Model FSM w zastosowaniu do klasyfikacji.

Model FSM w zastosowaniu do klasyfikacji. 5DIDá$GDPF]DN:áRG]LVáDZ'XFK.DWHGUD0HWRG.RPSXWHURZ\FK8QLZHUV\WHW0LNRáDMD.RSHUQLND XO*UXG]LG]ND7RUXHPDLO^UDDGGXFK`#SK\VXQLWRUXQSO Streszczenie 6LHFL )60 PDM SURVW VWUXNWXU SRGREQ GR VLHFL 5%) MHGQDN G]LNL X*\FLX VHSDUo- ZDOQ\FK IXQNFML WUDQVIHUX ]DPLDVW UDGLDOQ\FK PDM V]HUV]H ]DVWRVRZDQLH 2PyZLRQR Dr- FKLWHNWXU LQLFMDOL]DFM NRQVWUXNW\ZLVW\F]Q\ DOJRU\WP XF]HQLD RSW\PDOL]DFM VLHFL Rbroty zlokalizowanych funkcji transferu, rozpoznawanie wektorów w czasie klasyfikacji RUD] PR*OLZRFL ]DVWoVRZD GR HNVWUDNFML UHJXá 1. Wprowadzenie :G*HQLXGR]UR]XPLHQLDOXG]NLHMLQWHOLJHQFMLLXP\VáXZ\Uy*QLüPR*QDGZDSDUDG\JPDW\ 3LHUZV]\] QLFK V]WXF]QD LQWHOLJHQFMD ED]XMH QD SU]HWZDU]DQLX V\PEROLF]Q\P D ZLF (Uó- GáHP V WX SURFHV\ SR]QDZF]H Z\VRNLHJR SR]LRPX GUXJL VLHFL QHXURQRZH Z\ZRG]VL] QHXURG\QDPLNLLLQVSLURZDQHVSU]H]VWUXNWXUQHXURQRZPy]JX6LHFLQHXURQRZHSRSU]H] VZRMRGPLHQQRüZSRGHMFLXGRSUREOHPXLQWHOLJHQFMLLXP\VáXZQRV]QRZHPR*OLZRFL GRG]LHG]LQ\V]WXF]QHMLQWHOLJHQFML'RW\FKF]DVVLHFLQHXURQRZHZ\GDMVLE\üQDMOHSV]\P UR]ZL]DQLHPGOD]DGDSR]QDZF]\FKQLVNLHJRSR]LRPXWDNLFKMDNSUREOHP\ZLG]HQLDF]\ UR]SR]QDZDQLDPRZ\OXEWH*GODSURVW\FK]DGDNODV\ILNDF\MQ\FKSU]H]FRVRQHZSHZLHQ VSRVyE RJUDQLF]RQH Z LFK PR*OLZRFLDFK UHDOL]DFML SUHGHILQLRZDQ\FK VWUXNWXU ZLHG]\ L Z X*\FLXW\FKVWUXNWXUZVHNZHQF\MQ\PSURFHVLHSU]\F]\QRZ\P1LHPDZWSOLZRFL*HZ\*- V]H IXQNFMH SR]QDZF]H V UH]XOWDWHP DNW\ZQRFL Py]JX D ZLF SRZLQQR E\ü PR*OLZH LFK odtworzenie przez sieci neuronowe [2], [4], [15]-DVQ\PMHVW*HREHFQ\UR]ZyMVLHFLQHXUo- QRZ\FKMHVWSRZL]DQ\]EUDNLHPPRGXODUQRFLLUDF]HMQLHZLHON]áR*RQRFLPRGHOXQL*] LFK ZHZQWU]Q\P RJUDQLF]HQLHP MDNR PRGHOX 'X*R MX* ZLDGRPR R V]F]HJyáDFK SURFHVyZ QHXURQRZ\FKRGSRZLHG]LDOQ\FK]DG]LDáDQLHPy]JXLQHXURG\QDPLN2EHFQLHQDZHWQLHNWó- UHG]LDá\SVyFKRORJLLNRU]\VWDM]RVLJQLüneurodynamiki [16]. &]\MHVWPR*OLZH]UR]XPLHQLHSURFHVyZP\ORZ\FKEH]SRUHGQLR]SURFHVyZQHXURQRZ\FK ZPy]JX":\GDMH VL*H QLH 1DZHW Z FKHPLL L IL]\FH NRQFHSFMH IHQRPHQRORJLF]QH NWyUH QLHVáDWZRUHGXNRZDOQHGRIXQGDPHQWDOQ\FKRGG]LDá\ZDZFL*VZX*\FLX7HRULHPDNUo- VNRSRZHZ]DVDG]LHVUHGXNRZDOQHGRPLNURVNRSRZ\FKZSUDNW\FHMHGQDNEDUG]LHMRZRFQH MHVWSU]\EOL*HQLHIHQRPHQRORJLF]QHGR]áR*RQ\FKV\VWHPyZ-]\NLQHXURORJLLLSV\FKRORJLL V]XSHáQLHUy*QH:\GDMHVLMHGQDN*HPXVL LVWQLHü WHRULD SR]ZDODMFD X]\VNDü NRQFHSFMH SV\FKRORJLF]QHMDNRDSURNV\PDFMHQHXURG\QDPLF]QHJRSRGHMFLDGRG]LDáDQLDPy]JX*áyw- Q\PLFHODPLWDNLHMWHRULLV

1. :SURZDG]HQLH DSURNV\PDFML GR QHXURG\QDPLNL SU]\ VSHáQLHQLX IDNWyZ QHXURELRORJLFz- Q\FK SURZDG]FHM GR QRZHM PDWHPDW\F]QHM NRQFHSFML EH]SRUHGQLR RSLVXMFHM VWDQ\ poznawcze. 2. 8*\FLHW\FKNRQFHSFMLMDNRM]\NDGR]EXGRZDQLDWHRULLV\VWHPXSR]QDZF]HJR 3. =DVWRVRZDQLHWHMWHRULLGRZ\MDQLHQLD FHFK SURFHVX SR]QDZF]HJR F]áRZLHND WDNLFK MDN LGHQW\ILNDFMDDVRFMDFMDJHQHUDOL]DFMDUy*QHVWDQ\XP\VáX 4..RQVWUXNFMD V\VWHPX DGDSWDF\MQHJR RGSRZLDGDMFHJR VSHF\ILNDFMRP V\VWHPX NWyU\ E- G]LHXF]\áVL] SU]\NáDGyZ L RJyOQ\FK SUDZ ZQLRVNRZDá X*\ZDá QDWXUDOQHJR M]\ND L NWyU\EG]LHVSHáQLDáLQQHIXQNFMHSR]QDZF]H =JRGQLH]GXFKHP$OODQD1HZHOOD8QLILHGWKHRULHVRIFRJQLWLRQWHRULDSRZLQQDE\üZVSo- PDJDQD SU]H] RSURJUDPRZDQLH SR]ZDODMFH ]ZHU\ILNRZDü SU]HVáDQNL L PRGHOH SU]H] QL XWZRU]RQH6\VWHP62$5VWZRU]RQ\SU]H]1HZHOODLMHJRZVSyáSUDFRZQLNyZED]XMHQDWZo- U]HQLXUHJXáDOHQLHPDQLFZVSyOQHJR]QHXURELRORJL0R*HE\üX*\WHF]Q\ZPRGHORZDQLX SHZQ\FKIXQNFMLSR]QDZF]\FKDOHQLHSRPR*HQDP]UR]XPLHüSRZL]DQLDW\FKSURFHVyZ] G\QDPLN]DFKRG]FZPy]JX6\VWHP)60[1]MHVWLQVSLURZDQ\QDG]LDáDQLXPy]JXLGo- VWDUF]DPR*OLZRFLQLHW\ONRPRGHORZDQLDDOHUyZQLH*UR]XPLHQLDSURFHVyZSR]QDZF]\FKL LFKUHODFML]G\QDPLNPy]JX 0RGHOHIXQNFMLPy]JXZ\PDJDMV]HUHJXDSURNV\PDFML:SLHUZV]\PNURNXZSURZDG]DVL PRGHO QHXURQX MDNR XU]G]HQLD HOHNWU\F]QHJR [15] SU]H] FR GRNRQXMH VL GUDVW\F]QHJR uproszczenia z punktu widzenia procesów biochemicznych i bioelektrycznych. Ta aproksy- PDFMD SR]ZDOD X*\ü Z PRGHOX W\ONR NLONX SDUDPHWUyZ WDNLFK MDN SUyJ Z]EXG]HQLD L ZDJL V\QDSW\F]QH -HVW UyZQLH* NRQLHF]QD GR ]UR]XPLHQLD SURFHVyZ SR]QDZF]\FK Z\*V]HJR So- ]LRPX3URFHV\SR]QDZF]HQLVNLHJRSR]LRPXUHDOL]RZDQHQDMF]FLHM SU]H] Uy*QH PDS\ Wo- SRJUDILF]QH GHILQLXM FHFK\ ZHZQWU]QHM UHSUH]HQWDFML 7H FHFK\ UHSUH]HQWXM ZLHOH W\SyZ GDQ\FK DQDORJRZH V\JQDá\ VHQVRURZH ]PLHQQH OLQJZLVW\F]QH OLF]E\ REUD]\ 3UDZG]LZH RELHNW\XP\VáXVNáDGDMVLJáyZQLH]SU]HWZRU]RQ\FKZVWSQLHGDQ\FKVHQVRURZ\FKUHSUe- ]HQWDFML REUD]NRZHM G]LDáDQLD SHUFHSF\MQHJR 2ELHNW\ XP\VáX ]QDMGXMVLZSU]HVWU]HQL XP\VáXNWyUDMHVWGODQLFK]ELRUQLNLHP1DWXUDOQSUDNW\F]QUHDOL]DFMWHMLGHLMHVWPRGXODr- QDVLHüQHXURQRZD]Z]áDPLVSHFMDOL]XMF\PLVLZRSLVLHJUXSRELHNWyZZSU]HVWU]HQLXPy- VáX:]á\WDNLHMVLHFLQLHUHSUH]HQWXMSRMHG\QF]\FKQHXURQyZDOHUDF]HMXUHGQLRQDNW\w- QRü]ELRUXNRPyUHNQHXURQRZ\FK7HJRW\SXVLHüPR*HE\üWUDNWRZDQDMDNRVLHüQHXURQRZD ED]XMFDQD]ORNDOL]RZDQ\PSU]HWZDU]DQLXOXEWH*MDNRUR]P\W\V\VWHPHNVSHUWRZ\NWyUHJR wiedza zapisana jest w postaci zbiorów rozmytych. 2. FSM 0RGHO)60)HDWXUH6SDFH0DSSLQJRSDUW\MHVWQDHVW\PDFMLJVWRFLUR]NáDGXSUDZGRSo- GRELHVWZDSUH]HQWRZDQ\FKGDQ\FK3DWU]F]Uy*Q\FKSHUVSHNW\ZPR*QDJRXZD*Dü]DVLHü QHXURQRZSRGREQGRVLHFL]UDGLDOQ\PLIXQNFMDPLED]RZ\PLFKRFLD*IXQNFMHQLHPXV]D E\üUDGLDOQHW\ONRVHSDURZDOQHV\VWHPQHXURUR]P\W\DNW\ZQRüZ]áyZVLHFL]VHSDURZDl- Q\PL IXQNFMDPL WUDQVIHUX PR*QD SU]HDQDOL]RZDü X*\ZDMF NRQFHSFML ]ELRUyZ UR]P\W\FK URG]DMV\VWHPXRSDUWHJRQDODGDFKSDPLFLPHPRU\EDVHGV\VWHPV\VWHPVDPRRUJDQL]XM- F\VLDQDZHWMGURV\VWHPXHNVSHUFNLHJRZ\NRU]\VWXMFHJRZLHG]UR]P\WOXERIHUXMFHJR SU]\GDWQHKHXU\VW\NLZSURFHVLHV]XNDQLDUR]ZL]D6NáDGRZHZHNWRUDZHMFLRZHJRLZ\j- FLRZHJRGHILQLXMUD]HPSU]HVWU]HFHFK1DSRGVWDZLHGDQ\FKWUHQLQJRZ\FKVWDQRZLF\FK SURWRW\S\ZSU]HVWU]HQLFHFKWZRU]\VLUR]P\WHRELHNW\UHSUH]HQWXMFHáF]Q\UR]NáDGSUDw- GRSRGRELHVWZDGODZHNWRUyZZHMFLRZ\FKLZ\MFLRZ\FK5R]NáDGWHQPR*HE\üX*\W\GR DSURNV\PDFMLQLH]QDQ\FK]DOH*QRFLOXEGRNODV\ILNDFML

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ZHMFLRZ\SRV]XNXMHP\Z]áDNWyU\XOHJDQDMZLNV]HPXZ]EXG]HQLX-HOLWHQZ]HáQDOH*\ GRNODV\ZHNWRUDZHMFLRZHJR WR SU]HSURZDG]DP\ MHJR RSW\PDOL]DFM Z SU]HFLZQ\P UD]LH UR]SRF]\QDVLGUXJDID]DXF]HQLDF]\OLGostawianie nowego neuronu. :REOLF]DQLXIXQNFMLDNW\ZDFMLVNDORZDQLHGDQ\FKQLHPDZSá\ZXQDZDUWRüWHMIXQNFMLSo- QLHZD*ND*G\]Z\PLDUyZUR]SDWU\ZDQ\MHVWQLH]DOH*QLH']LNLWHPXZNáDGND*GHJR]Zy- PLDUyZGRIXQNFMLDNW\ZDFML]DZV]HQDOH*\GRSU]HG]LDáX>@3RQLHZD*MHGQDNGRRNUHOenia podoelhvwzd PLG]\ Z]áHP D ZHNWRUHP ZHMFLRZ\P X*\ZDQD MHVW RGOHJáRü HXNOide- VRZDWRSU]HVNDORZDQLHGDQ\FKPR*HPLHüZSá\ZQDSURFHVXF]HQLDJG\*QRZHZ]á\PRJ E\üZVWDZLDQHZLQQ\PPLHMVFXQL*SU]HGSU]HVNDORZDQLHP'ODWHJRWH*SU]HGUR]SRF]FLHP XF]HQLDGRNRQXMHVLVWDQGDUyzacji danych. $GDSWDFMDSDUDPHWUyZSROHJDQDWDNLPLFKGRSDVRZDQLXE\]ZLNV]\üZDUWRüZ]EXG]HQLD Z]áD 'RNRQXMHP\ WHJR SRSU]H] ]PLDQ SRáR*HQLD Z]áDWDNDE\ZND*G\P Z\PLDU]H ] RVREQD]PQLHMV]\üRGOHJáRüPLG]\QLPDZHNWRUHPZHMFLRZ\P κ Ri = Ri + ( Xi Ri) m -HGQRF]HQLH ]ZLNV]DP\ UR]P\FLH Z]áD SURSRUFMRQDOQLH GR RGOHJáRFL ] ZHNWRUHP ZHj- FLRZ\PSRGREQLHMDNSRáR*HQLHGODND*GHJRZ\PLDUXRVREQRRUD]GRDNWXDOQHJRZ]Eu- G]HQLDWHJRZ]áDLRGZURWQLHSURSRUFMRQDOQLHGRF]DVXMHJR*\FLDτ τ n : (1 GXR ( ;, σ)) Xi Ri σi = σi + γ 1 + / Λ ( τ τ ) &]DV*\FLDMHVWWRUy*QLFDDNWXDOQHJRQXPHUXHSRNLτLF]DVXSRZVWDQLDZ]áDτ n (czyli nume- UXHSRNLZNWyUHMZ]HáSRZVWDá,PVWDUV]\Z]HáW\PWUXGQLHMMHVW]PLHQLDüMHJRSDUDPHWU\ DGDSWDF\MQH2F]\ZLFLHZWUDNFLHXF]HQLDQXPHUHSRNLτ XOHJDFLJáHPX]ZLNV]HQLXWDN ZLFUy*QLFDτ τ n MHVW]DZV]HGRGDWQLDOXEMHOLZ]HáSRZVWDáZDNWXDOQHMHSRFHUyZQDMHVW 0. Parametry uczenia κ, γ GRSDVRZ\ZDQH V Z VSRVyE DXWRPDW\F]Q\ LQG\ZLGXDOQLH GOD ND*- dego w]ád γ = Γ 1 + τ / ; Λ ( τ ) n n κ = Κ 1 + τ / Λ ( τ ) Parametr ΛRNUHODV]\ENRü]PQLHMV]DQLDVLSDUDPHWUyZXF]HQLDSDUDPHWUWHQXVWDORQ\MHVW QDSRF]WNXXF]HQLDLZáDFLZLHZHZV]\VWNLFKGRW\FKF]DVRZ\FK]DVWRVRZDQLDFKPLDá]Dw- V]H WDNVDP ZDUWRü QDWRPLDVW Γ i ΚV SRF]WNRZ\PL ZDUWRFLDPL SDUDPHWUyZ XF]HQLDNWyUHWU]HEDXVWDOLüSU]HGURzSRF]FLHPXF]HQLD 3RQLHZD*]PLDQD UR]P\FLD MHVW SURSRUFMRQDOQD GR G), QDWRPLDVW ZDUWRü PDNV\PDOQHJR Z]EXG]HQLDZ\QRVLWRLPZLNV]DZDUWRüZ]EXG]HQLDW\PPQLHMV]H]ZLNV]HQLHUR]Py- FLD 6WG UyZQLH* RJUDQLF]HQLH FR GR IXQNFML DNW\ZDFML DE\ MHM ZDUWRFL E\á\ ] SU]HG]LDáX >@-HOLZ]HáNODV\ILNXMHSRSUDZQLHQRZ\ZHNWRUWRMHJRPDVD]RVWDMH]ZLNV]RQDRMeden: m=m1dsrf]wnxqrzhmhsrnlpdvdzv]\vwnlfkz]áyzmhvwxvwdodqdqdzduwrü :FHOXXQLNQLFLD]E\WVLOQHJRQDNáDGDQLDVLZ]áyZUHSUH]HQWXMF\FKUy*QHNODV\QDVLHELH ZF]DVLHRSW\PDOL]DFMLSRGHMPRZDQDMHVWUyZQLH*SUyED]PQLHMV]HQLDSRGRELHVWZDGRZ]áD EGFHJR QDMZLNV]\P]DJUR*HQLHP:]Há NWyU\ E\á RSW\PDOL]RZDQ\ F]\OL Z]Há QDMEDU G]LHMSRGREQ\GRZHNWRUDZHMFLRZHJR ]RVWDMH Z\áF]RQ\ ] REOLF]H L SRV]XNLZDQ\ MHVW n

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:DUWRüSDUDPHWUXλMHVWPDáDGODQRZ\FKZ]áyZJG\*WHGRSLHURDGDSWXMVLQDWo- PLDVWZSU]\SDGNXVWDUV]\FKZ]áyZSDUDPHWUWHQPDGX*ZDUWRü =XZDJLQDWR*HSRZVWDZDQLHQRZ\FKZ]áyZMDNUyZQLH*RSW\PDOL]DFMDZ]áyZLVWQLHM- F\FK]DOH*QH V RG NROHMQRFL SRGDZDQLD ZHNWRUyZ WUHQLQJRZ\FK QD ZHMFLH VLHFL]D ND*- G\PUD]HPJG\VLHüXF]RQDMHVWQDW\FKVDP\FKGDQ\FKRWU]\PXMHVLNRQILJXUDFMVLHFLNWó- UHUy*QLVLRGVLHELH:ZLNV]RFLSU]\SDGNyZWHUy*QLFHVQLHZLHONLHFRáDWZR]DXZD*\ü QD]ELRU]HWHVWRZ\PJG\*Z\QLNZSRV]F]HJyOQ\FKSUyEDFKQD]ELRU]HWHVWRZ\PMHVWEDUG]R SRGREQ\*G\]ELyUWUHQLQJRZ\MHVW MHGQDN QLHZLHONL ZDULDQFMD PRGHOX PR*H E\ü GX*D FR SU]HMDZLDVLGX*Uy*QLFZNODV\ILNDFMLQD]ELRU]HWHVWRZ\PGODSRV]F]HJyOQ\FKSUyE 3URVW\PVSRVREHPQDUR]ZL]DQLHWHJRSUREOHPXMHVW]DVWRVRZDQLHW]ZNRPLWHWXVLHFL0e- WRGDWDSROHJDQDW\P*HQDGDQ\P]ELRU]HWUHQLQJRZ\PXF]\VLVLHüZLHORNURWQLH0DMFM PRGHOLVLHFLNODV\ILNDFMLZHNWRUyZ]H]ELRUXWHVWRZHJRGRNRQXMHVLSU]H]JáRVRZDQLHZLk- V]RFLRZHZ\ELHUDMFNODVNWyUDQDMF]FLHMZ\VWSXMHOXESU]H]ZD*RQNRPELQDFMURz- ZL]D]SRV]F]HJyOQ\FKVLHFL[9]. Metoda ta powoduje znaczne zmniejszenie wariancji mo- GHOXLMDNSRND]XMHGRZLDGF]HQLHGRVNRQDOHQDGDMHVLGRVLHFL)60 5.3. Obroty :FHOXOHSV]HJRGRSDVRZDQLDZ]áyZVLHFLGRGDQ\FKZ)60VWRVXMHVLQHXURQ\NWyU\FK funkcje transferu w n Z\PLDURZHMSU]HVWU]HQLGDMPR*OLZRüREURWXUHDOL]RZDQ\FKSU]H]QLH KLSHUSRZLHU]FKQLVWDá\FKZDUWRFLF]\OLJUDQLFGHF\]MLZ\]QDF]RQ\FKSU]H]QHXURQ:\No- QDQLHSHáQHJRREURWXMHVWREOLF]HQLRZREDUG]RNRV]WRZQHLSRZRGXMHJZDáWRZQH]PQLHMV]e- QLH VL V]\ENRFL XF]HQLD'ODWHJR WH*]DVWRVRZDQR REURW\ EGFH]áR*HQLHP REURWyZ GZu- Z\PLDURZ\FK 'OD SU]\NáDGX SU]HGVWDZLRQ\ ]RVWDQLH REUyW Z SU]HVWU]HQL WUyMZ\PLDURZHM 1DMSLHUZGRNRQXMHP\REURWXXNáDGXZVSyáU]GQ\FKGODSLHUZV]\FKGZyFKZ\PLDUyZRNW α, w wyniku czego z wektora (X,Y) otrzymujemy wektor (X,Y ): ; FRVα = < VLQα VLQα ; FRVα < :QDVWSQ\PNURNX ; = ; ;< = < LSRZWDU]DP\RSHUDFMHW\PUD]HPXZ]JOGQLDMFNWβSRáR*HQLDGDQHJRZ]áDPLG]\WU]e- FLPZ\PLDUHPLSáDV]F]\]QX,Y:RJyOQ\PSU]\SDGNXFDáDSURFHGXUDSRZWDU]DQDMHVWGOD ZV]\VWNLFK NROHMQ\FK Z\PLDUyZ.W\ REURWX GOD SRV]F]HJyOQ\FK Z]áyZ XVWDODQH VSRd- F]DVXF]HQLDGODND*GHJRZ]áDQLH]DOH*QLH =PLDQDNWyZQDFK\OHQLDQHXURQXGRRGSRZLHGQLFKRVLQDVWSXMH]DND*G\PUD]HPJG\Zy- NRQ\ZDQDMHVWDGDSWDFMDSRáR*HQLDLLQQ\FKSDUDPHWUyZWHJRZ]áD1DMSLHUZZ\]QDF]DQHV SRV]F]HJyOQHNW\QDFK\OHQLDθZHNWRUDPDMFHJRVZyMSRF]WHNZURGNXZ]áDDZLFMHVW WRSRáo*HQLHWHJRZ]áDDNRQLHFZPLHMVFXJG]LH]QDMGXMHVLDNWXDOQ\SXQNWZHMFLRZ\Z

3U]\NáDGREUyFRQ\FKGZyFKQHXURQyZ ZLHORZ\PLDURZHMSU]HVWU]HQLZHNWRUZHMFLRZ\PR*HE\üWUDNWRZDQ\MDNRSXQNW1DVWSQLH DNWXDOQHNW\QHXURQXφ VSU]HVXZDQHZNLHUXQNXZ\]QDF]oQ\FKZDUWRFL φ = φ + γ(θ φ) parametr γ MHVWWRWHQVDPSDUDPHWUNWyU\Z\VWSLáSRGF]DVXF]HQLDUR]P\ü -H*HOL Z GDQ\FK Z\VWSXM Z\UD(QLH QDFK\ORQH VNXSLVND WR ZLNV]Rü NWyZ Z\]QDF]RQ\FK GODSRV]F]HJyOQ\FKZHNWRUyZZSDGDMF\FKGRWHJRZ]áDEG]LHGRVLHELHSRGREQ\FKSU]H] FRáDWZRMHVWX]\VNDüRSW\PDOQ\NW-HGQDNJG\QLHPDZ\Uy*QLRQHJRNLHUXQNXGODVNXSLVND WRQDVWSXMHFLJáD]PLDQDZDUWRFLNWDφFRPR*HSRZRGRZDüWUXGQRFLZXF]HQLXVL'OD VNXSLVN Z\]QDF]RQ\FK SRGF]DV LQLFMDOL]DFML VLHFL NW\ ]QDMGRZDQH V ]D SRPRF SURVWHM ; = D ; GRSDVRZDQHMQDSRGVWDZLHZV]\VWNLFKZHNWRUyZQDOH*F\FKGRWHJRZ]áDVWG L L poszczególne parametry a i = k k :VSyáF]\QQLNLWHUyZQHVWDQJHQVRZLNWDSRPLG]\JáyZQRVLVNXSLVNDDRVLX 1. Tak ZLFSoV]F]HJyOQHNW\PR*QDZ\]QDF]\ü]HZ]RUX X X k 1 k i X X k i k i φ k = arctan(a k ) 1RZ\ Z]Há NWyU\ SRZVWDMH SRGF]DV XF]HQLD PD SRF]WNRZR NW\ ]HURZH SRQLHZD*W\ONR MHGHQ ZHNWRU QDOH*\ GR WHJR Z]áD L MHVW RQ MHJR URGNLHP,QLFMDOL]DFMD ] XZ]JOGQLHQLHP QLH]DOH*Q\FKREURWyZGODSRV]F]HJyOQ\FKZ]áyZ MHVW EDUG]LHM SUHF\]\MQD QL*]DVWRVRZDQLH DQDOL]\F]\QQLNyZJáyZQ\FK3&$OXELQQ\FKJOREDOQLHRNUHORQ\FKWUDQVIRUPDFMLGDQ\FK 1DZHWMHOLZF]DVLHXF]HQLDSDUDPHWU\REURWXQLHSRGOHJDMDGDSWDFMLZDUWRZSURZDG]LüPa- FLHU]HREURWXZRSLVDQ\SRZ\*HMVSRVyE,QQHPHWRG\WZRU]HQLDREUyFRQ\FKNRQWXUyZGHFyzji opisano w pracy [5].

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5.6. Rozpoznawanie 7HVWRZDQLHVLHFL)60SROHJDQDZ\V]XNLZDQLXGODGDQHJRZHNWRUDZHMFLRZHJRZ]áDNWyU\ XOHJD QDMZLNV]HPX Z]EXG]HQLX :HNWRU ZHMFLRZ\ MHVW SU]\SLVDQ\ GR NODV\ NWyU UHSUe- ]HQWXMH QDMOHSV]\ QHXURQ -H*HOL MHGQDN *DGHQ ] Z]áyZ QLH XOHJD Z]EXG]HQLX ZyZF]DV wektor wejflrz\qlh]rvwdmhvnodv\ilnrzdq\ 'RRV]DFRZDQLD MDNRFL NODV\ILNDFML VáX* GZD SDUDPHWU\ ZDUWRü Z]EXG]HQLD RUD] ZVSyá- F]\QQLN ]DXIDQLD :DUWRü Z]EXG]DQLH G MHVW ] ]DNUHVX >@ LP MHVW ZLNV]D W\P ZHNWRU ZHMFLRZ\EOL*V]\MHVWLVWQLHMFHPXSUoWRW\SRZLNWyU\SRZVWDáSRGF]DVXF]HQLD :VSyáF]\QQLN ]DXIDQLD QDWRPLDVW PR*QD WUDNWRZDü MDNR SUDZGRSRGRELHVWZR SRSUDZQHJR zaklasyfikowania wektora wejflrzhjrx do danej klasy S N = & L & * ; ' σ &L N &L & ; S N * ; ' σ N & N & & L L L = :OLF]QLNXVXPRZDQLHSU]HELHJDSRZV]\VWNLFKZ]áDFKUHSUH]HQWXMF\FKNODV]Z\FL]F\Z PLDQRZQLNXVXPDELHJQLHSRZV]\VWNLFKZ]áDFKXNU\W\FK Z VLHFL :]á\ SU]HFKRZ\ZDü PRJUyZQLH*LQIRUPDFMHV\PEROLF]QHNWyUHPRJE\üSU]HGVWDZLDQHQDZ\MFLX 6. 3U]\NáDGRZHUH]XOWDW\ 'RWHVWRZDQLDVLHFL)60X*\WRVWDQGDUGRZ\FK]DJDGQLHNODV\ILNDF\MQ\FKZ]LW\FK]UHSozytorium baz danych Uniwersytetu Kalifornijskiego w Irvine [8] JG]LH ]QDOH(ü PR*QD Go- NáDGQLHMV]\RSLVGDQ\FK:V]\VWNLHSRQL*V]HSU]\NáDG\SU]HGVWDZLDMZ\QLNLNWyUHSRZVWDá\ ZZ\QLNXXUHGQLHQLDNLONXUH]XOWDWyZGODGDQHMED]\ :V]\VWNLH GDQH ]RVWDá\ QDMSLHUZ ]HVWDQGDU\]RZDQH : SRQL*V]\FK WDEHODFK SRGDQD ]RVWDáD SURFHQWRZDSRSUDZQRüNODV\ILNDFMLQD]ELRU]HWHVWRZ\POXEWH*MHOL]ELyUWHVWRZ\QLHZy- VWSRZDáSU]HGVWDZLRQ\MHVWZ\QLN]NURWQHMNURVZDOLGDFML:SU]\SDGNXJG\LVWQLDá\]e- EUDQHZ\QLNLUy*Q\FKNODV\ILNDWRUyZGODGDQHJR]ELRUX)60]RVWDáSRUyZQDQ\]QDMOHSV]y- PL]QLFK-HOLWDNLHZ\QLNLQLHLVWQLDá\GRNRQDOLP\SRUyZQDQLD)60]QDMOHSV]\PPRGe- OHP0/3MDNLXGDáRVL]QDOH(üZOLWHUDWXU]HE\áDWR]Z\NáDZVWHF]QDSURSDJD]FMD5SURS Quickprop lub dla danych hypothyroid genetyczna optymalizacja parametrów), metody QDMEOL*V]\FKVVLDGyZk-NN [9] oraz drzewa decyzji C4.5 [10]. We wszystkich tabelach re- ]XOWDW RWU]\PDQ\ ] VLHFL )60 SU]HGVWDZLRQ\ MHVW Z RVWDWQLHM NROXPQLH ZV]\VWNLH SR]RVWDáH UH]XOWDW\ V Z NROHMQRFL PDOHMFHM GRNáDGQRFL NODV\ILNDFML :H ZV]\VWNLFK SU]\SDGNDFK Z\QLNLRVLJQLWH]DSRPRF)60V]EOL*RQHGRQDMOHSV]\FK:LFHMZ\QLNyZ]QDOH(üPR*- na na stronie internetowej: http://www.phys.uni.torun.pl/kmk/projects/datasets.html 'DQH'1$]DZLHUDMZHNWRUyZZ]ELRU]HWUHQLQJRZ\PLZHNWRUyZZ]ELRU]H WHVWRZ\P :\VWSXMH ELQDUQ\FK DWU\EXWyZ L WU]\ NODV\ R QDVWSXMF\P UR]NáDG]LH procentowym: w zbiorze treningowym 23.2%, 24.3%, 52.5%, w zbiorze testowym 25.6%, 23.6%, 50.8%.

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=DVWRVRZDQLDWHJRPRGHOXGRDSURNV\PDFMLMDNRSDPLFLDVRFMDF\MQHMRUD]MDNRIXQNFMLKHu- U\VW\F]QHM Z SUREOHPDFK RSW\PDOQHJR VSHáQLDQLD ZLHOX RJUDQLF]H [1] QLH ]RVWDá\ MHV]F]H SRGMWH 3RG]LNRZDQLD =D ZVSDUFLH ILQDQVRZH Z UDPDFK JUDQWX QU 7) MHVWHP\ ZG]LF]QL.RPLWHWRZL%DGD1DXNowych. Literatura [1] Duch W., Diercksen G. H. F. (1995): Feature Space Mapping as a universal adaptive system. -- Computer Physics Communications, Vol 87, pp. 341-371. [2] Duch W. (1997): Platonic model of mind as an approximation to neurodynamics. [w:] Brainlike computing and intelligent information systems (S-i. Amari, N. Kasabov, Ed.). Singapore Springer, rozdz. 20, s. 491-512. [3] Bishop C. (1995): Neural network for pattern recognition. Oxford: Clarendon Press. [4] Duch W. (1996): From cognitive models to neurofuzzy systems - the mind space approach. -- Systems Analysis-Modeling-Simulation, Vol. 24, pp. 53-65. [5] Duch W., Jankowski N. (1999): Survey of neural transfer functions -- Neural Computing Surveys, Vol. 2, pp. 163-213. [6] Duch W., Adamczak R., Jankowski N. (1997): Initialization of adaptive parameters in density networks -- Third Conference on Neural Networks and Their Applications, Kule, SD(G]LHUQLN 1997, s. 99-104. [7] Kohonen T. (1995): Self-organizing maps. -- Heidelberg Berlin: Springer-Verlag. [8] Blake C. L. and Merz C. J. (1999), UCI repository of machine learning databases. -- http://www.ics.uci.edu/~mlearn/mlrepository.html [9] 'XFK : *UXG]LVNL. The weighted k-nn method with selection of features and its neural realization. -- 4 th Conference on Neural Networks and Their Applications, Zakopane, Maj 1999, s. 191-196. [10] Quinlan J. R. (1993): C4.5: Programs for machine learning.-- Morgan Kaufmann, San Mateo, CA. [11] 'XFK : $GDPF]DN 5 *UEF]HZVNL. Methodology of extraction, optimization and application of crisp and fuzzy logical rules. -- IEEE Transactions on Neural Networks special issue on Data Mining. [12] Lahav O., Naim A., Sodre L. Jr. and Storne-Lombardi M. C. (1995): Neural Comptutation as a tool for galaxy classification: methods and examples. -- Institute od Astronomy, Cambridge, Technical report CB3 OHA. [13] Duch W., Adamczak R., Grbczewski K., )DO * +D\DVKL < Fuzzy and crisp logical rule extraction methods in application to medical data. -- Computational Intelligence and Applications (P.S. Szczepaniak. Ed.) Springer, Studies in Fuzziness and Soft Computing, Vol. 23. [14] Weiss S.M., Kapouleas I. (1990): An empirical comparison of pattern recognition, neural nets and machine learning classification methods. [w:] Readings in Machine Learning (Shavlik J.W. and Dietterich T.G. Ed.). -- Morgan Kauffman Publ, CA. [15] Churchland P.S., Sejnowski T.J. (1992): The computational brain. -- MIT, Bradford Book. [16] Thelen E., Smith L.B. (1994): A Dynamic Systems Approach to the Development of Cognition and Action. -- MIT Press. [17] Breiman L. (1998): Bias-variance, regularization, instability and stabilization. -- Neural Networks and Machine Learning (Bishop C. M. Ed.), s. 27 56. Springer-Verlag.