Visualization of Highly-Dimensional Data in 3D Space

3 downloads 0 Views 813KB Size Report
52.7% [400]. The number in square brackets indicates the number of iterations. ... [6] W. Dzwinel, D.A. Yuen, K. Boryczko, Y. Ben-Zion, S. Yoshioka, and T. Ito ...
9LVXDOL]DWLRQRI+LJKO\'LPHQVLRQDO'DWDLQ'6SDFH 

'DW71JX\HQ

:LWROG']ZLQHO

&RPSXWHU6FLHQFH'HSW6FKRRORI(QJLQHHULQJ 9LUJLQLD&RPPRQZHDOWK8QLYHUVLW\ :0DLQ6WUHHW5LFKPRQG9$86$ QJX\HQGW#YFXHGX

,QVWLWXWHRI,QIRUPDWLFV $*+8QLYHUVLW\RI6FLHQFHDQG7HFKQRORJ\ $O0LFNLHZLF]D.UDNRZ3RODQG

G]ZLQHO#XFLDJKHGXSO



.U]\V]WRI-&LRV &RPSXWHU6FLHQFH'HSW6FKRRORI(QJLQHHULQJ 9LUJLQLD&RPPRQZHDOWK8QLYHUVLW\ :0DLQ6WUHHW5LFKPRQG9$86$ NFLRV#YFXHGX DQG,,7L63ROLVK$FDGHP\RI6FLHQFHV3RODQG $EVWUDFW²0ROHFXODU G\QDPLFV PHWKRGLV XVHGIRU FRPSXWLQJ HTXLOLEULXP LQ PDQ\ SK\VLFDO V\VWHPV DV ZHOO DV D SRZHUIXO VROYHUXVHGIRUPLQLPL]DWLRQRIFULWHULRQIXQFWLRQVVXFKDVWKH VWUHVVIXQFWLRQLQ PXOWLGLPHQVLRQDOVFDOLQJ:H KDYH GHVLJQHG D QHZ WRRO IRU YLVXDOL]DWLRQ RI KLJKO\GLPHQVLRQDO GDWD LQ ' EDVHGRQWKHPHWKRG:HKDYHVKRZQRQVHYHUDOGDWDVHWVWKDW WKHQHZPHWKRGLVIDVWDQGDFFXUDWH .H\ZRUGVFRPSRQHQW YLVXDOL]DWLRQ RI KLJKO\GLPHQVLRQDO GDWDLQ'VSDFHPROHFXODUG\QDPLFV

,

,1752'8&7,21

,Q PDQ\ DUHDV RI VFLHQFH DQG HQJLQHHULQJ ZKHUH RIWHQ WKHUHLVODFNRIEDFNJURXQGNQRZOHGJHDERXWGDWDFOXVWHULQJ LV RQH RI WKH PRVW LPSRUWDQW WHFKQLTXHV IRU UHYHDOLQJ VWUXFWXUH LQ WKH GDWD &OXVWHULQJ LV D YHU\ FKDOOHQJLQJ SUREOHPLQSDUWLFXODUZKHQGDWDDUHKLJKO\GLPHQVLRQDO + ' 9LVXDOL]DWLRQRIVXFKGDWDLQDORZHUGLPHQVLRQDO /'  VSDFH LV WKXV LPSRUWDQW DV LW KHOSV WR EHWWHU XQGHUVWDQG WKH LQWHUQDO VWUXFWXUH RI GDWD 7R EH XVHIXO WKH WUDQVIRUPDWLRQ IURP WKH +' VSDFH LQWR WKH /' VSDFH KDV WR EH YHU\ DFFXUDWH LQ WKH VHQVH RI SUHVHUYLQJ WKH PRVW LPSRUWDQW FKDUDFWHULVWLFV RI WKH RULJLQDO GDWD VWUXFWXUH 8VXDOO\ WKH ILGHOLW\ RI D WUDQVIRUPDWLRQ LV PHDVXUHG E\ XVLQJ VRPH VLPLODULW\ PHDVXUHGDWD SRLQWV WKDW DUHFORVH LQWKH RULJLQDO +'VSDFHVKRXOGDOVREHFORVHLQWKH/'VSDFH7KHUHH[LVW PDQ\ PHWKRGV IRU YLVXDOL]LQJ +' GDWD VXFK DV SUR[LPLW\ SUHVHUYLQJ>@FOXVWHULQJDQGVHJPHQWDWLRQ>@DUWLILFLDO QHXUDO QHWZRUNV >@ DQG SURMHFWLRQ PHWKRGV VXFK DV SULQFLSOH FRPSRQHQW DQDO\VLV DQG OLQHDU GLVFULPLQDQW DQDO\VLV :H IRFXV KHUH RQ WKH 0ROHFXODU '\QDPLFV 0'  PHWKRG RULJLQDOO\ GHYHORSHG E\ RQH RI WKHVH DXWKRUV 7KH PHWKRG LV EDVHG RQ VLPXODWLQJ G\QDPLFV RI DWRPV DQG PROHFXOHV,WFDOFXODWHVWLPHGHSHQGHQWEHKDYLRURIDSDUWLFOH V\VWHP DQG LV XVHG WR VWXG\ WKH VWUXFWXUH G\QDPLFV DQG WKHUPRG\QDPLFV RI SDUWLFOH HQVHPEOHV 7KH PDLQ VWHSV RI 0'>@FDQEHVXPPDUL]HGDVIROORZV

c 978-1-4577-1675-1 2011 IEEE

•

GHILQH D V\VWHP FRQVLVWLQJ RI 1 SDUWLFOHV ZLWK D JLYHQLQLWLDOSK\VLFDOSDUDPHWHUV • VROYH 1HZWRQ V HTXDWLRQV RI PRWLRQ IRU HYHU\ SDUWLFOHXQWLOWKHWKHUPRG\QDPLFVWDWHRIWKHV\VWHP UHDFKHVHTXLOLEULXP • FDOFXODWHWKHV\VWHPWKHUPRG\QDPLFVWKHILQDOVWDWH RIWKHV\VWHP 7KH PHWKRG ZDV FRPELQHG ZLWK 0XOWL'LPHQVLRQDO 6FDOLQJ 0'6  DSSURDFK >@ EHFDXVH RI LWV UREXVWQHVV 7KHUHDUHVHYHUDOW\SHVRI0'6PHWKRGVVXFKDVWKHRULJLQDO .UXVNDO PHWKRG >@ 6DPPRQ >@ DQG 1LHPDQQ >@ DOJRULWKPVSULQFLSDOFXUYHV>@DQGWULDQJXODWLRQ>@)RU H[DPSOH6DPPRQ¶V SURMHFWLRQPDSVWKH+'VSDFHLQWRDQ /'VSDFHDQGSUHVHUYHVRULJLQDOVWUXFWXUHRIEHWZHHQSRLQW GLVWDQFHVE\PLQLPL]LQJWKHIROORZLQJIXQFWLRQ ‫ܧ‬ൌ

ͳ ‫כ‬ σ௜ழ௝ ݀௜௝

෍ ௜ழ௝

‫כ‬ ሺ݀௜௝ െ ݀௜௝ ሻଶ ሺͳሻ ‫כ‬ ݀௜௝

ZKHUH G LM LV GLVWDQFH EHWZHHQ LWK DQG MWK REMHFWV LQ WKH RULJLQDO VSDFH DQG GLM LV WKH GLVWDQFH EHWZHHQ WKHLU SURMHFWLRQV ,W VLPSO\ PLQLPL]HV WKH VTXDUHG HUURU IXQFWLRQ (VRPHWLPHVDOVRFDOOHG6DPPRQ VVWUHVV 7KH VWUXFWXUH RI WKLV SDSHU LV DV IROORZV ,Q 3DUW ,, 0HWKRG ZH ILUVW EULHIO\ RYHUYLHZ WKH RULJLQDO 0' PHWKRG DQGWKHQGHVFULEHWKHQHZRQH5HVXOWVRIH[SHULPHQWVXVLQJ WKHQHZ PHWKRGDUHVKRZQLQ3DUW,,,7KHSDSHUHQGVZLWK FRQFOXVLRQVDQGIXWXUHZRUN ,,

0(7+2'

)LUVW ZH UHYLHZ WKH 0'6 DSSURDFK ,W UHSUHVHQWV QRQ OLQHDU WUDQVIRUPDWLRQ RI WKH +' IHDWXUH VSDFH LQWR /' IHDWXUH VSDFH >@ ,W LV LPSRUWDQW WR QRWH WKDW 0'6 LV GLIIHUHQW IURP PDQ\ SURMHFWLRQ PHWKRGV DV LW GRHV QRW XVHIHDWXUHYHFWRUVLQDQH[SOLFLWZD\7KHDUUD\RIGLVWDQFHV EHWZHHQ GDWD SRLQWV LV XVHG LQVWHDG ZKLFK IRU GDWD OLNH SURWHLQ VHTXHQFHVLV PRUH GHVLUDEOH WKDQ GHILQLQJ VRPH

225

IHDWXUHYHFWRUUHSUHVHQWDWLRQ9DULRXVGLVWDQFHPHDVXUHVFDQ EHXVHGWRUHSUHVHQWGLIIHUHQWVLPLODULW\W\SHV 7KH JRDO RI WKH 0'6 DOJRULWKP LV WR FRQVHUYH DOO WKH GLVWDQFHVEHWZHHQSRLQWV5L∈ω⊂ℜ1LQWKH(XFOLGHDQ' RU '  VSDFH ZLWK D PLQLPXP HUURU 7KH ³VWUHVV IXQFWLRQ´ FULWHULRQLVXVXDOO\GHILQHGDVIROORZV  ƍ ௠ ି௪Ǥ௠ Ǥ ሺ‫ܦ‬௜ǡ௝ି ‫ݎ‬௜ǡ௝ ሻ ቑሺʹሻ ‫ܧ‬ሺ߱ǡ ߱ƍ ሻ ൌ ‹ ቐ෍ ‫ܦ‬௜ǡ௝ ௝ழ௜

ZKHUH

ZKHUHYLQULQDUHWKHYHORFLW\DQGSRVLWLRQRISDUWLFOHL UHVSHFWLYHO\QLVWKHWLPHVWHSQXPEHUDQGP LVSDUWLFOH¶V PDVV $V LQ >@ WKH V\VWHP RI ³SDUWLFOHV´ GHVFULEHG E\ WKH GLVFUHWH HTXDWLRQV   HYROYHV LQ WLPH DFFRUGLQJ WR WKH 1HZWRQHTXDWLRQVRIPRWLRQXQWLOWKHPLQLPXPRISRWHQWLDO HQHUJ\LQ  LVUHDFKHG2QO\WZRIUHHSDUDPHWHUVλDQGN QHHG WR EH WXQHG WR REWDLQ D VWDEOH VWDWH ZKHUH WKH ILQDO SRVLWLRQVRIWKHIUR]HQ³SDUWLFOHV´UHIOHFWWKHUHVXOWRI+'WR 'PDSSLQJ 

ƍ ‫ݎ‬௜ǡ௝ ൌ ሺ‫ݎ‬௜ െ ‫ݎ‬௝ ሻǤ ൫‫ݎ‬௜ െ ‫ݎ‬௝ ൯݅ǡ ݆ ൌ ͳǡ Ǥ Ǥ ǡ ‫ܯ‬

'LM LVD VTXDUHGGLVWDQFHV EHWZHHQ SRLQWV 5L 5M∈ω⊂ℜ1 DQG UL UM∈ωµ⊂( DUH FRRUGLQDWHV RI WKH UHVSHFWLYH SRLQWV LQ 'VSDFHDQGZHORRNIRUDPLQLPXPRIWKLVIXQFWLRQ 5HVXOWRIWKHPDSSLQJGHSHQGVRQWKHTXDOLW\RIWKHORFDO PLQLPXP REWDLQHG E\ XVLQJ D ³VWUHVV IXQFWLRQ´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³SDUWLFOHV´LVJHQHUDWHGLQℜDQGHYHU\³SDUWLFOH´ FRUUHVSRQGVWRWKHUHVSHFWLYH1GLPHQVLRQDOSRLQWLQℜ1DQG WKH³SDUWLFOHV´LQWHUDFWZLWKHDFKRWKHUYLDΦLMSRWHQWLDO

 )LJXUH 'LDJUDPLOOXVWUDWLQJ0'6WUDQVIRUPDWLRQXVLQJ0'PHWKRG

,Q>@WKHDXWKRUVPLQLPL]HGWKHSRWHQWLDOHQHUJ\HUURU IXQFWLRQ (H  VLPLODU WR 6DPPRQ¶V LQ    +HUH HYHU\ ³SDUWLFOH´ FRUUHVSRQGV WR 1GLPHQVLRQDO GDWD SRLQW LQ ℜ1 7KH SDUWLFOHV L DQG M LQWHUDFW YLD WZRERG\ µµSRWHQWLDO´ 9LM ZKLFKLVDIXQFWLRQRIGLVWDQFH'LMEHWZHHQSRLQWVLDQGMLQ WKHRULJLQDO1GLPHQVLRQDOVSDFH 7HPSRUDO HYROXWLRQ RI WKH HQVHPEOH RI SDUWLFOHV LV GHVFULEHGE\WKH1HZWRQLDQODZVRIPRWLRQ ௠

φ

௜ǡ௝



݇ ି௪Ǥ௠ ƍ ௠ ‫ܦ‬ Ǥ ሺ‫ܦ‬௜ǡ௝ െ ‫ݎ‬௜ǡ௝ ሻ ሺ͵ሻ ʹ݉ ௜ǡ௝

ZKHUH N LV D VWLIIQHVV IDFWRU 7KH LQWHUDFWLRQ EHWZHHQ HDFKSDLURISDUWLFOHVFDQEHGHVFULEHGXVLQJYDULRXVW\SHVRI ORQJUDQJHSRWHQWLDOVZKLFKGHSHQGRQWKHGLVWDQFHEHWZHHQ SDUWLFOHVULMDQGWKHGLVWDQFH'LMEHWZHHQWKHFRUUHVSRQGLQJ PXOWLGLPHQVLRQDO SRLQWV LQ ℜ1 7R HQDEOH WKH HQHUJ\ GLVVLSDWLRQIURPWKHSDUWLFOHVLQWKHHQVHPEOHDIULFWLRQIRUFH LVXVHG8VLQJWKHOHDSIURJQXPHULFDOVFKHPHWKHIROORZLQJ IRUPXODIRUYHORFLWLHVDQGSRVLWLRQVRI³SDUWLFOHV´ZDVXVHG ௡ା

‫ݒ‬௜

ଵ ଶ

ൌ

ͳ െ ߮ ௡ିଵଶ Ǥ‫ݒ‬  ൅ ͳ൅߮ ௜



ఈο௧

ሺଵାఝሻ

ି௪௠

Ǥ ሺ‫ܦ‬௜௝ ሻ

௡ାଵȀଶ

‫ݎ‬௜௡ାଵ ൌ  ‫ݎ‬௜௡ ൅  ‫ݒ‬௜

௡ Ǥ ሼσ௄ ௝ୀଵሺ‫ݎ‬௜௝

௝ୀଵ

   ݀‫ݎ‬௜ ൌ  ‫ݒ‬௜ ݀‫ݐ‬ 7KH WRWDO IRUFH HIIHFW RQ WKH SDUWLFOH L LV HTXDO WR WKH JUDGLHQW RI WKH SRWHQWLDO HQHUJ\ (  VHH   7KH IULFWLRQ IRUFH ‫ܨ‬௜ ൌ  െߣ‫ݒ‬௜ ሺ͸ሻ



‫ܦ‬௜௝ ሻ௠ିଵ ‫ݎ‬௜௝௡ ሽ

Ǥ ο‫ݐ‬ሺͶሻ

λ ݇ Ǥ ο‫ ݐ‬൏ ͳ ‫ן‬ൌ  ǡ ߮ ൌ  ʹ݉ ݉

226

݀‫ݒ‬௜ ൌ  െ݇ ෍ ‫ܸ׏‬௜௝ െ ߣ‫ݒ‬௜  ݉௜ ݀‫ݐ‬

GLVVLSDWHVWKHHQHUJ\IURPWKHHQWLUHSDUWLFOHV\VWHP :HVKDOOXVHPRUHJHQHUDOIRUPXODWKDQWKHRQHVKRZQLQ  QDPHO\ ‫ܧ‬௘ ሺ݇ሻ ൌ ෍ ෍ ܸ௜௝ ሺ‫ܦ‬௜௝௞ െ  ‫ݎ‬௜௝௞ ሻ ሺ͹ሻ ௜



ZKHUH9LMFDQEHFDOFXODWHGDV

2011 11th International Conference on Intelligent Systems Design and Applications

ܸ௜௝ ൌ

ଶ ൫‫ܦ‬௜௝ଶ  െ  ‫ݎ‬௜௝ଶ ൯

ܸ௜௝ ൌ ቆ

‫ܦ‬௜௝ଶ െ  ‫ݎ‬௜௝ଶ ‫ܦ‬௜௝ଶ



ቇ 

7$%/(, ଶ

ܸ௜௝ ൌ  ൫‫ܦ‬௜௝  െ  ‫ݎ‬௜௝ ൯ ܸ௜௝ ൌ ቆ

‫ܦ‬௜௝ െ  ‫ݎ‬௜௝ ቇ ‫ܦ‬௜௝

'DWD6HW

*5$3+2)7+(727$/(1(5*@ >@ >@ >@ >@ >@ >@

>@ >@ >@ >@ >@ >@ >@

7KHQXPEHULQVTXDUHEUDFNHWVLQGLFDWHVWKHQXPEHURILWHUDWLRQV

  :H KDYH LPSOHPHQWHG ERWK PHWKRGV XVLQJ 0DWODE DQG WKHXVHUVFDQFKRRVHWRGLVSOD\WKHUHVXOWVLQHLWKHU'RU' URWDWH]RRPWKHILJXUHVDQGDGMXVWWKHD[HV7DEOH,9VKRZV YLVXDO UHVXOW LQ ERWK ' DQG ' RI IHZ GDWD VHWV LQ RXU H[SHULPHQWV

2011 11th International Conference on Intelligent Systems Design and Applications

7$%/(,9 'DWD VHW

5(68/762)7+(1(:$/*25,7+09,68$/,=(',1'$1' '63$&(6 '

DOJRULWKPVDEOHWRILQGFOXVWHUVLQWKHGDWDZLWKRXWUHTXLULQJ WKHXVHUWRJXHVVWKHLUQXPEHU

'

$&.12/('*(0(176 7KLVZRUNZDVSDUWLDOO\VXSSRUWHGE\WKH16)*$11JUDQW '71 DQGWKH1DWLRQDO,QVWLWXWHVRI+HDOWKXQGHUJUDQW 5+'$ .-& 

,ULV

5()(5(1&(6













6SHFW

:LQH

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µGLVWDQFH¶EHWZHHQ DSDLURISDUWLFOHV  ,Q DGGLWLRQ WR YLVXDOL]LQJ GDWD VHWV LQ WKH ' VSDFH ZH SODQ WR FRPELQH RXU DOJRULWKP ZLWK VPDUW FOXVWHULQJ

>@ ' +DQG + 0DQQLOD DQG 3  6P\WK ³3ULQFLSOHV RI 'DWD 0LQLQJ´ 7KH0,73UHVVSS >@ '-DLQDQG5&'XEHV´$OJRULWKPVIRU&OXVWHULQJ'DWD´3UHQWLFH +DOO$GYDQFHG5HIHUHQFH6HULHVSS >@ 6 7KHRGRULGLV DQG . .RXWURXPEDV ´3DWWHUQ 5HFRJQLWLRQ´ QG (GLWLRQ$FDGHPLF3UHVV6DQ'LHJR&$SS >@ 0 +DONLGL @ : ']ZLQHO ³9LUWXDO 3DUWLFOHV DQG 6HDUFK IRU *OREDO 0LQLPXP´ )XWXUH*HQHUDWLRQ&RPSXWHU6\VWHPVSS >@ 0 6WH\YHUV´0XOWLGLPHQVLRQDO 6FDOLQJ´ ,Q (QF\FORSHGLD RI &RJQLWLYH6FLHQFH1DWXUH3XEOLVKLQJ*URXS/RQGRQ8. >@ -% .UXVNDO DQG0 :LVK ³0XOWLGLPHQVLRQDO 6FDOLQJ´QR LQ 6DJH 8QLYHUVLW\ 3DSHU6HULHV RQ 4XDQWLWDWLYH $SSOLFDWLRQV LQ WKH 6RFLDO6FLHQFHV6DJH3XEOLFDWLRQV%HYHUO\+LOOV >@ -% .UXVNDO ³0XOWLGLPHQVLRQDO VFDOLQJ E\ RSWLPL]LQJ JRRGQHVV RI ILW WR D QRQPHWULF K\SRWKHVLV´ 3V\FKRPHWULND    SS ± >%HOO7HOHSKRQH/DERUDWRULHV0XUUD\+LOO1-@ >@ 5.DUEDXVNDLWơ DQG *']HP\GD ³0XOWLGLPHQVLRQDO 'DWD 3URMHFWLRQ $OJRULWKPV 6DYLQJ &DOFXODWLRQV RI 'LVWDQFHV´ ,QIRUPDWLRQ 7HFKQRORJ\ $QG &RQWURO .DXQDV 7HFKQRORJLMD 9RO  1R  SS >@ +1LHPDQQDQG-:HLVV³$IDVWFRQYHUJLQJDOJRULWKPIRUQRQOLQHDU PDSSLQJRIKLJKGLPHQVLRQDOGDWDWRDSODQH´,(((7UDQV&RPSXW &SS >@ 0 $ &DUUHLUD3HUSLQDQ ³$ UHYLHZ RI GLPHQVLRQ UHGXFWLRQ WHFKQLTXHV´ 7HFKQLFDO UHSRUW &6 'HSDUWPHQW RI &RPSXWHU 6FLHQFH8QLYHUVLW\RI6KHIILHOG8. >@ :']ZLQHODQG-%áDVLDN³0HWKRGRISDUWLFOHVLQYLVXDOFOXVWHULQJ RI PXOWLGLPHQVLRQDO DQG ODUJH GDWD VHWV´ )XWXUH *HQHUDWLRQ &RPSXWHU6\VWHPVSS± >@ - 0 +DLOH ³0ROHFXODU '\QDPLFV 6LPXODWLRQ´ :LOH\ 6RQV 1HZ @ & 1JX\HQ DQG .- &LRV ³*$.5(0 $ QRYHO K\EULG FOXVWHULQJ DOJRULWKP´,QIRUPDWLRQ6FLHQFHVSS± >@ 0+DOO()UDQN*+ROPHV%3IDKULQJHU35HXWHPDQQDQG,+ :LWWHQ ³7KH :(.$ 'DWD 0LQLQJ 6RIWZDUH $Q 8SGDWH´ 6,*.'' ([SORUDWLRQV9ROXPH,VVXH

  



2011 11th International Conference on Intelligent Systems Design and Applications

229

7$%/(9

$UWLILFLDO 'DWD6HWV

5(68/762)7+(1(:$/*25,7+021)285$57,),&,$/'$7$6(76 ,QFRUUHFWO\ FOXVWHUHG LQVWDQFHVE\ XVLQJ(0DOJ LQ:HND 

7RWDO(QHUJ\

9LVXDOL]DWLRQLQ' 

-0.2

QRQ RYHUODSSHG FOXVWHUV 1RUPDO GLVWULEXWLRQ   GLPHQVLRQV  LQVWDQFHV

5DZGDWD KLJK GLPHQVLRQ   'GDWDDIWHU XVLQJDOJ >@

-0.4 -0.6 -0.8 -1 1 0 -1



1

0.5

0

-0.5



0.8

QRQ RYHUODSSHG FOXVWHUV )6WXGHQW GLVWULEXWLRQ   GLPHQVLRQV  LQVWDQFHV

0.7 0.6

5DZGDWD KLJK GLPHQVLRQ   'GDWDDIWHU XVLQJDOJ >@

0.5 0.4 0.3 0.2 0.1 0 -0.1 -1 0 1 1

0.6

0.8

0.2

0.4

0





1.1

RYHUODSSHG FOXVWHUV )6WXGHQW GLVWULEXWLRQ   GLPHQVLRQV  LQVWDQFHV

1

5DZGDWD KLJK GLPHQVLRQ   'GDWDDIWHU XVLQJDOJ >@

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 1 0 -1

0.1

0

0.4

0.3

0.2

0.5

0.6

0.8

0.7



0

FOXVWHUV &KL6TXDUH GLVWULEXWLRQ   GLPHQVLRQV  LQVWDQFHV

5DZGDWD KLJK GLPHQVLRQ   'GDWDDIWHU XVLQJDOJ >@ 

-0.2

-0.4

-0.6 -0.8 0.4 0.2 0 -0.2 -0.4





230

2011 11th International Conference on Intelligent Systems Design and Applications

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0