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 Rb-
roty 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":\GDMHVL*HQLH1DZHWZFKHPLLLIL]\FHNRQFHSFMHIHQRPHQRORJLF]QHNWyUH

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*HPXVLLVWQLHüWHRULDSR]ZDODMFDX]\VNDüNRQFHSFMH

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\MDQLHQLDFHFKSURFHVXSR]QDZF]HJRF]áRZLHNDWDNLFKMDN

LGHQW\ILNDFMDDVRFMDFMDJHQHUDOL]DFMDUy*QHVWDQ\XP\VáX

4.

.RQVWUXNFMDV\VWHPXDGDSWDF\MQHJRRGSRZLDGDMFHJRVSHF\ILNDFMRPV\VWHPXNWyU\E-

G]LHXF]\áVL]SU]\NáDGyZLRJyOQ\FKSUDZZQLRVNRZDáX*\ZDáQDWXUDOQHJRM]\NDL

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-
PDFMDSR]ZDODX*\üZ 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]FLHMSU]H]Uy*QHPDS\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 ]QDMGXM VL Z SU]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

Zastosowanie funkcji separowalnych pozwala na przeszukiwanie przestrzeni cech pomimo
Z\VWSRZDQLD ZDUWRFL EUDNXMF\FK 8PR*OLZLD WR Z\V]XNDQLH Z]áD QDMEDUG]LHM RGSRZLa-

GDMFHJRDNWXDOQ\PGDQ\PZHMFLRZ\PMDNUyZQLH*GRSHáQLHQLHEUDNXMFHMZDUWRFLSRSU]H]

X]XSHáQLHQLHIDNWXQDSRGVWDZLHWHRULLRSLV\ZDQHMSU]H]Z\V]XNDQ\Z]Há:LHG]D]DSLVDQD

ZSU]HVWU]HQLFHFKMHVWZLFX*\ZDQDZSURFHVLHSU]HV]XNLZDQLDZWDNLVDPVSRVyEMDNZLe-

G]DKHXU\VW\F]QDX*\ZDQDMHVWSU]H]HNVSHUWDGR]PQLHMV]HQLDSU]HVWU]HQLSRV]XNiZD

0RGHO)60PR*HE\üUyZQLH*]DVWRVRZDQ\GRRGNU\ZDQLDZLHG]\SUDZNWyUHPRJ]RVWDü

Z\GHGXNRZDQH]SU]\NáDGyZ3UDZDWHPRJE\üUHSUH]HQWRZDQHSU]H]IXQNFMHJDXVVRZVNLH

ZyZF]DVUR]P\FLHIXQNFMLJDXVVRZVNLHMRGSRZLDGDMFHMGDQHPXIDNWRZLMHVWPLDU]DXIDQLD

GRWHJRIDNWXJG]LH]DXIDQLHED]XMHQDOLF]ELH]DSUH]HQWRZDQ\FKSU]\NáDGyZ

7RSRJUDILF]QDVWUXNWXUDSU]HVWU]HQLFHFKPR*HSRGOHJDüRJUDQLF]HQLRP]ZL]DQ\P]V\PEo-

OLF]QZLHG]DSULRU\F]Q]DOH*QRFLSRPLG]\HOHPHQWDPLZHNWRUDZHMFLRZHJR6]NLHOHW

WHMVWUXNWXU\WZRU]\VLNRU]\VWDMF]PHWRGLQLFMDOL]DFMLRSDUW\FKQDNODVWHU\]DFMLDV]F]HJyá\

XVWDODM VL Z Z\QLNX SURFHVX XF]HQLD : SHZQ\P VHQVLH MHVW WR ZLF PHWDPRGHO JG\*

PR*OLZDMHVWUy*QDVSHF\ILNDFMDMHJRPDWHPDW\F]Q\FKDVSHNWyZ3LHUZRWQLQVSLUDFMGRMHJR

VWZRU]HQLDE\áDSUyEDZSURZDG]HQLDSRUHGQLHJRSR]LRPXRSLVXIXQNFMLSR]QDZF]\FKMDNR

SU]\EOL*HQLDGRneurodynamiki [2]Z\VRNDDNW\ZQRüQHXURQyZZ\V\áDMF\FKLPSXOV\RSi-

V\ZDQDMHVWSU]H]GX*JVWRüSUDZGRSRGRELHVWZDZ W\P REV]DU]H SU]HVWU]HQL NWyU\ Rd-

SRZLDGD NRPELQDFML FHFK NRQLHF]Q\FK GR Z\ZRáDQLD WDNLHM DNW\ZQRFL 3UREDELOLVW\F]Q\
punkt widzenia jest bardzo przydatny do opisu sieci neuronowych [3].

:WHMSUDF\RJUDQLF]\P\VLW\ONRGR]DVWRVRZDQLDPRGHOX)60GR]DJDGQLHNODV\ILNDFML

SRGQDG]RUHP3U]H]SRMFLHNODV\ILNDFMLUR]XPLHVLG]LHOHQLHGRZROQHJR]ELRUXHOHPHQWyZ

QDJUXS\GRNWyU\FK]DOLF]DVLHOHPHQW\Uy*QLFHVLDOHSRGREQHWMPDMFHZáDVQRFLZy-

Uy*QLDMFHGDQJUXS=ELyUHOHPHQWyZQDOH*F\FKGRMHGQHMJUXS\QD]\ZDQ\ MHVW NODV D

ND*G\HOHPHQWNODV\±RELHNWHP:NODV\ILNDFMLSRGQDG]RUHPVWUXNWXUDNDWHJRULLMHVW]QDQD

F]\OLG\VSRQXMHVLFKDUDNWHU\VW\NNODV]NWyU\FKSRFKRG]RELHNW\.ODV\ILNDWRU\RSDUWHQD
sieciach neuronowych na podstawie zadanego zbioru N

SU]\SDGNyZ]ZDQHJRFLJLHPWUHQLn-

gowym (X

i

, C

i

), i= 1..N, gdzie X jest m-

Z\PLDURZ\P ZHNWRUHP FHFK RSLVXMF\P GDQ\

obiekt, natomiast C

i

MHVWRGSRZLHGQLR]DNRGRZDQHW\NLHWNODV\GRSDVRZXMSDUDPHWU\Dd-

aptacyjne W (

SURFHVWHQQD]\ZDVLXPRZQLHÄXF]HQLHP´ZWDNLVSRVyEE\GRNRQDüSRQL*-

V]HJRSU]\EOL*RQHJRPDSRZania

(

;

)

i

i

f

C

=

X W

gdzie f

MHVWIXQNFMNWyUUHDOL]XMHVLHü-HVWWRRGZ]RURZDQLHSU]\EOL*RQHJG\*QLHZ\Pa-

JDP\]Z\NOHE\VLHüGDZDáDQDZ\MFLXGRNáDGQLHZDUWRüC

i

DMHG\QLHZDUWRüSR]ZDODMFD

Z\UD(QLHRGUy*QLüC

i

od C

j

,ORüSDUDPHWUyZDGDSWDF\MQ\FKMDNLDOJRU\WPXF]HQLD]DOH*RG

architektury sieci.

3. Architektura sieci FSM.

3RZD*Q\P SUREOHPHP ZLHOX DOJRU\WPyZ UHDOL]XMF\FK PRGHOH VLHFL QHXURQRZ\FK MHVW WDNL

GREyUDUFKLWHNWXU\VLHFLOLF]E\XNU\W\FKQHXURQyZOLF]E\ZDUVWZXNU\W\FKWRSRORJLLSRá-

F]HDE\X]\VNDüMDNQDMOHSV]JHQHUDOL]DFM,VWQLHMHZLHOHWHFKQLNRSW\PDOL]DFMLDUFKLWHNWu-

U\SURZDG]F\FKGRWHJRFHOX2EV]HUQDNODVDPHWRGRSDUWDMHVWQDDOJRU\WPDFKNRQVWUXNWy-

ZLVW\F]Q\FK SUyEXMF\FK ZEXGRZDü RSW\PDOL]DFM DUFKLWHNWXU\ VLHFL Z DOJRU\WP XF]HQLD

6WRVXMHVLWU]\WHFKQLNLNRQVWUuowania sieci:

1.

5R]SRF]\QD VL ] VLHFL SRVLDGDMF GX* QDGPLDURZ OLF]E Z]áyZ NWyUH Z PLDU

PR*OLZRFLVXVXZDQHSRGF]DVXF]HQLD

2.

7ZRU]\ VL VLHü RG ]HUD W]Q QD SRF]WNX LVWQLHMH W\ONR ZDUVWZD ZHMFLRZD L Z\MFLRZD

QDWRPLDVWZDUVWZ\XNU\WHMQLHPDZFDOHOXEWH*MHVWDOH]QLHZLHONOLF]EZ]áyZ:

WUDNFLH XF]HQLD VWRSQLRZR GRVWDZLDQH V NROHMQH QHXURQ\ RUD] HZHQWXDOQLH NROHMQH ZDr-

VWZ\XNU\WH'RWHMNDWHJRULL]DOLF]\üPR*QDWDNLHPRGHOHVLHFLMDNNRUHODFMDNDVNDGRZD

VLHü5$1MDNLZHUVMPRGHOX)60MHOLQLHVWRVXMHP\ZVWSQHMLQLFMDOL]DFML

3.

6LHü GRSDVRZXMH VZRM VWUXNWXU GR QDSá\ZDMF\FK GDQ\FK ]PLHQLDMF ]áR*RQRü SU]H]

GRGDZDQLHXVXZDQLHLáF]HQLHQHXURQyZ6LHü)60QDOH*\GRWHMNDWHJorii.

:VLHFL)60Z\VWSXMW\ONRWU]\ZDUVWZ\QHXURQyZZHMFLRZDXNU\WDLZ\MFLRZD/LF]ED

Z]áyZZZDUVWZLHZHMFLRZHMMHVWXVWDORQDQDSRF]WNXSURFHVXXF]HQLDLMHVWUyZQDZ\PLa-

URZLZHNWRUyZZHMFLRZ\FK:ZDUVWZLHZ\MFLRZHMZ\VWDUF]\W\ONRMHGHQZ]HáPR*QDWH*

X*\ZDüMHGQHJRZ]áDQDMHGQNODVNWyUHJR]DGDQLHPMHVWRNUHOHQLHQDSRGVWDZLHZ]Eu-

G]HQHXURQyZZZDUVWZLHXNU\WHMGRNWyUHMNODV\QDOH*\ZHNWRUZHMFLRZ\X:]á\ZDr-

VWZ\XNU\WHMSRáF]RQHV]HZV]\VWNLPLQHXURQDPLZDUVWZ\ZHMFLRZHMRUD]]Z]áHPZ\j-

FLRZ\P6LHü)60PR*HPLHüVWUXNWXUPRGXáRZVNáDGDMFVL]NLONXSRGVLHFLVSHFMDOi-

]XMF\FKVLZNODV\ILNDFML GDQ\FK ZHMFLRZ\FK RNUHORQ\FK SU]H] FHFK\ MHGQHJR W\SX [4],
ale dla celów tutaj przedstawionych nie jest ona wykorzystywana.

x

1

x

2

x

3

x

4

Σ

1

2

3

5

W

W

W

W

2

3

4

5

W

2

2

2

2

1

s(x)

s

s

s

s

FSM(x)

4

Informacje dodatkowe

:VSyáF]\QQLN

zaufania

Architektura sieci FSM

:V]\VWNLHZ]á\ZZDUVWZLHXNU\WHMUHDOL]XMGRZROQIXQNFMIDNWRU\]RZDOQ *

; '

σ

.

:DUXQHNIDNWRU\]RZDOQRFLSR]ZDODWUDNWRZDüND*G\]Z\PLDUyZMDNRQLH]DOH*Q\RGSR]o-

VWDá\FK)DNWRU\]RZDOQHIXQNFMHWUDQVIHUXPDMDSRVWDü

( ; , )

(

;

,

)

i

i

i

i

i

G

G X R

σ

σ

=

∏

X R

JG]LH ND*G\ ]H VNáDGQLNyZ VSDUDPHWU\]RZDQ\ MHVW SU]H] SRáR*HQLH L GRGDWNRZ\ SDUDPHWU

NWyU\GODIXQNFML]ORNDOL]RZDQ\FKSHáQLUROG\VSHUVML&HFKFKDUDNWHU\VW\F]QIXQNFML]Oo-

NDOL]RZDQ\FKMHVWWR*HZDUWRüPDNV\PDOQRVLJDMRQHZVZRLPFHQWUXPZPLDURGGa-

ODQLDVLRGFHQWUXPZDUWRüWDPDOHMHGR]HUD1DMEDUG]LHM]QDQ\PSU]\NáDGHPWHJRURG]DMX

IXQNFMLMHVWIXQNFMDJDXVVRZVND&KRFLD*WHRUHW\F]QLHQLHPDLQQ\FKRJUDQLF]HQDIXQNFMH

DNW\ZDFMLZ)60ZSUDNW\FHMHGQDNQDUD]LHVWRVRZDQHE\á\W\ONRIXQNFMH]ORNDOL]RZDQHR

ZDUWRFLDFKSU]HVNDORZDQ\FKGRSU]HG]LDáX>@=PLDQDZDUWRFLDNW\ZDFMLZPLDURGGa-

ODQLDVLRGFHQWUXPPR*HE\üUyZQLH*VNRNRZDFRPDPLHMVFHZSU]\SDGNXX*\FLDIXQNFML

SURVWRNWQHM'RW\FKF]DVZ)60VWRVRZDQHE\á\QDVWSXMFHIXQNFMHDNW\ZDFMLJDXVVRZVNLH
trapezoidalne, bicentralne [5]

SURVWRNWQHLWUyjNWQH

1DMOHSV]HUH]XOWDW\]DUyZQRSRGZ]JOGHPOLF]E\SRZVWDá\FKZ]áyZMDNLJHQHUDOL]DFMLX]y-

VNLZDQHE\á\GODIXQNFMLJDXVVRZVNLHM:\EyUIXQNFMLDNW\ZDFML]DOH*Q\MHVWRGFHOXNWyU\

FKFHP\X]\VNDüQSGRVWZRU]HQLDNODV\ILNDWRUDNWyUHJRG]LDáDQLHPR*HP\ZSURVW\VSRVyE

SU]HOHG]LüQDMOHSLHMQDGDMVLUHJXá\ORJLF]QHNWyUHZ)60PR*QDX]\VNDüVWRVXMFIXQNFMH

SURVWRNWQH8*\ZDMFQDWRPLDVWIXQNFMLJDXVVRZVNLHMPR*QDUyZQLH*X]\VNDüUHJXá\VWR

MHGQDN UHJXá\ UR]P\WH NWyU\FK LQWHUSUHWDFMD MHVW ]QDF]QLH WUXGQLHMV]D RG NODV\F]Q\FK UHJXá

ORJLF]Q\FK.D*G\Z]HáXNU\W\FKDUDNWHU\]RZDQ\MHVWSU]H]SRáR*HQLHR, i rozmycie

σ

, które

SRWU]HEQHVGRZ\OLF]HQLDIXQNFMLDNW\ZDFML3R]DW\PZ\VWSXMMHV]F]HZLHONRFLNWyUHQLH

PDMZSá\ZXQDZDUWRüZ]EXG]HQLDDOHVSRWU]HEQHZWUDNFLHXF]HQLDGRRNUHOHQLDZLHl-

NRFL]PLDQSR]RVWDá\FKSDUDPHWUyZ6WRPDVDm RNUHODMFDOLF]EZHNWRUyZNODV\ILNo-

ZDQ\FKSU]H]GDQ\ Z]Há L F]DV SRZVWDQLD

τ

n

, czyli numer epoki, w której

GDQ\ Z]Há So-

ZVWDá

4. Inicjalizacja

3RQLHZD* DOJRU\WP XF]HQLD Z )60 MHVW DOJRU\WPHP NRQVWUXNW\ZLVW\F]Q\P WR PR*QD SU]y-

VSLHV]\üSURFHVXF]HQLDSRSU]H]ZVWSQHRV]DFRZDQLHOLF]E\Z]áyZXNU\W\FKLRGSRZLHGQLH
ich zainicjowanie [6]

2V]DFRZDQLHWRSRZLQQRE\üUDF]HMRSW\PLVW\F]QHW]QOLF]EDZ]áyZ

XWZRU]RQD SRGF]DV LQLFMDOL]DFML SRZLQQD E\ü ]DQL*RQD : SU]HFLZQ\P Z\SDGNX ZVWSQD

LQLFMDOL]DFMDSURZDG]LGR]E\WQLHJRUR]GUREQLHQLDLQDZHWSRX*\FLXRSW\PDOL]DFMLQLHX]\VND

VLGREU\FKUH]Xltatów.

']LNL VWRVRZDQLX IXQNFML ]ORNDOL]RZDQ\FK GR XVWDOHQLD OLF]E\ Z]áyZ XNU\W\FK MDN L LFK

]DLQLFMRZDQLDPR*QDX*\üPHWRGRSDUW\FKQDJUXSRZDQLX:Z\QLNXNODVWHU\]DFMLRWU]\Pu-

MHP\]ELyUVNXSLVNSURWRW\SyZZURGNXNWyU\FKXVWDZLDQHVZ]á\VLHFL3RáR*HQLHND*Ge-

JR]WDNSRZVWDá\FKQHXURQyZREOLF]DQHMHVWMDNRUHGQLD]SRáR*HGODND*GHJRZ\PLDUX

RVREQR ZV]\VWNLFK ZHNWRUyZ ZSDGDMF\FK GR GDQHJR VNXSLVND NODVWUD 5R]P\FLD W\FK

SURWRW\SyZXVWDODQHVQDSRGVWDZLHZLHONRFLRGSRZLDGDMF\FKLPNODVWUyZ*G\NWyUH]

UR]P\üPDZDUWRü]HURZV]\VWNLHZHNWRU\PDMWVDPZDUWRüMHGQHM]FHFKSU]\MPRZa-

QDMHVWPLQLPDOQDZDUWRüQLH]HURZD=XZDJLQDWR*HIXQNFMDDNW\ZDFMLMHVWLORF]\QHPSR

SRV]F]HJyOQ\FKZ\PLDUDFKMHOLFKRüMHGQD]HVNáDGRZ\FKPDZDUWRüWRFDáDIXQNFMDDk-

W\ZDFMLMHVW]HURZD7DNXVWDORQHUR]P\FLD]RVWDMQDVWSQLHSURSRUFMRQDOQLH]ZLNV]RQHSR

WRDE\VLHüZSRF]WNRZHMID]LHXF]HQLDRGUD]XNODV\ILNRZDáDEH]Z]JOGXQDSRSUDZQRü

ZV]\VWNLHZHNWRU\]FLJXWUHQLQJRZHJR']LNLWHPXXQLNDVLSU]\SDGNRZHJRZVWDZLDQLD

Z]áyZQDSoF]WNXXF]HQLD
Jednym z algorytmów stosowanych w FSM do inicjalizacji sieci jest drzewo decyzyjne budo-
ZDQHQDSRGVWDZLHKLVWRJUDPXXWZRU]RQHJRGODND*GHJRZ\PLDUXRVREQR

0

5

10

15

20

25

30

35

Dany wymiar dzielony jest na k

SU]HG]LDáyZR;QDU\VXQNX:ND*G\PSU]HG]LDOH]OLF]a-

QDMHVWOLF]EDZHNWRUyZNWyUDGRQLHJRZSDGDR<QDU\VXQNX.D*G\]SU]HG]LDáyZPR*H

E\üáF]RQ\]VVLHGQLPLSU]HG]LDáDPLWZRU]FZWHQVSRVyEVNXSLVNRZSU]HVWU]HQLMHGQo-

Z\PLDURZHM-H*HOLZGDQ\PZ\PLDU]HZ\VWSXMHZLHOHVNXSLVNWREGRQHRGG]LHORQHSu-

VW\PL SU]HG]LDáDPL OXE WH* PLG]\ NROHMQ\PL SU]HG]LDáDPL Z\VWSL EDUG]R GX*D Uy*QLFD Z

]DZDUWRFL ZHNWRUyZ SU]HGVWDZLRQR WR QD SRZ\*V]\P U\VXQNX JG]LH PR*QD Z\Uy*QLü

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ND*G\RV]HURNRFLs. Wówczas pozycja oraz rozmiar skupiska w oryginalnej przestrzeni mo-

*H]RVWDüSU]HGVWDZLRQDZQDVWSXMF\VSRVyE

k

X

X

s

ls

i

s

X

C

x

x

|

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2

1

)

2

1

(

min

max

min

−

=

=

+

+

=

σ

x

1

=

a

1

x

2

=

a

2

V

1

=

f(a

1

;a

2

;a

3

)g

x

3

=

a

3

b

2

V

2

=

f(a

1

;b

2

;a

3

)g

a

3

b

1

a

2

V

3

=

f(b

1

;a

2

;b

3

)g

b

3

c

2

V

4

=

f(b

1

;c

2

;b

3

)g

b

3

x

3

a

3

b

3

x

2

a

2

b

2

c

2

x

2

a

1

b

1

Drzewo decyzyjne

.D*GH ] W\FK MHGQRZ\PLDURZ\FK VNXSLVN PR*H ]RVWDü QDVWSQLH ]U]XWRZDQH QD ZLHOH URz-
separowanych N-

Z\PLDURZ\FKVNXSLVN3RGF]DVLQLFMDOL]DFMLZHNWRU\DQDOL]RZDQHVZND*-

G\PZ\PLDU]HQLH]DOH*QLHWDNZLFZSLHUZV]\PZ\PLDU]HGDQ\ZHNWRUPR*HQDOH*HüQSGR

skupiska

i

C

1

, w drugim wymiarze do skupiska

j

C

2

D*ZUHV]FLHZN-tym wymiarze

l

N

C

.D*G\

taki N-

Z\PLDURZ\NODVWHUPR*HE\üSU]HGVWDZLRQ\MDNRáDFXFKQL*HMZ\PLDURZ\FKVNXSLVN

l

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j

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...

2

1

VWGWHJRW\SXSURFHGXUDWZRU]\GU]HZRGHF\]\MQH:OLFLDFKGU]HZD

]OLF]DQH V ZHNWRU\ NWyUH QDOH* GR GDQHJR N-wymiarowego skupiska. Gdy w przypadku

NWyUHJRNROZLHN]Z\PLDUyZOLF]EDNODVWUyZMHVW]E\WGX*D]PQLHMV]RQD]RVWDMHUR]G]LHOF]Rü
k

FRSRZRGXMH]PQLHMV]HQLHOLF]E\NODVWUyZGODGDQHJRZ\PLDUX*G\ZV]\VWNLHNODVWU\V

MX*XWZRU]RQHREOLF]DQDMHVWRGOHJáRüPLG]\QLPL7HVNXSLVNDPLG]\NWyU\PLRGOHJáRü
jest mniej

V]DRG]DGDQHJRSURJXVáF]RQHZMHGHQ

: SRZ\*V]\PGU]HZLHGHF\]\MQ\PUR]G]LHOF]Rü KLVWRJUDPyZ MHVW VWRSQLRZR ]ZLNV]DQD

,QQ\P UR]ZL]DQLHP RSDUW\P QD PHWRG]LH GHQGURJUDPyZ NWyUH F]DVHP SURZDG]L GR OHp-

V]\FKUH]XOWDWyZMHVWVWRSQLRZH]PQLHMV]DQLHUR]G]LHOF]RFL3RF]WNRZRND*G\ZHNWRUFL-

JXWUHQLQJRZHJRMHVWRGG]LHOQ\PVNXSLVNLHP:\]QDF]RQD]RVWDMHPDFLHU]RGOHJáRFLPLG]\

SRV]F]HJyOQ\PLVNXSLVNDPLLQDMHMSRGVWDZLHQDMEOL*V]HVNXSLVNDV]HVREáF]RQH&DáD

SURFHGXUDWUZDWDNGáXJRD*OLF]EDVNXSLVNMHVWZ\VWDUF]DMFRPDáDOXEWH*D*RGOHJáRüPL-

G]\VNXSLVNDPLMHVWZLNV]DRG]DGDQHMSURJRZHM3RQL*V]\U\VXQHNSU]HGVWDZLDVFKHPDW\Fz-

QLHLGHGHQGURJUDPyZ

Clusters

d(c

i

;

c

j

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•

c

1

•

c

2

•

c

3

•

c

4

•

c

5

•

c

6

•

c

7

•

c

8

Dendrogram

:DGPHWRG\GHQGURJUDPyZMHVWNRQLHF]QRüWZRU]HQLDPDFLHU]\RGOHJáRFLFRZSU]\SDGNX

GX*HMOLF]E\ZHNWRUyZWUHQLQJRZ\FKSURZDG]LGR]QDF]QHJRVSRZROQLHQLDSURFHVXJUXSRZa-

QLD RUD] GX*HJR ]DSRWU]HERZDQLD QD SDPLü : WDNLHM V\WXDFML GREU\P UR]ZL]DQLHP MHVW
zmniejsze

QLHUR]G]LHOF]RFLGDQ\FK

2EOLF]HQLD ] UHJXá\ Z\NRQ\ZDQH V GOD OLF]E ]PLHQQRSU]HFLQNRZ\FK PDMF\FK EDMWRZ

UHSUH]HQWDFM FR GOD GDQ\FK SU]HQRUPDOL]RZDQ\FK GR SU]HG]LDáX >@ GDMH UR]G]LHOF]Rü

7

10

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r

'ODUR]G]LHOF]RFL r ZV]\VWNLHGDQH]SU]HG]LDáX

]

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[

r

a

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PDMWVDPZDUWRü

3U]HGGRNRQDQLHPREFLFLDGRNáDGQRFLZV]\VWNLHGDQH]FLJXWUHQLQJRZHJRSU]HVNDORZy-
ZDQHVGRPDNV\PDOQHJR]DNUHVX

]

2

,

0

[

32

min

max

32

min

2

);

(

X

X

C

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X

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r

r

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=

−

=

$E\ X]\VNDü UR]G]LHOF]Rü

k

r

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k

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k

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33

33

min

2

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1

=

k

wszystkie dane X

V PDSRZDQH GR GZyFK NODVWUyZ GOD N RWU]\PXMHP\ GDQH

RU\JLQDOQH/LF]ED]QDF]F\FKELWyZMHVW]ZLNV]DQDWDNGáXJRD*RVLJQLWD]RVWDQLHGRSXVz-
czalna liczba skupisk.
:ID]LHJUXSRZDQLDG*\VLGRWHJRDE\SRZVWDáHNODVWU\RSLV\ZDá\MHG\QLHRGG]LHOQHZy-

UD(QHVNXSLVNDGODGDQHMNODV\DQLHLFK]áR*RQVWUXNWXUZHZQWU]Q=DSHZQLDWR*HVWo-

VRZDQHRV]DFRZDQLHEG]LHÄRSW\PLVW\F]QH´$OJRU\WPLQLFMDOL]DFMLDXWRPDW\F]QLHZ\]QDF]D

OLF]EVNXSLVNGODGDQHJRSUREOHPX3URFHVJUXSRZDQLDPR*HE\üSU]HSURZDG]RQ\GODND*GHM

NODV\RVREQRFRSR]ZDOD]QDOH(üVNXSLVNDFKDUDNWHU\VW\F]QHGODWHMNODV\RUD]]DLQLFMRZDü

VLHü Z WDNL VSRVyE DE\ ND*GD ] NODV E\áD UHSUH]HQWRZDQD SU]H] FR QDMPQLHM MHGHQ Z]Há

0R*QDWH*SURFHVJUXSRZDQLDSU]HSURZDG]LüGODZV]\VWNLFKNODVMHGQRF]HQLH:W\PSU]y-

SDGNXSRGF]DVJUXSRZDQLDZ\NRU]\VWXMHVLGRGDWNRZLQIRUPDFMSU]\QDOH*QRüGRNODV\L

EXGXMFVNXSLVNRDQDOL]XMHVLMHJRGRNáDGQRüW]QOLF]EZHNWRUyZ]LQWHUHVXMFHMQDVNODV\

ZVWRVXQNXGRZV]\VWNLFKZHNWRUyZQDOH*F\FKGRWHJRVNXSLVND:PRPHQFLHJG\MDNRü

VNXSLVND]QDF]QLHVLSRJDUV]DSU]HU\ZDVLáF]HQLHJUXSGRWHJRVNXSLVND-HVWWREDUG]R
wygodny punkt stopu dla metody dendrogramów.
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SRVLDGDMX*MDNLHZ]á\XNU\WH

5. Algorytm Uczenia

1DZHMFLHVLHFLSRGDZDQ\MHVWZHNWRUZ\ELHUDQ\ORVRZR]FLJXWUHQLQJRZHJR:\EyUGo-

NRQ\ZDQ\MHVWZWDNLVSRVyEDE\ND*G\]ZHNWRUyZZGDQHMVHULLSRMDZLáVLGRNáDGQLH raz.

*G\FDá\FLJWUHQLQJRZ\]RVWDQLHMX*SRND]DQ\SURFHGXUD]RVWDMHSRZWyU]RQD.D*GDWDND

VHULD QD]\ZDQD MHVW HSRN 3URFHV XF]HQLD WUZD WDN GáXJR D* VSHáQLRQH ]RVWDQLH NU\WHULXP
zako

czenia opisane poni*ej&Dá\SURFHVXF]HQLDSRG]LHOLüPR*QDQDGZLHID]\

)D]D0RG\ILNDFMDSDUDPHWUyZLVWQLHMF\FKSURWRW\SyZWMSRáR*HQHXURQyZLFKUR]P\ü
mas i czasów powstania.
Faza 2: Dostawianie nowych neuronów.

5.1. Faza I

-HOLZHNWRUZHMFLRZ\MHVWGRVWDWHF]QLHSRGREQ\GRLVWQLHMFHJRZ]áDZ\VWDUF]\]PRG\Ii-

NRZDüSDUDPHWU\RSLVXMFHWHQZ]Há3RGRELHVWZRZ\]QDF]DQHMHVWQDSRGVWDZLHRGOHJáo-

FLHXNOLGHVRZHMPLG]\ZHNWRUHPZHMFLRZ\PDSRV]F]HJyOQ\PLQHXURQDPLZVLHFLOXEWH*

QDSRGVWDZLHSREXG]HQLDZ]áyZ:SU]\SDGNXJG\GZD Z]á\ UHSUH]HQWXMFH Uy*QH NODV\

PDMWVDPZDUWRüIXQNFMLDNW\ZDFMLZSU]\SDGNXIXQNFMLJDXVVRZVNLFKPR*HVLWR]Ga-

U]Dü U]DGNR MHGQDN Z SU]\SDGNX IXQNFML SURVWRNWQ\FK EDUG]R F]VWR Z\ELHUDQ\ MHVW WHQ

NWyU\QDOH*\GRLQQHMNODV\QL*ZHNWRUZHMFLRZ\SU]H]FRZREOLF]DQLXNRFRZHMNODV\ILNa-

FMLPDP\GODWDNLHJRZHNWRUDZHMFLRZHJREáG=DQDMEDUG]LHMSRGREQ\X]QDZDQ\MHVWWHQ

Z]HáNWyU\MHVWQDMEOL*V]\ZVHQVLHHXNOLGHVRZ\PF]\OL min (||

||)

k

k

−

X R

) do wektora wej-

FLRZHJRX-H*HOLQDMEOL*V]\MHVWZ]Há]WHMVDPHMNODV\FRZHNWRUZHMFLRZ\GRNRQXMHP\

RSW\PDOL]DFML MHJR SDUDPHWUyZ -H*HOL MHVW WR QHXURQ UHSUH]HQWXMF\ LQQ NODV QL* ZHNWRU

ZHMFLRZ\SRV]XNXMHP\Z]áDNWyU\XOHJDQDMZLNV]HPXZ]EXG]HQLX-HOLWHQZ]HáQDOH*\

GRNODV\ZHNWRUDZHMFLRZHJRWRSU]HSURZDG]DP\MHJRRSW\PDOL]DFMZSU]HFLZQ\PUD]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*MHGQDNGRRNUHOe-
nia podo

ELHVWZDPLG]\Z]áHPDZHNWRUHPZHMFLRZ\PX*\ZDQDMHVWRGOHJáRüHXNOide-

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]áD WDN DE\ Z ND*G\P Z\PLDU]H ]

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(

)

i

i

i

i

R

R

X

R

m

κ

= +

−

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FLRZ\PSRGREQLHMDNSRáR*HQLHGODND*GHJRZ\PLDUXRVREQRRUD]GRDNWXDOQHJRZ]Eu-

G]HQLDWHJRZ]áDLRGZURWQLHSURSRUFMRQDOQLHGRF]DVXMHJR*\FLD

τ−τ

n

:

(

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|

1

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i

i

i

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n

G X R

X

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σ

σ σ γ

τ τ

−

−

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+ −

Λ

&]DV*\FLDMHVWWRUy*QLFDDNWXDOQHJRQXPHUXHSRNL

τ

LF]DVXSRZVWDQLDZ]áD

τ

n

(czyli nume-

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DGDSWDF\MQH2F]\ZLFLHZWUDNFLHXF]HQLDQXPHUHSRNL

τ

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τ− τ

n

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0. Parametry uczenia

κ, γ

GRSDVRZ\ZDQHVZVSRVyEDXWRPDW\F]Q\LQG\ZLGXDOQLHGODND*-

dego w

]áD

(

)

1

/

n

γ

τ τ

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=

+ −

Λ

;

(

)

1

/

n

κ

τ τ

Κ

=

+ −

Λ

Parametr

Λ

RNUHODV]\ENRü]PQLHMV]DQLDVLSDUDPHWUyZXF]HQLDSDUDPHWUWHQXVWDORQ\MHVW

QDSRF]WNXXF]HQLDLZáDFLZLHZHZV]\VWNLFKGRW\FKF]DVRZ\FK]DVWRVRZDQLDFKPLDá]Dw-

V]H WDN VDP ZDUWRü QDWRPLDVW

Γ

i

Κ

V SRF]WNRZ\PL ZDUWRFLDPL SDUDPHWUyZ

XF]HQLDNWyUHWU]HEDXVWDOLüSU]HGURzSRF]FLHPXF]HQLD

3RQLHZD*]PLDQDUR]P\FLDMHVWSURSRUFMRQDOQDGR

−

G),

QDWRPLDVWZDUWRüPDNV\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]RQDRMe-
den: m=m

1DSRF]WNXQRZHMHSRNLPDVDZV]\VWNLFKZ]áyZMHVWXVWDODQDQDZDUWRü

:FHOXXQLNQLFLD]E\WVLOQHJRQDNáDGDQLDVLZ]áyZUHSUH]HQWXMF\FKUy*QHNODV\QDVLHELH

ZF]DVLHRSW\PDOL]DFMLSRGHMPRZDQDMHVWUyZQLH*SUyED]PQLHMV]HQLDSRGRELHVWZDGRZ]áD

EGFHJRQDMZLNV]\P]DJUR*HQLHP:]HáNWyU\E\áRSW\PDOL]RZDQ\F]\OLZ]HáQDMEDU

G]LHM SRGREQ\ GR ZHNWRUD ZHMFLRZHJR ]RVWDMH Z\áF]RQ\ ] REOLF]H L SRV]XNLZDQ\ MHVW

Z]HáQDMEDUG]LHMZ]EXG]DMF\VL-H*HOLMHVWRQ]LQQHMNODV\QL*ZHNWRUZHMFLRZ\QDOH*\

]PQLHMV]\üMHJRSRGRELHVWZRSoprzez zmniejszenie przypisanego mu rozmycia:

(

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|

|

; ,

1

/

i

i

i

i

n

X

R

G X R

σ σ υ

σ

τ τ

−

= −

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:DUWRüSDUDPHWUX

υ

GODGX*\FKZEXG]H*!Z\QRVLGODPDá\FKZSU]\SDGNXJG\

UR]P\FLHSU]\MPXMHXMHPQZDUWRüEUDQDMHVWZDUWRüEH]Z]JOGQD

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F]\OL]ZLNV]DP\MHJRF]DVSRZVWDQLD

(

)

/ 2

n

n

n

τ

τ

τ τ

= + −

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]H]JRGQDWRE\Z]á\UHSUH]HQWXMFHWVDPNODVQDNáDGDá\VLQDVLHELH0R*QDZLF

VWZLHUG]Lü*HSRGF]DVWHMID]\XF]HQLDQDVWSXMHVDPRRUJDQL]DFMD[6],[7] z nadzorem czyli z

XZ]JOGQLeniem informacji o klasach.

5.2. Faza II

1RZ\Z]HáZVWDZLDQ\MHVWGRVLHFLZWHG\JG\GODLVWQLHMFHJRZHNWRUDZHMFLRZHJR]DUyw-

QRQDMEOL*V]\ZVHQVLHHXNOLGHVRZ\PMDNLQDMEDUG]LHMZ]EXG]DMF\VLZ]HáV]LQQHMNODV\

QL*ZHNWRUQDZHMFLXVLHFL:VSyáU]GQHSRáR*HQLDQRZHJRZ]áDVWDNLHVDPHMDNZHNWRUD

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1

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n

R

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m

τ

τ

=

=

=

/LF]EDWZRU]RQ\FKZ]áyZZMHGQHMHSRFHMHVWograniczona i równa jest liczbie klas znajduj-

F\FKVLZ]ELRU]HWHUQLQJRZ\P7DNLHRJUDQLF]HQLHXPR*OLZLDPDNV\PDOQ\UR]URVWZ]áRP

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V]HQLHMHJRUR]P\FLDSURSRUFMRQDOQLHGRSURFHQWRZHMZDUWRFLEádu.

σ σ λ

σ

= −

−

4

:DUWRüSDUDPHWUX

λ

MHVWPDáDGODQRZ\FKZ]áyZJG\*WHGRSLHURDGDSWXMVLQDWo-

PLDVWZSU]\SDGNXVWDUV]\FKZ]áyZSDUDPHWUWHQPDGX*ZDUWRü

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F\FK]DOH*QHVRGNROHMQRFLSRGDZDQLDZHNWRUyZWUHQLQJRZ\FKQDZHMFLHVLHFL]DND*-

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

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3URVW\PVSRVREHPQDUR]ZL]DQLHWHJRSUREOHPXMHVW]DVWRVRZDQLHW]ZNRPLWHWXVLHFL0e-

WRGDWDSROHJDQDW\P*HQDGDQ\P]ELRU]HWUHQLQJRZ\PXF]\VLVLHüZLHORNURWQLH0DMFM

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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-

QLHVLV]\ENRFLXF]HQLD'ODWHJRWH*]DVWRVRZDQRREURW\EGFH]áR*HQLHPREURWyZGZu-

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α

, w wyniku czego z wektora (X,Y) otrzymujemy wektor (X

’

,Y

’

):

;
<

;
<

FRV

VLQ

VLQ

FRV









 =

−





















α

α

α

α

:QDVWSQ\PNURNX

;

;

=

;

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=

LSRZWDU]DP\RSHUDFMHW\PUD]HPXZ]JOGQLDMFNW

β

SRáR*HQLDGDQHJRZ]áDPLG]\WU]e-

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NRQ\ZDQDMHVWDGDSWDFMDSRáR*HQLDLLQQ\FKSDUDPHWUyZWHJRZ]áD1DMSLHUZZ\]QDF]DQHV

SRV]F]HJyOQHNW\QDFK\OHQLD

θ

ZHNWRUDPDMFHJRVZyMSRF]WHNZURGNXZ]áDDZLFMHVW

WRSRáo*HQLHWHJRZ]áDDNRQLHFZPLHMVFXJG]LH]QDMGXMHVLDNWXDOQ\SXQNWZHMFLRZ\Z

3U]\NáDGREUyFRQ\FKGZyFKQHXURQyZ

ZLHORZ\PLDURZHMSU]HVWU]HQLZHNWRUZHMFLRZ\PR*HE\üWUDNWRZDQ\MDNRSXQNW1DVWSQLH

DNWXDOQHNW\QHXURQX

φ

VSU]HVXZDQHZNLHUXQNXZ\]QDF]oQ\FKZDUWRFL

φ = φ + γ(θ − φ)

parametr

γ

MHVWWRWHQVDPSDUDPHWUNWyU\Z\VWSLáSRGF]DVXF]HQLDUR]P\ü

-H*HOLZGDQ\FKZ\VWSXMZ\UD(QLHQDFK\ORQHVNXSLVNDWRZLNV]RüNWyZZ\]QDF]RQ\FK

GODSRV]F]HJyOQ\FKZHNWRUyZZSDGDMF\FKGRWHJRZ]áDEG]LHGRVLHELHSRGREQ\FKSU]H]

FRáDWZRMHVWX]\VNDüRSW\PDOQ\NW-HGQDNJG\QLHPDZ\Uy*QLRQHJRNLHUXQNXGODVNXSLVND

WRQDVWSXMHFLJáD]PLDQDZDUWRFLNWD

φ

FRPR*HSRZRGRZDüWUXGQRFLZXF]HQLXVL'OD

VNXSLVN Z\]QDF]RQ\FK SRGF]DV LQLFMDOL]DFML VLHFL NW\ ]QDMGRZDQH V ]D SRPRF SURVWHM

;

D ;

L

L

=

GRSDVRZDQHMQDSRGVWDZLHZV]\VWNLFKZHNWRUyZQDOH*F\FKGRWHJRZ]áDVWG

poszczególne parametry

∑

∑

=

k

k

i

k

i

k

k

i

k

i

X

X

X

X

a

1

:VSyáF]\QQLNLWHUyZQHVWDQJHQVRZLNWDSRPLG]\JáyZQRVLVNXSLVNDDRVLX

1

. Tak

ZLFSoV]F]HJyOQHNW\PR*QDZ\]QDF]\ü]HZ]RUX

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]áyZMHVWEDUG]LHMSUHF\]\MQDQL*]DVWRVRZDQLH

DQDOL]\F]\QQLNyZJáyZQ\FK3&$OXELQQ\FKJOREDOQLHRNUHORQ\FKWUDQVIRUPDFMLGDQ\FK

1DZHWMHOLZF]DVLHXF]HQLDSDUDPHWU\REURWXQLHSRGOHJDMDGDSWDFMLZDUWRZSURZDG]LüPa-

FLHU]HREURWXZRSLVDQ\SRZ\*HMVSRVyE,QQHPHWRG\WZRU]HQLDREUyFRQ\FKNRQWXUyZGHFy-
zji opisano w pracy [5].

5.4. Optymalizacja

:NRFRZ\PHWDSLHXF]HQLDW]QJG\RVLJQLWDMDNRüNODV\ILNDFML]JRGQDMHVW]SR*GDQ

QDVWSXMHRSW\PDOL]DFMDSROHJDMFDQDRGU]XFHQLXZ]áyZNWyUHPDMEDUG]RPDáHUR]PLDU\

W]Q GR NWyU\FK ZSDGD QLHZLHOND OLF]ED QS OXE ZHNWRUyZ ] FLJX WUHQLQJRZHJR 3o-

ZVWDMRQHQDVNXWHN*GDQLD]E\WZ\VRNLHMGRNáDGQRFLNODV\ILNDFMLOXEWH*QLHZ\VWDUF]DMFe-

JRUR]P\FLDGX*\FKZ]áyZLVWQLHMF\FKZVLHFL-H*HOLSU]\F]\QWZRU]HQLDPDá\FKZ]áyZ

MHVW ]E\W V]\ENLH LFK WZRU]HQLH WR SR LFK RGU]XFHQLX SUyED GRXF]HQLD LVWQLHMF\FK Z]áyZ

VSRZRGXMH]ZLNV]HQLHLFKUR]P\ü:SU]HFLZQ\PSU]\SDGNXSRQRZQLH]RVWDQXWZRU]RQH

PDáHZ]á\3UyEDRGU]XFDQLDLGRXF]DQLDSRZWDU]DQDMHVWNLONDNURWQLHSRF]\PHWDSXF]HQLD

MHVW]DNRF]RQ\-DNRüNODV\ILNDFMLSRW\PHWDSLHPR*HE\üPQLHMV]DRG*GDQHMSRQLHZD*

F]üZ]áyZ]RVWDáDRdrzucona.

(WDSNROHMQ\WRNRFRZDRSW\PDOL]DFMDVLHFLSRNWyUHMQLHQDVWSXMHMX*GRXF]DQLH2GU]XFa-

QH V Z]á\ NWyU\FK OLNZLGDFMD QLH SRZRGXMH ]PLDQ\ SR]LRPX DNWXDOQHM NODV\ILNDFML $E\

XQLNQüVSUDZG]DQLDND*GHJRZ]áD]RVREQDW]QRGU]XFDQLDJRLVSUDZG]DQLDNODV\ILNDFML

QDFDá\P]ELRU]HWUHQLQJRZ\PFRE\áRE\EDUG]RNRV]WRZQHGODND*GHJRZHNWRUDWUHQLQJo-

ZHJRREOLF]DQDMHVWDNW\ZDFMDZV]\VWNLFKZ]áyZL]DSDPLW\ZDQDZDUWRüDNW\ZDFMLZ]áD

QDMEDUG]LHMZ]EXG]DMFHJRVL7HQZ]Há]RVWDMHZ\áF]RQ\:\V]XNLZDQ\MHVWNROHMQ\Z-

]HáQDMEDUG]LHMZ]EXG]DMF\VLL]DSDPLW\ZDQDMHVWZDUWRüMHJRZ]EXG]HQLD0DP\ZLF

PDFLHU] ] OLF]E HOHPHQWyZ GZD UD]\ ZLNV] QL* OLF]ED ZHNWRUyZ Z FLJX WUHQLQJRZ\P

QDWRPLDVWZDUWRFLW\FKHOHPHQWyZUyZQHVPDNV\PDOQ\PZ]EXG]HQLRPGODRGSRZLHGQLFK

ZHNWRUyZWUHQLQJRZ\FK:PDFLHU]\WHMXVXZDP\MHGHQZ]Há'ODZHNWRUDGODNWyUHJRZ-

]HáWHQPLDáQDMZLNV]ZDUWRüDNW\ZDFMLZVWDZLDQDMHVWGRPDFLHU]\ZDUWRü]HUR1DVWp-

QLHQDSRGVWDZLHSR]RVWDá\FKZDUWRFLZ\OLF]DQDMHVWMDNRüNODV\ILNDFML-H*HOLMDNRüNODVy-

ILNDFML QLH SRJRUV]\áD VL WR DQDOL]RZDQ\ Z]Há MHVW XVXZDQ\ Z SU]HFLZQ\P SU]\SDGNX

ZVWDZLDQHVGRPDFLHU]\SoSU]HGQLHZDUWRFL

5.5. Selekcja cech

'OD ND*GHJR ] Z]áyZ XNU\W\FK PR*QD UyZQLH* ]DVWRVRZDü HOLPLQDFM FHFK. W tym celu

Z\ELHUDP\NROHMQRZ]á\LGODND*GHJR]QLFKRGU]XFDP\]FLJXWUHQLQJRZHJRZHNWRU\NWó-

UHGRGDQHJRZ]áDZSDGDMF]\OLNWyUHVSU]H]QLHJRNODV\ILNRZDQH0R*HP\WRXF]\QLü

JG\* Z\áF]HQLH FHFK\ Z GDQ\P Z(OH ] XZDJL QD WR *H VWRVXMHP\ IXQNFMH VHSDURZDOQH

PR*HE\üWUDNWRZDQHMDN ZVWDZLHQLH GR LORF]\QX ZDUWRFL D ZLF PDNV\PDOQHM ZDUWRFL

DNW\ZDFMLGODGDQHJRZ\PLDUX0R*HWRVSRZRGRZDüW\ONR]ZLNV]HQLHDNW\ZDFMLZ]áDGOD

ZV]\VWNLFKZHNWRUyZWUHQLQJRZ\FK1LHPR*HVLZLF]PLHQLüNODV\ILNDFMDZHNWRUyZNWyUH

E\á\SRSUDZQLHNODV\ILNRZDQHERGODW\FKZHNWRUyZWHQZ]HáLWDNPLDáQDMZLNV]HZ]Eu-

G]HQLH'ODWHJRREOLF]DP\PDFLHU]Z]EXG]HW\ONRGODSR]RVWDá\FKZHNWRUyZWUHQLQJRZ\FK

.D*GD]FHFKGODGDQHJRZ]áD]RVWDMHNROHMQRRGU]XFDQD3RZRGXMHWRZ]URVWIXQNFMLDNWy-

ZDFMLWHJRZ]áD-HOLDNW\ZDFMDWDGODZHNWRUyZ]LQQHMNODV\QL*RSW\PDOL]RZDQ\Z]HáQLH

SU]HNUDF]DDNW\ZDFMLZ]áyZSRSUDZQLHMHNODV\ILNXMF\FK]DSLVDQ\FKZWDEOLF\DNW\ZDFML
to taka cecha nie jest potrzebna.

3URFHGXU\RGU]XFDQLDZ]áyZRUD]HOLPLQDFMLFHFKSRZWDU]DQHVWDNGáXJRD**DGHQZ]Há

QLHPR*HMX*]RVWDüRGU]XFRQ\$OWHUQDW\ZQDPHWRGDVHOHNFMLFHFKSROHJDMFDQDPRG\ILNDFML

IXQNFMLEáGXRSLVDQD]RVWDáDZSUDF\[13].

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 wej

FLRZ\QLH]RVWDMHVNODV\ILNRZDQ\

'RRV]DFRZDQLDMDNRFLNODV\ILNDFMLVáX*GZDSDUDPHWU\ZDUWRüZ]EXG]HQLDRUD]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 wej

FLRZHJRX do danej klasy

S

* ; '

* ; '

N

&L

N

&L

&

&

&

N

&

&

&

L

L

L

L

=

∑

∑

∑

σ

σ

;

S

N

N

∑

=

:OLF]QLNXVXPRZDQLHSU]HELHJDSRZV]\VWNLFKZ]áDFKUHSUH]HQWXMF\FKNODV]Z\FL]F\Z

PLDQRZQLNX VXPD ELHJQLH SR ZV]\VWNLFK Z]áDFK XNU\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]UHSo-
zytorium 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%.

Radial

Dipol92

Alloc80

QuaDisc

Discrim

FSM

'RNáDGQRüQD

zbiorze testowym

95.9%

95.2%

94.3%

94.1%

94.1%

94.3%

•

'DQHÄMRQRVIHUD´]DZLHUDMZHNWRUyZ]F]HJRSLHUZV]\FKX*\ZDVLGRWUHQo-

ZDQLDQDWRPLDVWSR]RVWDáHGRWHVWRZDQLD'DQHWHUHSUH]HQWXMV\JQDáUDGDURZ\RGELW\RG

MRQRVIHU\.D*G\]ZHNWRUyZ]DZLHUDDWU\EXW\RZDUWRFLDFKFLJá\FK:\VWSXMGZLH

NODV\ SLHUZV]D ZLDGF]FD R Z\VWSRZDQLX Z MRQRVIHU]H SHZQ\FK VWUXNWXU L GUXJD

ZLDGF]FDREUDNX W\FK VWUXNWXU 2ELH NODV\ Z ]ELRU]H WUHQLQJRZ\P V SUDZLH UyZQo-
liczne.

k-NN

MLP

C4.5

FSM

'RNáDGQRüQD]ELRU]H

testowym

98.7%

96.0%

94.9%

97.7%

•

'DQH ÄK\SRWK\URLG´ ]DZLHUDM ZHNWRU\ Z ]ELRU]H WUHQLQJRZ\P L Z ]ELRU]H

WHVWRZ\P6WRGDQH]GZyFKNROHMQ\FKODWEDGDSU]HVLHZRZ\FK]DZLHUDMFHLQIRUPa-

FMHRQLHGRF]\QQRFLQDGF]\QQRFLOXEQRUPDOQLHG]LDáDMFHMWDUF]\F\3URFHQWRZ\URz-

NáDGW\FKWU]HFKNODVMHVWQDVWSXMF\ZSOLNXWUHQLQJRZ\PWHVWRZ\P

:\VWSXMHDWU\EXWyZELQDUQ\FKLFLJá\FK

C4.5

C-MLP2LN

CART

FSM

'RNáDGQRüQD]ELRU]H

testowym

99.5%

99.36%

99.36%

99.1%

•

'DQHÄVDWLPDJH´VNáDGDMVL]LQWHQV\ZQRFLSLNVHOL]QDMGXMF\FKVLZVVLHG]WZLH[

RWU]\PDQ\FK]F]WHUHFK]GMüVDWHOLWDUQ\FKZUy*Q\FK]DNUHVDFKVSHNWUDOQ\FKVWGZ\VW-

SXMH DWU\EXWyZ PDMF\FK ZDUWRFL ] SU]HG]LDáX : ED]LH MHVW ZHNWRUyZ

WUHQLQJRZ\FK L WHVWRZ\FK 'DQH SRG]LHORQH V QD V]Hü NODV FKRG]L R Uy*QH So-

ZLHU]FKQLH RGELMDMFH PDMF\FK QDVWSXMF SURFHQWRZ OLF]HEQRü Z SRV]F]HJyOQ\FK
zbiorach: zbiór treningowy 24.2%, 10.8%, 21.6%, 9.4%, 10,6%, 23.4%, testowym 23.1%,
11.2%, 19.9%, 10.5%, 11.8%, 23.5%.

k-NN

LVQ

Dipol92

Radial

FSM

'RNáDGQRüQD]ELRU]H

testowym

90.6%

89.5%

88.9%

87.9%

89.8%

•

'DQHÄVRQDU´]DZLHUDMZHNWRUyZNWyUHSRG]LHORQHUyZQRQD]ELyUWUHQLQJRZ\LWe-

VWRZ\:\VWSXMGZLHNODV\.D*G\]ZHNWRUyZSRVLDGDFLJá\FKDWU\EXWyZ&HOHP
jest od

Uy*QLHQLHV\JQDáXVRQDUXRGELWHJRRGPHWDOXRGV\JQDáXRGELWHJRRGVNDá\

MLP+BP

k-NN

C4.5

FSM

'RNáDGQRüQD]ELRU]H

testowym

90.4%

84.2

65.4

88.8%

•

'DQHÄVKXWWOH´]DZLHUDMZHNWRUyZZ]ELRU]HWUHQLQJRZ\PLZ]ELRU]HWe-

VWRZ\P:\VWSXMHVLHGHPNODVPDMF\FKQDVWSXMF\XG]LDáSURFHQWRZ\ZSRV]F]HJyl-

nych zbiorach: zbiór treningowy 78.41%, 0.09%, 0.3%, 15.51%, 5.65%, 0.01%, 0.03%,
WHVWRZ\P'DQHSRVLDGDMFL-

Já\FKDWU\EXWyZ

NewId

BayTree

Cn2

Cal5

FSM

'RNáDGQRüQD]ELRU]H

testowym

99.99%

99.98%

99.97%

99.97%

99.97%

•

'DQHÄOHWWHUV´]DZLHUDMZHNWRU\RSLVXMFHGX*\FKOLWHU]DOIDEHWXM]\NDDQJLHOVNLHJR

:\VWSXMHZHNWRUyZ]F]HJRSU]H]QDF]RQ\FK]RVWDáRGRWUHQRZDQLDVLHFLD

SR]RVWDáHGRWHVWRZDQLD'DQHWHXWZRU]RQH]RVWDá\]Uy*Q\FKIRQWyZ'RND*GHM

OLWHU\ VSRUyG W\FK IRQWyZ GRGDQ\ ]RVWDá V]XP 8WZRU]RQR F]DUQR ELDáH SURVWRNWQH

REUD]\NWyUHQDVWSQLHSU]HGVWDZLRQRZSRVWDFLZHNWRUDVNáDGDMFHJRVL]FHFKQu-

PHU\F]Q\FK :V]\VWNLH FHFK\ ]RVWDá\ SU]HVNDORZDQH WDN DE\ ZDUWRFL W\FK FHFK\ E\á\

FDáNRZLWHZ]DNUesie od 0 do 15.

Alloc80

k-NN

LVQ

QuaDisc

FSM

'RNáDGQRüQD]ELRU]H

testowym

93.6%

93.2%

92.1%

88.7%

92.2%

•

'DQHÄJDOD[LHV´]DZLHUDMRSLVJDODNW\N]NDWDORJX(62/9[12]. Celem jest wykonanie
automatycznej klasyfikacji, która porównywalna jest do klasyfikacji eksperta. Zbiór ten
]DZLHUD SRQDG ZHNWRUyZ 6LHü WUHQRZDQD MHVW QD ]ELRU]H ]DZLHUDMF\P HOe-

PHQWyZLWHVWRZDQDQD]ELRU]HZHNWRUyZ.D*G\ZHNWRUVNáDGDVL]FHFKLPo-

*HQDOH*HüGRMHGQHM]GZyFKNODVJDODNW\NLZF]HVQHJRW\SXOXEWH*JDODNW\NLSy(QHJR
typu.

k-NN

C4.5

MLP+BP

FSM

'RNáDGQRüQD]ELRU]HWHVWo-

wym

92.82%

92.4%

89.6%

93%

•

'DQHÄKHSDWLWLV´GRW\F]FKRUyEZWURE\RWU]\PDQH]7RNLMVNLHJRXQLZHUV\WHWXPHG\Fz-
nego [13]

'DQHWH]ZLHUDMSU]\SDGNyZZW\PX*\WH]RVWDá\GRWHVWRZDQLDD

SR]RVWDáHGRWUHQRZDQLDVLHFL.D*G\SU]\SDGHNRSLVDQ\]RVWDáSU]H]FHFK:\VWSXM
klasy.

k-NN

C4.5

MLP

FSM

'RNáDGQRüQD]ELRU]HWHVWo-

wym

82.8%

75.5%

68%

82.2%

•

Dane „

VHJPHQWDWLRQ´]DZLHUDMZHNWRUyZZ]ELRU]HWUHQLQJRZ\PLZ]ELRU]H

WHVWRZ\P:\VWSXMHNODVND*GD]NODVZ]ELRU]HWUHQLQJRZ\PSRVLDGDZHNWRUyZD

Z]ELRU]HWHVWRZ\P:V]\VWNLHZHNWRU\RSLVDQHVSU]H]FHFKRZDUWRFLDFKFL-

Já\FK

k-NN

C4.5

MLP

FSM

'RNáDGQRüQD]ELRU]HWHVWo-

wym

90.33%

89.8%

88.33%

91.2%

•

'DQHÄEUHDVWFDQFHUZLVFRQVLQ´]DZLHUDMSU]\SDGNyZZUyGNWyU\FKZ\VWSXMH

FKRU\FKRUD]]GURZ\FKSU]\SDGNyZ.D*G\SU]\SDGHNRSLV\ZDQ\MHVWSU]H]FHFK

PDMF\FKZDUWRüZ]DNUHVLHRG'ODSU]\SDGNyZMHGQDZDUWRüMHVWEUDNXMFD:
miej

VFDZDUWRFLEUDNXMFHMZVWDZLRQD]RVWDáDZDUWRüUHGQLDGODGDQHMFHFK\

IncNet

k-NN

FDA

FSM

'RNáDGQRüREOLF]RQD]

krotnej kroswalidacji

97.1%

97.1%

96.8%

96.5%

•

Dane „appendictis” [14]

]DZLHUDMSU]\SDGNyZRSLVDQ\FK]DSRPRFFHFK:\VW-

SXMGZLHNODV\PDMFHQDVWSXMF\XG]LDáSURFHQWRZ\

k-NN

MLP

C4.5

FSM

'RNáDGQRüREOLF]RQD]

krotnej kroswalidacji

89.3%

83.9%

83.5%

84.2%

7. Podsumowanie

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FLXZU]HF]\ZLVWRFLZ\NRQXMHVLQLHPDODXWRPDW\F]QLHQLHZ\PDJDMFLQJHUHQFMLX*\WNRw-

QLNDZSURFHVXF]HQLDVLOXEZ\ELHUDQLDDUFKLWHNWXU\

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RUD]RGUHDNFMLVLHFLQDWHQZHNWRUZ]EXG]HQLDLVWQLHMF\FKZ]áyZ3RF]WNRZHSURWRW\S\

]QDMGRZDQHV]DSRPRFZVWSQHMLQLFMDOL]DFMLRSDUWHMQDJUXSRZDQLX,QLFMDOL]DFMDWDNDSo-

]ZDOD Z\VWDUWRZDü ] RSW\PDOQ\FK SURWRW\SyZ FR SRZRGXMH F]VWR SU]\VSLHV]HQLH SURFHVX

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