The Method of Steepest Descent for Feedforward Artificial Neural Networks

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IOSR Joural o Mahac (IOSR-JM) -ISSN: 78-578, p-issn:39-765x. Volu, Iu Vr. II. (F. 4), PP 53-6.oroural.org Th Mhod o Sp Dc or Fdorard Arcal Nural Nor Muhaad Ha, Md. Jah Udd ad Md Adul Al 3 Aoca Proor, Dpar o Appld Mahac, Noahal Scc ad Tcholog Uvr, Noahal 384, Bagladh. Lcurr, Dpar o Appld Mahac, Noahal Scc ad Tcholog Uvr, Noahal 384, Bagladh. 3 Aa Proor, Chagog Uvr, Chagog 433, Bagladh. Arac: I h papr, pl h hod o Sp Dc gl ad ullar dorard arcal ural or. I all prvou or, all h upda gh quao or gl or ullar dorard arcal ural or ha calculad choog a gl acvao uco or varou procg u h or. W, a r, calcula h oal rror uco paral or gl ad ullar dorard arcal ural or ad h calcula h hr upda gh quao or ag dr acvao uco dr procg u paral gl ad ullar dorard arcal ural or. A apl gv o ho uul o h plao. Kord: Fdorard Arcal Nural Nor, Bac propagao Larg, Acvao Fuco, Trag. I. Iroduco Fd-orard arcal ural or (FNN) [ -3] hav dl ud or varou a, uch a par rcogo, uco approao, dacal odlg, daa g, ad r orcag. Th rag o FNN al udra ug h ac-propagao (BP) [4-5 ] ad larg. Th Bacpropagao rag algorh or rag d-orard or a dvlopd Paul Wro[Paul Wro84], ad lar Parr[Parr85] ad Rulhar [Rulhar 94]. Th p o or cogurao h o coo u, du o a o rag. I ad ha ovr 8% o all ural or proc dvlop u acpropagao. Th rao or h a "acprogagao" ha h oupu rror ar "propagad ac" ro h oupu lar o h hdd lar, ad ar ud h upda quao or h hdd lar gh. Thr ar o pha larg ccl, o o propaga h pu par hrough h or ad h ohr o adap h oupu, chagg h gh h or. I h rror gal ha ar ac propagad h or oprao o h hdd lar(). Th poro o h rror gal ha a hdd-lar uro rcv h proc a a o h coruo o a parcular uro o h oupu rror. Adug o h a h gh o h coco, h quard rror, or o ohr rc, rducd ach ccl ad all zd, pol. A Bac-Propagao or co o a la hr lar o u: a pu lar, a la o rda hdd lar, ad a oupu lar. Tpcall, u ar cocd a d-orard aho h pu u ull cocd o u h hdd lar ad hdd u ull cocd o u h oupu lar. Wh a Bac- Propagao or ccld, a pu par propagad orard o h oupu u hrough h rvg pu-o-hdd ad hdd-o-oupu gh. Fgur Srucur o a dorardd arcal ural or..oroural.org 53 Pag

Th Mhod o Sp Dc or Fdorard Arcal Nural Nor Th hod o p dc [7-8] o popular aog a ahaca: vr pl, a o u, ad ach rpo a. Bu h gg advaag o h hod l h ac ha guarad o d h u hrough urou o rao a log a. Hovr, h hod alo ha o g la: I ud o a adl cald, ll d up gog hrough a ur o rao or locag h u, ad c ach o p a durg rao ar rl all, hu h covrgc pd pr lo, h proc ca lrall a orvr! Al- hough a largr p z ll cra h covrgc pd, u could alo rul a a h larg rror. For apl, hr a log ad arro vall h rror urac, h copo o h grad h drco ha po alog h a o h vall vr all hl h copo alog h vall all qu larg. Th rul oo or h drco o h all v hough hav o ov a log dac alog h a ad a all dac alog h all. I h papr, pl h hod, paral, gl ad ullar dorard arcal ural or ad hav or uul rul. Sgl-Lar Nor Codr a gl lar dorard ural or o uro h -h oupu a ho h Fgur. Thr ar pu Fgur. Sgl lar dorard ural or, hr...,., W =...................., h ghd ar h z ud o do h rgh o h coco ro h h pu o h h procg l.,, hr...,, ar h a or -h procg u,, hr...,, ar h pu or -h procg u, hr...,, ar h acvao uco or -h procg u ad, hr...,, ar h oupu or uro. No ha h,, ar al gh or - h procg u ad o h al pu gal. W alo codr, ad ar h arg(drd), rror gal ad Ma-Squar rror ( Su o Squard rror) uco rpcvl. W hav h ollog calculao N pu:... hr...,.oroural.org 54 Pag

Th Mhod o Sp Dc or Fdorard Arcal Nural Nor.oroural.org 55 Pag....... () Ba:... () Fro () ad () hav;.......... (3) Nor Oupu: (4) rror Sgal: Whr,, ar arg oupu or gv uro h oupu lar. (5) Ma-Squar rror uco:

Th oal rror(or pu par): oal Th Mhod o Sp Dc or Fdorard Arcal Nural Nor (7) Mulpl-Lar Nor Codr a hr lar dorard ural or a ho h Fgur 3. (6) Fro pu o hdd lar: Thr ar pu Fgur 3. Thr lar dorard ural or, hr...,.,...................., h ghd ar h z ud o do h rgh o h coco ro h h pu o h h procg l., Thr ar uro h hdd lar,, hr...,, ar h a or -h procg u,, hr...,, ar h pu or -h procg u or -h procg u ad, hr...,, hr...,,, ar al gh or -h procg u ad o W hav h ollog calculao N pu:....... Ba:..., ar h acvao uco, ar h oupu or uro. No ha h h al pu gal. (8).oroural.org 56 Pag

Th Mhod o Sp Dc or Fdorard Arcal Nural Nor.oroural.org 57 Pag.... (9) Fro (8) ad (9) hav;.......... () Nor Oupu h hdd lar:. () Fro hdd lar o oupu lar: Thr ar pu, hr...,,...................., h ghd ar h z ud o do h rgh o h coco ro h h pu o h h procg l., Thr ar uro h oupu lar,, hr...,, ar h a or -h procg u,, hr...,, ar h pu or -h procg u, hr...,, ar h acvao uco or -h procg u ad, hr..., ar h oupu or uro. No ha h,, ar al gh or -h procg u ad h al pu gal. W hav h ollog calculao N pu:.......

Th Mhod o Sp Dc or Fdorard Arcal Nural Nor.oroural.org 58 Pag... () Ba:.... (3) Fro () ad (3) hav;.......... (4) Nor Oupu h oupu lar:.. (5) rror Sgal:. Whr,, ar arg oupu or gv uro h oupu lar. (6) Ma-Squar rror uco: (7) Th oal rror h oupu lar(or pu para):

Th Mhod o Sp Dc or Fdorard Arcal Nural Nor.oroural.org 59 Pag oal (8) Iplao Sgl lar Nor Fro quao (7) hav oal (9) W hav; oal. () Ug Sp Dc Mhod hav h upda gh quao a p p. () Mulpl lar or Fro (8) hav oal () oal (3) Ug Sp Dc Mhod hav h upda gh quao a p p ad.. oal oal. Ug Sp Dc Mhod hav h upda gh quao a

Th Mhod o Sp Dc or Fdorard Arcal Nural Nor p p. (4) Nurcal apl Codr h gl lar dorard ural or a ho pu.,. 6, W =..3.oroural.org.3.4 gur. Suppo ha hr ar, h ordr ghd ar ud o do h rgh o h coco ro h pu o procg u., h a or o procg u ar,, h pu or o procg u ar,,, ar h acvao uco or h procg u ad,, ar h oupu or uro. No ha h.,. ar al gh or o procg u ad h al pu gal., Codr, ad ar h rror gal ad Ma-Squar rror (Su o Squard rror) uco rpcvl ad.7,. 8 ar h arg(drd). U a p z o =., W hav h ollog calculao N pu:...6.3....3.6.4..3 Nor Oupu:. 55..3.3.3. 394.3 rror Sgal:.7.55.478.8.394.496 Ma-Squar rror uco:.9.3 Th oal rror (or pu par): oal To upda h gh, u quao ().9.3.3...478.47.. 73..3.478.47.6. 59..3.496.85.. 5798.4.496.85.6. 395 Th upda gh ar:. o 6 Pag

Th Mhod o Sp Dc or Fdorard Arcal Nural Nor W.73.5798.59.395.73..59.6..356.5798..395.6..8796 Nor Oupu:. 588.356.8796.8796. 76.8796.8796 rror Sgal:.7.588..8.76.938 Ma-Squar rror uco:.6.43 Th oal rror (or pu par): oal Ovoul, oal.6.43.5 < oal ; ha, h acual oupu o h ural or ha co clor o h arg oupu a a rul o updag h gh. II. Cocluo A pl u cv dcrpo o dorard arcal ural or ha ad hr gvg phaz o h acpropagao algorh, c dl ud ad a ohr algorh ar drvd ro. W hav pld h p dc hod gl ad ulpl-lar dorard arcal ural org prol ad -up a urcal apl. Frl, W hav calculad h oal rror uco paral or gl ad ullar dorard arcal ural or ad h calculad h hr upda gh quao or ag dr acvao uco dr procg u paral gl ad ullar dorard arcal ural or. Th covrgc havor o our apl ho ha h rul o h acual or oupu a clo o our drd(arg) oupu. Acoldg Th Noahal Scc ad Tcholog Uvr ad h Uvr o Chagog, or provdg a ulag vro or rarch coco h h arcl. Rrc [] Ad, P.R. ad Dpr, M.A.H. 974. Iroduco o Opzao Mhod. Had Pr, N Yor. [] Ba, R. 99. Fr ad cod-ordr hod or larg: B Sp Dc ad No hod. Nural Copuao 4: 4-66. [3] Johao,.M., Dola, F.U. ad Gooda, D.M. 99. Bacpropagao larg or ul-lar d-orard ural or ug h couga grad hod. Il. J. Nural S, : 9-3 Judd, J.S. 99. Nural Nor Dg ad h copl o Larg. MIT Pr, Cardg, MA [5] Muhaad Ha.. Opal o Ucorad Nolar Prograg Prol. M.Phl Th, Uvr o Chagog, Chagog, Bagladh. [6] Mhra] P., ad Wah, B. W. 99. Arcal ural or: cocp ad hor I Copu. Soc Pr,. [7]. X. Yu, M. O., ad O. Kaa.. A gral acpropagao algorh or d-orard ural or larg. I Tra. Nural Nor. 3:5 54. [8] X. H. Hu ad G. A. Ch.997. c acpropagao larg ug opal larg ra ad ou. Nural Nor :57-57. [9] Zurada, J. M.. Iroduco o arcal ural. M. G. Road, Mua: Jaco..oroural.org 6 Pag