aupcharikpane

