On-line Unsupervised Outlier Detection Using Finite
Mixtures with Discounting Learning Algorithms
Kenji Yamanishi
NEC Corporation
4-1-1,Miyazaki,Miyamae,
Kawasaki,Kanagawa
216-8555,JAPAN
!
Jun-ichi Takeuchi
NEC Corporation
4-1-1,Miyazaki,Miyamae,
Kawasaki,Kanagawa
216-8555,JAPAN
" #$% &'
!
ABSTRACT
798:<;=>@?BA >C:<>D@:<=EGFH=IKJ3LM8FAJONP>F:QJG;R=ISIS8>=FTAJU:QJVNP=F=F W X
ISYZ>CD=4[$D\JO;;4]K=F^L0?QJO8$AKA >C:<>CDC:<=E1F2XF >C:`_!EG?<ab=F:S?<8 IS=EGFBA >C:<>D@:<=EGF2X
F >C:`_!EG?<abNPE1F=4:<EO?<=F W XZ>@:<D1c9dN*JO?S:@d=4L0:<>C?\X$_fe =D@eg_!>JOhh ?<>Ci=JU:<>
JOIjddZX#=I*JGFVE18 :<;=>C?*A>C:<>DC:<=EGFk>F W1=F>lJ1A?S?<>ISIS=FW:<e =ImY ?<EGh n
;>NoL0?<E1No:<e>i=>C_fYZEG=F:pEOLqIr:QJU:<=Ir:<=D\JO;s;>\JU?<F=FWj:<e>EO?S]cutqe=I
YJGYZ>C?lY ?<EUi=A >IbJv:<e>EO?<>C:<=D\JG;RhJGIS=IlL0EG?Kd d,JGFA,>NPY=4?<=D\JG;;4]
A>NPE1F Ir:S?QJO:<>If=4:<If>Cw>DC:<=i&>CF>ISIcqddjA >C:<>D@:<IxEG8 :<;=>C?<Ix=FgJGFgEGF n
;=F>mY ?<ED>CISIR:<e ?<E18 W1e^:<e>uE1Fny;=F >8F IS8YZ>C?<i=IS>\A^;>\JO?<F =FWjEGL!J
Y?<E1hJGh=;=Ir:<=DRNPEA >;z8IS=FWuJR[$F =:<>xNP=4{:<8 ?<>fNPEA >;}|EGL:<e>x=F n
L0EG?<N*JU:<=EGFISEG8 ?<D>1c~JGDQe:<=NP>JbAJU:<8N=Ip=FY 8 :pdd^>NPY;E\]I
JOFO$y
MG
M@<G
M*SGQ
0*1 &GQ
M0T:<Eu;>\JO?<Fj:<e>xY ?<EGh n
JOh=;=Ir:<=DNPEA>;cHISDEO?<>u=IfW1=i&>CFb:<E:<e >pAJU:<8NhJGIS>\AlEGFb:<e >
;>\JU?<F>\ANPEA >C;'XU_f=4:<emJxe =WGemISDCEG?<>q=F$A=D\JO:<=FWJfe=W1euYZE1ISIS=h=;=4:`]
EOLqhZ>=F WgJ*Ir:QJO:<=Ir:<=D\JG;sE18 :<;=>C?\ctqe>mFEUi&>;L0>\JO:<8?<>IpEGL5ddKJO?<>1
|=4:=IJ1AJOY :<=i&>q:<ERF E1FnIr:QJU:<=E1F$JU?S]ISEG8 ?<D>CIsEOL+AJO:QJ1|#JRISDEO?<>
eJGImJlD;>\JU?Ir:QJU:<=Ir:<=D\JO;}O=F L0EG?<N*JO:<=EGF n':<e>EO?<>C:<=DlNP>\JOF=FW&|p=4:
=IuDE1NPY 8 :QJU:<=EGF$JO;;4]=F >C{YZ>FIS=i&>GJGF$Av&|R=:mD\JOFe$JGFA ;>PhZEG:<e
DJO:<>WGEG?<=D\JG;qJGF$ABDE1F:<=F8EG8IRiGJO?<=JGh ;>IcjFB>C{YZ>C?<=NP>F:QJG;JOY n
Y ;=DJO:<=E1FK:<E*F>C:_qEG?<ab=F:S?<8 IS=E1FBA >C:<>CDC:<=E1F^ISeE\_fI9:<eJO:Rddb_qJGI
JOh;>:<EP=}A>F:<=4L0]lAJO:QJ%_f=4:<e^e=WGe^ISDEG?<>Ix:<e$JU:DCEG?S?<>ISYZEGF$A >A^:<E
JU:S:QJGDQaIXZ_f=:<eK;E\_DEGNPY8 :QJU:<=E1F$JO;DEGIr:<Icp8?S:<e>C?x>C{YZ>C?<=NP>Fn
:QJO;5JGY Y;=D\JO:<=EGFVeJGIu=A >F:<=4[$>\AJKF8 NhZ>C?EOLfNP>\JGF =F WGL08;s?QJU?<>
DJGIS>I=FvJODC:<8$JO;se >\JG;4:<e=F IS8 ?QJGF D>%YJO:<eEG;E1WG]AJU:QJjL}?<E1N 8 Irn
:S?QJO;=}J¡ I9¢9>JG;4:<eg£`F IS8 ?QJOFD>¤!EGNPNP=ISIS=EGF2c
1.
tqe >YINTRODUCTION
?<E1h;>NoEGL!E18 :<;=>C?A>C:<>DC:<=EGF=IREGF>EOL!:<e >mNPEGIr:9LM8 F$A JOn
NP>CF:QJO;#=ISIS8>Ip=FBAJU:QJbNP=F=FWc£:9=IpDC;EGIS>;4]K?<>;JO:<>\A^:<EbL}?QJG8$A
A>C:<>DC:<=EGF2XF>@:`_qEO?<a=F:S?<8IS=E1FvA >C:<>D@:<=EGF2X>C:<DGcXIS=F D>bD@?<=NP=FJG;
EO?fIS8ISY =DC=EG8IfJODC:<=i=4:<=>I5N*J]%EOL0:<>Fb=F$A 8 D>xIr:QJO:<=Ir:<=D\JG;+E18:<;=>C?<Ic
> LMED8 IEGFg:<e>p=ISIS8>EGLG
0 QU¦ @Q§\
MCS^G'
y@m@S
¥ p
GP=Fl_fe=DQel:<e>LME1;;E\_f=FW*DE1FA =4:<=E1F IJU?<>p?<>\¨8=4?<>\A+
|©q'
y@Q^GSK&@<CSkªQOS3G, QU¦ @Q§\
MCSkSGQ
M3`«
0
M\«O@%G
'G¬@GSQ\®£F¯W1>F >C?QJG;pIr:QJU:<=Ir:<=DJG;uJGY Y ?<E&JOD@e >I
Graham Williams
CSIRO Mathematical and
Information Sciences
GPO Box 664, Canberra ACT
2601, Australia
(*) #+#, -.0/0/#1234 ) 5#6
:<E%EG8 :<;=>C?A >C:<>D@:<=EGF2XE1F>R[ ?<Ir:f;>\JO?<F I9JOFl8FA >C?<;4]=FWmNPEA >;+EGL
:<e>!NP>D@eJGF =ISNHLMEG?sA JO:QJOnyWG>F>C?QJU:<=E1F%L0?<EGN>C{ JGNPY ;>CIX&JOF$Au:<e >F
>iGJG;8$JU:<>I!e E\_°;JO?<WG>9JRWG=i&>FP=FY 8 :sAJU:<8N±=I!A>i=}JU:<>\A?<>;JO:<=i&>
:<Ef:<e>!NPEA>;$zIS>>s>1c W cX$² @³ |@c ¥ >?<>\¨8=4?<>!e >C?<>s:<eJO::<e >!;>\JU?<F=FW
Y ?<EDC>ISI9hZ>8F IS8YZ>C?<i=IS>\Acf;4:<eEG8WGeg:<e>IS8YZ>C?<i=IS>\Ag;>\JU?<F=FW
h$JOIS>\AJOYY?<E&JGDQeB=IpYZEGY8 ;}JU?=FL0?QJO8$ABA >C:<>CDC:<=E1F´zS² ³ X}² µ ³ X² 1@³ |@X
:<e>8 FIS8YZ>@?<i=IS>\Ab;>JO?<F=F WPh$JGIS>AgE1F>=I9F EG:xE1F ;4]gNPEG?<>R:<>CD@en
F=D\JO;;]%A =4¶PD8 ;4:sh 8 :JO;ISENPEO?<>qY ?QJODC:<=D\JG;;4]%=NPYZEG?S:QJOF:\X&IS=FD>f=F
?<>\JO;IS=4:<8$JU:<=EGFIf;JGhZ>;>\Ag>@{JONPY;>I5NP=W1e:fF EG:fhZ>J\i1JO=;}JOh;>1c
1|^·2u¦S\Q@<b
MPG$y
M\Ktqe$JU:%=IX>i&>@?S]:<=NP>*J^AJU:<8N =I
=FY 8 :\X$=4:=Ix?<>\¨8 =?<>Al:<EP>i1JO;8$JO:<>e EU_H;JO?<WG>u:<e >AJO:<8 N®=IA >@n
i=JO:<>\A%?<>;JO:<=i&>x:<EJpF EG?<N*JG;Y$JO:S:<>@?<F2c£`FPDCE1F:S?QJGIr:\XNPE1Ir:!>C{=Ir:Sn
=FW*_qEO?<a^E1FBE18 :<;=>C?A>C:<>DC:<=EGFkz>1c WcX² C³ X² ¸ ³ X² µ ³ X² GC³ |m=FBIr:QJO:<=Irn
:<=DI5JOF$A*AJU:QJNP=F =F Wp=IqDE1F D>C?<F >\A%_f=:<e*hJO:<DQe nA >C:<>CDC:<=E1F*Y ?<EOn
D>ISIS>CIX!=F_fe=DQeVEG8 :<;=>C?<IDJGF3hZ>lA>C:<>DC:<>AvE1F;4]3JUL0:<>C?%IS>>=FW
:<e>f>F:<=4?<>AJO:QJOIS>C:\ctqe>xE1Fny;=F >xIS>@:S:<=F W=I!NPEG?<>5?<>\JG;=Ir:<=D:<eJGF
:<e>9h$JO:<DQelEGF>R_fe >FlEGF>A >JG;I5_f=:<eb:<e>9:S?<>NP>CF$A EG8IfJONPE18F:
EGLA JO:QJu=FlF>C:_qEG?<ajNPE1F =4:<EG?<=FWX>C:<DGc
¹ OE :<>j:<eJO:u:<e>C?<>*>C{=Ir:<I%EGF;4]JgLM>@__qEO?<a,z>1c W ck² ³ |L0ED8IS=FW
E1F^:<e >mEGF ny;=F >m8 FIS8 YZ>C?<i=IS>Ag;>JO?<F=F WbhJGIS>\AKJGY Y ?<E1JGDQe2cptqe =I
Y$JOYZ>C?#=F:S?<EA 8 D>IdN*JU?S:@d=4L0:<>@?5z'JGh h ?<>i=JO:<>\AuJGI#ddR:<e ?<E18 W1e E18 :
:<e=IfY$JOYZ>C?@|@X_fe=D@ebNP>>C:<Iq:<e >R?<>\¨8=4?<>NP>F:<I |fJOF$Al1|@c
tqe>JOYY?<E&JGDQegEOLdN*JU?S:@d=4L0:<>C?f=IJGI5LMEG;;E\_fI
£S|xddl8 IS>IRJPY?<E1h$JOh=;=Ir:<=DmNPEA >;JGI9JP?<>CY ?<>IS>F:QJU:<=EGFKEGL!JGF
8FA >C?<;4]=FWNP>DQe$JOF=ISNºEOLA JO:QJOnyWG>F>C?QJU:<=E1F2cstqe >9NPEA >C;$:QJGa&>I
Jbe =>C?QJO?<DQe=D\JO;!Ir:S?<8D@:<8 ?<>1X2=FB_fe =DQevJg
M<y<GSO»&@<
M¼_f=4:<e
JPF8NhZ>@?EOLD>;;IR=IR8IS>\Al:<EP?<>Y?<>IS>F:9JjY?<E1h$JOh=;=4:`]^A>FIS=4:]
EUi&>C?P:<e >gA EGN*JG=FVEGLpD\JU:<>W1EO?<=D\JG;i1JU?<=}JOh;>IjJGFA3L0EG?j>\JOD@ekD>;;
JP½
Mjm
¾G<bP\&C2=Iu8IS>\A:<Eg?<>Y?<>IS>F:u:<e>*Y ?<EGh$JGh =;=4:]
A >CFIS=4:`]jEUi&>C?f:<e>RA E1N*JO=FlEGLDE1F:<=F8E18 Ifi1JU?<=}JOh;>Ic
£S£S|~i&>C?S]:<=NP>*JKAJU:<8N =I=FY 8 :\Xsd d>NPY;E\]IJOFE1Fn;=F>
;>\JO?<F =FWJG;WGEG?<=4:<eN:<ER8 YAJO:<>q:<e >qNPEA >C;'c ¥ >5e$J\i&>qA >i&>C;EGYZ>\A
:<e>¿ÀÁ2¬Ã'¿SÄC@
'GM ¼RÀp
M@<G
MRÁ@¦$&Q!ÂqQ
0PG
'O&ÅsJG;4n
W1EO?<=4:<eNÆLMEO?;>\JU?<F=FW,:<e >e=Ir:<E1WO?QJGN´A >CFIS=4:`]ÇLMEO?:<e >vD\JU:<>Cn
W1EO?<=D\JG;AE1N*JG=Fvzyd>D1c c |@XJGFAb:<e>P¿ÀxÂ!ÈÉÃ'¿SÄC@
'GM ¼%Àp
MQ
<G
MKÂs¾@¦ SCyG
'O¬GZKÈB\¾G
M
Ê
0CÅ*JG;WGEG?<=4:<eNËzyd>D1c c G|
LMEO?P;>\JO?<F =FWK:<e>*[$F=4:<>jNP=4{:<8?<>PLMEG?:<e>jDE1F:<=F8E18 I%AE1N*JG=F+c
tqe>C=?uNPEGIr:=NPYZEO?S:QJGF:RL0>\JO:<8?<>P=Ip:<eJO:p:<e>@]°O
M@QO :<e>%>CL}n
LM>CDC:xEGLY$JOIr:x>C{ JGNPY;>I5=Fj:<e>pE1Fny;=F >RY ?<ED>CISIc
£S£S£S|d dvW1=i&>IPJKISDEO?<>b:<EB>\JGDQe°A JO:<8 N.EGFV:<e >bhJGIS=IPEGLx:<e>
;>\JO?<F >\AbNPEA>;XNP>\JGIS8?<=FWe E\_¯;JO?<W1>R:<e >9NPEA>;Ze$JOI5D@eJGFWG>\A
JOL}:<>C?q;>\JU?<F=FWctqe8IsJRe=W1ePISDEO?<>=FA =D\JO:<>CIqJpe=W1ePYZEGISIS=h=;=:]
:<e$JU:5:<e>A JO:<8Nº=IxJOFgE18:<;=>C?\c
tqe >pFEUi&>;LM>JO:<8 ?<>CIxEOLsddjJO?<>pIS8NPN*JU?<=>\AjJGI5LMEG;;E\_fI
J1|¿¿m
Ms&&@¦
M§G!y9ZGy<yG
'OZGQ¼COrQ@#£`FpDCE1Fi&>F:<=E1FJG;
Ir:QJU:<=Ir:<=DJG; JGYY?<E&JOD@e >IX&=4:#=I8 IS8$JG;;4]uJGISIS8 NP>\Ap:<e$JO:JGFu8FA >C?<;4]n
=F W%=F LMEO?<N*JO:<=E1FlISE18 ?<DC>L0EG?AJU:QJOnyW1>CF>C?QJU:<=EGF^=IxIr:QJU:<=E1F$JU?S]² @³ c
tqe =IR=IXeE\_q>i1>C?\XFEO:9?<>\JO;=Ir:<=Dm_fe >FKE1F >A>\JG;I9_f=4:<eBA?<=4L0:<=F W
ISEG8 ?<D>CI9EG?x:<=NP>CnyIS>C?<=>IxAJU:QJcftqe >A =ISDE18 F:<=F W*JG;W1EO?<=4:<eN >N%n
Y ;EU]&>\Ajh]bd d*;>\JU?<FIq:<e>ISE18?<D>RLMEO?<W1>C:S:<=FWE18 :SnyEOL0nAJU:<>9Ir:QJO:<=Irn
:<=DIuEGLxA JO:QJX8IS=FW^J^A>D\J]BLJGD@:<EG?\Xe>CFD>P=Iu>C{YZ>DC:<>\AK:<E^hZ>
JGAJOY :<=i&>R:<E%F E1F nyIr:QJU:<=EGF$JU?S]bISEG8 ?<D>CIc
hZ
| C<GS<1CGSlªC¼P¿ ¿^Gj<OpQyO
M<
'<1
0\«GQPO
'G$'0SGS@
'*SG
MT£F°NPE1Ir:jY?<>i=EG8IP_qEO?<aZXxJ
ISDCEG?<>j=ImD\JG;D8 ;JO:<>\A8IS=F WBe >8 ?<=Ir:<=DIuIS8DQe3JGImDE1Ir:l² ³ X}² ³ JGF$A
;JOD@aI%JgIr:QJU:<=Ir:<=DJG
; r8 Ir:<=4[$D\JU:<=EGF2X#_fe =;>*:<e
> gJOe$JG;JOFE1h =IPA =Irn
:QJOFD>B² C³ X:<e>j¨8$JGA?QJO:<=DbA =Ir:QJGF D>K² ³ X² ¸ ³ _q>C?<>j8IS>\A:<EKISDEO?<>
EG8 :<;=>C?<I*=FkISEGNP>b_qEO?<aZc,d dA >C[F>IPJBISDEG?<>bLMEG?jJBAJU:<8N.=F
:<>@?<NPIxEOLsJ%Ir:QJO:<=Ir:<=D\JG;A=Ir:QJOFD>NP>\JOIS8 ?<=FWPe E\_T;JO?<WG>u:<e >A =Irn
:S?<=h 8 :<=E1F;>JO?<F>ABL0?<EGN:<e>AJU:<8NeJGIpNPEUi&>\AgL}?<E1N:<e >%E1F >
hZ>@LMEG?<>x;>\JO?<F =FW ctqe8 I=4:=IsFJO:<8?QJG; :<Ep=F:<>C?<Y?<>C:#:<e$JU:qJRA JO:<8 N
EOLe=W1ebISDEG?<>=IX_f=4:<ege =W1elY?<E1hJGh=;=4:`]XJGFbE18 :<;=>C?\c
DU|p¿¿
0uQO9¦$yG
'OZ1M ¼l
MS¾@¦ @ Q
0§G\tqe >DEGNPY8:QJO:<=E1FJG;
DCE1NPY;>C{=4:`]9EGLZddLMEO?#D\JO;DC8;JO:<=FW9JxISDCEG?<>sL0EG?>\JOD@euA JO:<8N¬=I;=F n
>JO?q=F:<e >5F8NhZ>@?EGL+Y$JU?QJGNP>C:<>C?<I=F%:<e>5NPEA>; JGF$AP¨8J1A?QJU:<=D
=F¯:<e>KF8NmhZ>C?jEGLmi1JU?<=JGh;>IcºEO?g>C{ JGNPY ;>1Xx=:lD\JGFÇY?<ED>ISI
JOhZE18:pµ X bAJU:QJ_f=:<e^L0E18 ?RJO:S:S?<=h8:<>I9=FBO¸*IS>CDE1FA Iz >CF n
:<=8 N £S£S
£ l
¢ U|@c
A$|p¿¿3<G3&<G
M0ª<G0<G'&GQ
'<1!GZ^<G
M G§OO@
1ª@tEpEG8 ?aFE\_f;>\A WG>1X dd=I:<e>q[ ?<Ir:E1F ny;=F>f8F IS8YZ>C?<i=IS>\A
EG8 :<;=>C?sA >C:<>CDC:<EG?:<e$JU:#D\JOFPA >\JO;_f=:<ehZEG:<eDJO:<>WGEG?<=D\JG;JGFAmDEGF n
:<=F8EG8IfiGJO?<=JGh ;>CIc
tqe >gA>IS=W1F3EGLRdd_qJGI%=FISY =4?<>\Ah]:<e>P_qEO?<ah]!8?<W1>bJGF$A
de$J_5ntJ];EO?P² ³ cu798?9_qEO?<a^A =4w>C?<IL0?<E1N.² ³ =F^:<e>LME1;;E\_f=FW
?<>CW&JO?QAI |9d db:S?<>\JO:<IhZEG:<eKD\JU:<>W1EO?<=DJG;JGFAKDCE1F:<=F8 E18 IiGJO?<=4n
JOh;>IX&_fe =;>p² ³ A>\JG;IE1F;4]_f=4:<eDEGF:<=F8 E18I#EGF>IcsG| ¥ e=;>p² ³
8 IS>Iq:`_!ENPEA>;I5=F*:<e>9JG;W1EO?<=4:<eNg:<e>;EGFWu:<>C?<NNPEA >C;JGF$A
:<e >fISeEG?S:s:<>C?<N±E1F >1X ddm8 F=4[$>CIs:<e>CN =F:<EpE1F >NPEA>; _f=4:<e%:<e >
JO=N.EOL9JgDC;>JO?<>C?Ir:QJO:<=Ir:<=D\JG;5NP>\JOF=FWgJGF$AJg;E\_q>@?%DEGNPY8 :QJUn
:<=EGF$JG;DEGIr:\c&|#dd8IS>I#>C=:<e >C?sJYJO?QJGNP>@:S?<=Ds?<>Y ?<>IS>CF:QJU:<=E1FL0EG?
JmY ?<E1hJGh =;=Ir:<=DpNPEA >;EO?xJFEGF nyY$JU?QJGNP>C:S?<=D9EGF>1X_fe=;>pE1F ;4]jJ
F E1FnYJO?QJONP>C:S?<=DPE1F>*=Iu8IS>\A=F¯² ³ c^£F3d>CD1c c X_q>*DEGNPY$JU?<>
EG8 ?#YJO?QJONP>C:S?<=DsNP>C:<e EAR_f=:<e:<e>FEGF nyY$JU?QJGNP>C:S?<=DE1F >:<ExISeE\_
:<eJO::<e>qL0EG?<NP>C?E18:<YZ>C?SLMEO?<NPI:<e >5;JO:S:<>C?shZEG:<e%=FPJODD8?QJGDC]%JGF$A
DCE1NPY8:QJO:<=E1FbDE1Ir:<Ic
> >NPY=4?<=D\JO;;4]%A >NPEGFIr:S?QJO:<>q:<e >5Y ?QJODC:<=D\JG;$>@w>DC:<=i&>F >ISIEGLdd
¥ 5
8 IS=FWK:<e>lF >C:`_!EG?<av=F:S?<8IS=EGF°A JO:QJGIS>@:^z¤!8Y µGµ1µ&|l² ³ c
x;4:<eE18 W1e=:9_5JGI8 IS>\A=FK:<e>%DEGF:<>C{:pEGLqJbIS8YZ>@?<i=IS>\AB=F:S?<8n
IS=EGFA>C:<>DC:<EO?R;>\JO?<F =FWjY ?<E1h ;>No=
F ¤!8 Y µ1µGµX_q>u8IS>\A
=4:*=Fk:<e >gISD>FJO?<=EvEOLpE1Fn;=F>l8FIS8 YZ>C?<i=IS>\AV=F:S?<8IS=EGF,A >@:<>DCn
:<=EGF2cv£F3E18 ?>C{YZ>C?<=NP>F:\X#LMEO?PJKF>C:_qEG?<avJGDD>CISI%;E1WAJO:QJOIS>C:
EOLRIS= >^ G¸X G¸=FDC;8A =FW ¸ =F:S?<8IS=E1F IXq=4:*A>C:<>DC:<>\
A !
=F:S?<8IS=EGFIq=F*:<e>f:<E1Y AJO:QJpEOLe=WGe>Ir:!ISDEG?<>IXJGFA*¸& ±=F n
:S?<8 IS=E1FIf=Fl:<e >9:<E1"
Y AJU:QJEGLe=W1e >Ir:xISDEG?<>Ic ¥ >RJG;ISEP8IS>\A
Jje>\JO;4:<e=FIS8?QJGF D>YJO:<eEG;E1WG]A JO:QJGIS>@:IS8YY ;=>ABh]g:<e >%8 Irn
:S?QJO;=}JOFk¢>\JG;4:<e£FIS8 ?QJOFD>b¤!EGNPNP=ISIS=EGF3:<EKA>NPE1F Ir:S?QJO:<>P:<e$JU:
d d*_qJGIJGh;>R:<E%=A>F:<=L}]jIS>i&>C?QJO;NP>\JOF=FWOLM8;Z?QJU?<>uDJGIS>If=Fg=4:\c
2.
OUTLINE OF SMARTSIFTER
# >C:Rz$%'&|A>FEO:<>9JAJU:<8N±_fe>C?<>($KA >CFEG:<>CIqJpi&>DC:<EO?qEOLD\JU:<>Cn
WGEG?<=D\JO;#i1JU?<=}JOh;>IJGFA)&3A >F EG:<>IxJ%i&>CDC:<EG?EGLDEGF:<=F8 E18IfiGJO?<=4n
JOh;>Ic ¥ >R_5?<=4:<>p:<e*
> rEG=F:9A =Ir:S?<=h8:<=E1FgEOLfz$+%'&|5JGI+,z$+%-&#|+.
,
z $/| ,z &10 $3| 2 # >C4
: ,z $|qhZ>?<>CY ?<>IS>F:<>\Agh]lJj
M<y<GSO @<
M¼
_f=4:<e^Ju[$F=4:<>RF8 NhZ>C?5EOLA =5I `E1=F:DC>;;Iuzyd>CD1c c |@X$JGF$A*LMEO?9>\JOD@e
DC>;;'XLMEG?RJG;
; $+I5:<e$JO:xLJO;;=F:<EP=4:\X;>@1
: ,z &10 $|qhZ>R?<>Y?<>IS>F:<>\Agh]
JGFl=}A>F:<=D\JG;LMEO?<N EOLJR½
Mp
¾G<P\CZzyd>D1c c 1|@cs¢9>CFD>
_q>^Y?<>Y$JU?<>^JGIjN*JGF]v[F=4:<>gNP=4{:<8 ?<>bNPEA >;IjJGI*D>;;Ij=FV:<e>
e=Ir:<EGWG?QJGN®A>FIS=4:]c¤!E1F IS=}A>C?f:<e>IS=:<8JO:<=E1Fj_fe>C?<>RJmIS>\¨8>CFD>
EGL!AJU:QJj=IRWG=i&>F2z $67%'&6@3| %\z $98%'&98;
| :<:7:9=FJGFKE1Fny;=F >mY?<ED>ISIc
tqe>LM8FAJONP>F:QJG;ZIr:<>Y I5EGLdN*JO?S:@d=4L}:<>C?fJO?<>pWG=i&>FbJGI5LMEG;;E\_fI
c =9=i1>F:<e?
> >`:<e3=FY8:PA JO:<8N z $A@B%'&A@r|@X=A >CF:<=4L}]:<e>jD>;;
:<e$JO
: $ @ LJO;;Ib=F:<EvJGF$Ak8YAJU:<>g:<e>^e =Ir:<EGWG?QJONËA>FIS=4:]
8IS=FWp:<e>9C
d # ~vJO;WGEG?<=4:<eNzyd>D1cc |:<EEGh :QJG=D
F ,9E @5F z $|@c
tqe>F+XL0EG?%:<eJO:D>;;Xq8YA JO:<>P:<e>*[$F =4:<>bNP=4{:<8 ?<>*NPEA >C;
8IS=FW:<e >C
d R1
~ ^GC
d G JO;WGEG?<=4:<eN zyd>CD1c c 1|!:<E%EGh :QJG=F
@F
, E
z &*0 $|@cEG?xEG:<e >C?xD>;;IX$IS>C+
: , E @F z &10 $
| .H, E @JI 6 F z &10 $3| 2
cf¤qJG;D8;JU:<>JBISDEG?<>gL0EG?*:<e>lAJU:<8N EGFk:<e>bh$JOIS=I*EOLR:<e>
NPEA >;I5hZ>CL0EG?<>uJGFAlJOL}:<>C?8YAJU:<=FWlzyd>D1c c 1|@c
2.1
Categorical
!>;E\_
_!>mA>ISDC?<=hZ>ueE\T
_ Variables
:<EP;>\JU?<FK:<e >e=Ir:<E1WO?QJGNoA >F IS=:]gEUi&>C?
:<e>9D\JO:<>WGEG?<=D\JO;A E1N*JO=F2c # >@:5:<e>pF8NmhZ>C?qEOLD\JO:<>WGEG?<=D\JO;i1JU?<=4n
JGh ;>I9hZD
> K#c # >C:x:<e>p?QJOFW1>uEGL:<e >L':<e^DJO:<>WGEG?<=D\JG;iGJO?<=JGh ;>mhZ>
F
F
F
MNEO
.QPR ES6 O %7:7:7:T%BR EO
z L1. %7:7:<:A%BK2|@cm¤!;JGISIS=4L0]B:<e>CN :<EjE1hn
U!VW
F
F
:QJG=F3Jl[F=4:<>*F8 NhZ>C?EOLA =5I rEG=F:mIS>C:<IX
PZY E6 O %7::<:A%BY [BEO V W z L.
F
F
F
F
EO
EO
> Y ]_
Y EO
.baud
z c"b
e.
f|JOF$A M
.hg [ V 6 Y EO 2
%:<:7:A%\K3| %U_fe >C?<*
^
]<i
]
`
F
6 F
; Y ]BE jk :<:7: k Y ]\Elm :<e>mdz c 6 %<:7:7:T%nc l |:<eBQCM c ¥ >
¥ >D\JG;;Z:<e>xD>;T
e$J\i&p
> oq.brs6 k :7:7: k r l D>C;;Ix=Fl:<EG:QJO;'cqtqe=Ix=FA 8 D>IfJ%Y$JU?S:<=4n
:<=E1F =F W%EGL#:<e >pA EGN*JG=F2c
9=i&>FIS8DQeJlYJO?S:<=4:<=E1F =F WlEOLq:<e>PAE1N*JO=F+X2JK
M<y<GSO»&@$
<
M¼5LMEO?<NPIqJpY ?<EGh$JOh=;=:]*A =Ir:S?<=h8:<=E1F2X1_fe=D@eP:QJOa&>IqJRDCE1FIr:QJOF:
iGJG;8>uE1FB>\JGDQeBD>;;cutqe>ue=Ir:<E1WO?QJGN A>FIS=4:`]g=I9ISYZ>D=4[$>\AKh]^J
Y$JU?QJGNP>C:<>@
? tu. z v 6 %7:<:7:A%\v ` |q_fe>C?<x
> w ]<` i 6 v ] . %yv ]xz *JOF$A
v
A
>
F
G
E
<
:
>
m
I
<
:
e
l
>
Y
<
?
1
E
h
G
J
h
=
;
4
=
`
:
3
]
G
i
G
J
;
8
j
>
LMEO?P:<eN
> cG:<eVD>;;ck£Lx:<e>C?<>
]
JO?<
> { ] Ir] NmhZE1;I=F%:<e 4
> cGny:<ePDC>;;'X:<e >fY ?<E1hJGh =;=4:`]i1JO;8>fEGL+>\JOD@e
Ir]NhZEGT
; $B=Fg=4:x=IfWG=i1>Flhp
] ,z $|
| .bv ]} { ] 2
=
> =F:S?<EA 8 D>Pe>@?<>%:<e>jdC # ~TJO;W1EG?<=4:<e Ngcgtqe =Iu=IJgiGJO?<=JOF:
¥ P
EGL:<e> # JOY;JGDC>%;J\_pX+h]g_fe =DQeKE1F >>Ir:<=N*JO:<>CI:<e>mY ?<EGh$JGh =;=4:]
iGJG;8>5EUi&>C?sJRA=ISDC?<>C:<>fA EGN*JG=F_f=4:<e,2~ zR|. z5;T?| } z5N)o#|
LMEO?l>JGDQe¯>;>NP>F?
: RV_fe >C?<
> X=I*:<e>^IS=>KEGLuJ
AJU:QJjIS>¨8 >FDC>1
X ;*=I:<e>uF8 NhZ>C?xEOL!EDDC8 ?S?<>F D>IREO*
L Rg=F^:<e>
IS>\¨8>CFD>1X+JOF$
A o =I9:<e>uF8NmhZ>C?xEGLs>;>NP>F:<I9=F^:<e>mA =ISDC?<>C:<>
A EGN*JG=F2c5tqe>C
d # ~°JG;WGEG?<=4:<eNo=IISYZ>D=4[$>Agh]lJPA =ISDEG8F:<=FW
Y$JU?QJGNP>C:<>@
? \z
&|!_fe >C?<>uJISN*JG;;>C
? P=FA =D\JO:<>CIx:<eJO:9C
d # ~
e$JOIgJv;JO?<WG>C?^=
F 8>F D>^EGLuYJGIr:g>@{JONPY;>IKzIS>>=W c |@c tqe>
L x
=FKC
d # ~fc
# JOY;JGDC>u;J_¬=Ix?<>\A8D>Aj:<E:<e >RD\JGIS>pEO
2.2
>!A >ISDC?<=hZ>qe E\_v:<Variables
E;>\JU?<Fm:<e >sNPEA>;EUi&>C?:<e >!DEGF:<=F8 E18I
¹ >@{:2_qContinuous
A GE N*JG=F2c ¥ >DEGFIS=A >C?9:`_qEbi&>C?<IS=E1F I9:<e >Y$JU?QJGNP>C:S?<=Dmi&>C?<IS=E1F
JGFAj:<e >pFE1FnyY$JO?QJONP>C:S?<=DRE1F >1c
2.2.1
£`F¯:<e >Y$Parametric
JU?QJGNP>C:S?<=Di&>CVersion
?<IS=E1FÇ_q>v>CNPY;E\]¯JGIKJ[$F =4:<>NP=4{:<8 ?<>
NPEA >C;1EUi&>C?+:<e>DEGF:<=F8EG8I+A EGN*JG=FJxfG<<
'G%m
¾G<!P\&C
z&*0 t&|.
,
`
6
O i
O
z&10
,
%'
O
O
|3%
_ e>@?<>xfl=IJPYZE1IS=4:<=i&>=F:<>WG>C?\X O z C%yw ` 6 O . JGFAl>\JOD@e
f
O i
,z&10
%'
|l=IKJ&nA =NP>F IS=E1F$JO ;p=RJG8 ISIS=}JOF
A = Ir:S?<=h8:<=E1FH_f=4:<e
O
O
A >CFIS=4:`]jISYZ>D=4[>\Alh]jNP>\JG
F O JGFAbDEUiGJO?<=JGF D>pN*JO:S?<=4{ O
I
/|
O' J¡O-¢T£
_fe >C?<>xL1.
> IS>C:tD.z
¥ 9
/¥7¦
¢§7¨
8¤
¡|O
6
8©'ª«x¬®
¨
¤
/
O-¢¯9¡
O
6
°
OJ¢±
KJGFAg=I9:<e>mA =NP>F IS=EGFKEGLq>JGDQeA JO:<8Ngc
%'
%'
|@c
`
`
`
%:7:7:T%Bf
67%B|67%B6<%:7:7:T%
¥
F
« "!#$"#$%&!'( )©+*$!,-"#/.1032 E6 O 545464 2
; < .=% >Z©5#/?
@ J © « ?BACEDF#$ G""HI3 "!#JCA
K ¤ ©LNM O 6 54I45®4 O l ¢T£QP
OO
O\ 8 £
V .£
¤SR
RUT
¤
@ J © « ¥ ?BACE
WX
, ©L- ©5N4
Y «*3 "#$%-CA
ZN)$"SG © V M ME.X[\
, «]SG ©^["BH ©
@
_ ©6R *a` £ 9b 6 5454I®4 b l ¢ ¢
c !
©Id\) O 6 54I4I®4 O l ¢fe )aBd ©IG"Gfg
M @ O 6 I4I4I4® O l ¢ . £ ; ¢ M @JI 6 "O 6
¤
@5F
M @ "O 6 I4I45®4 O l
@
l E O 6 I4I4I®4 O l ¢ . £
; ¢ ¢n
¤
6 F
¤
F
"E .±z
O
6454I4® :¢ ?
54I454® O l i¢ hkj @ O 6 546454® O
¢/hm<
; hUop<
F
g
El
] m
"O 6 645454 O l ¢
F
8 F
E
E
El
2 ]Bj 4 2 ]\v 46454 2 ] m
ZN)©5-© j @ "O 6 I4I454® O l ¢p£
'x)© V e )y*3 z$,{'fG"G"[|"#} !& ) ©
¤ @ O 6
O 6 54I4I4® O l ¢fe )adB©IG"Gfg#$*
j
I4546
4 O l ¢T£~P ! )©5 ZN"[J©?
V .£ V h
¤9
X}
a
"
@5F
E
`
l
@F
z5|u£F:S?<EA8D>jJKA =ISDEG8F:<=FW^YJO?QJGNP>@:<>C? vz
HQ |p:<E
NPEA =4L0]*:<e>98YAJU:<=FW?<8 ;>zy1|q=F:<Em:<e>9L0E1;;EU_f=F W
645454 :¢\ £
¤
¤
8 F
c !+©Id\)q`sr+2 ]BE jut 2 ]\E vwt&4I4I4 2
F
7 9 8
EO
[BV
.£
¢
E
6 F
=4?<Ir:\XU_q>?<>i=>C_:<e >s=F DC?<>NP>F:QJG;1~1 JG;W1EO?<=4:<eN ² ³ L0EG?#;>\JU?<F n
=F W)=RJO8ISIS=JGFKNP=4{:<8 ?<>RNPEA>;Ic # >C:S:<=F WshZ>uJGF^=4:<>C?QJU:<=E1FK=F n
F
A>C{X _!>A >C[F>RIS8¶PD=>F:fIr:QJO:<=Ir:<=DI E zL9. %:7:7:T%Bf |qh]
E
F
3
£
O
p\
£
¤
F
O
E
V 4
_fe >C?<>
O
@
F
E
F
}\
O E Fz | .
E
O
6
U i
F
¡ O
F
E
w
O i
@
¢' F 9
¢4
6
E
O
I
6 F
E
6
O
z&
,
I
U
6 F
F
¥ >JG;ISE*A >@[$F> "E z r|9zL.
"
I
E
0
O
z&
,
O
O
U i
E
`
O
U
0
%7:7::;% f
6 F
O
E
U
@
F 9
¢4
6
E
U i
I
E
%\
O
6 F
I
|sLMEG?&
F
F
F
E z r| }. \ : E z r|3% E z r||:<&
O
>
O
O
O
|
I
E
6 F
U
U¯
z |
2
|
h]
[
F
O E z r|:7&
%
[
6 F
%'
O
&
[
2
[¯
tqe >!=FD@?<>NP>F:QJG;~4ºJG;WGEG?<=4:<eNTL0EG?4=RJO8ISIS=JGFmNP={:<8?<>NPEA>;I
DCE1FIS=Ir:<IxEGL#:<e >9LMEG;;E\_f=FWj~#nIr:<>CY^JGFA"bnyIr:<>Y² ³
¤ eEE1IS>%JlAJU:<8N
¡¢5£¤ ¥^ !
I 6 F
t E"
X DEGNPY8 :<>
E zFZ|+.
F
L}?<E1N:<e >IS>\¨8>CFD>u& cx=9=i&>F
U
E zF|3% E zF||:<&
O
O
F
:
>
O
&
@
F
tqe>CFA%fIS>C:¦ E . E
F
I
6 F
~ E
U
I
O E zFZ||:<&
%
F
O
O
O
O
2
U¯
F
zF|T§ E Fz |32
6 F
¨©¢5£¤ ¥^ ¤!E1NPY8:<>9:<e>pF >C_Ç>Ir:<=N*JO:<>DtsE F h]
F
F
F
F
F
F
E
E
.« ª E
JGFA E . ª E } E
}
O
&
U
O
E
O
F
E
O
F
¯
zyG|
2
tqe >qYZE1=F:=I:<e$JU:=Fu:<e>!~nyIr:<>Yu:<e>!IS8¶PD=>F:Ir:QJO:<=Ir:<=DIx E I 6 F
= I8 YAJU:<>\A9?<>;JO:<=i&>:<EfL0EG?JU?<h=4:S?QJO?<=;4]DQeE1IS>CFu& U c|s]9?<>YZ>\JO:<=F W
:<e >p=4:<>C?QJO:<=E1FlEGL#:<e>R~°JGFA" Ir:<>Y If_pc ?\c :\c 1XtCE" F DEGFi1>C?<W1>Ic
> =F:S?<EA8D>*e >C?<>%:<e>jdsp~1 JG;WGEG?<=4:<eN h]NPEA=4L0]=FWl:<e >
¥ P
=F DC?<>NP>F:QJG;2~4 JO;W1EG?<=4:<e NoJOI5LME1;;E\_fI
z'R|P¤!e EE1IS> & U =F°:<=NP>gEO?QA >C?\Xf=c >1cXxD@e EE1IS>& JO:*:<e>¬C:<e
?<E18 F$A=Fv:<e >b~#nyIr:<>Y2c gJGa&>*E1F ;4]vE1F >*=:<>@?QJO:<=E1F3EGLf:<e >
~°JOF$A) Ir:<>CYIqLMEO?x>\JGDQeU1ctqe=IfN*JGa&>CIq:<e>RYJO?QJGNP>@:<>C?<I
8YA JO:<>\Aj>i&>C?S]*:<=NP>pJ%A JO:<8 N=Ix=F Y8 :\c
l
¢
&|L E
F
F
F
&z "E z U|3% E" zU|-& % E" zU|-& & ¯ |3%
O
O
O
tqe=I?<8;>!N*JOa&>I:<e >!Ir:QJU:<=Ir:<=DI>C{YZEGF>F:<=JG;;4]uA >DJ\]p_f=4:<e
JmLJODC:<EG?mz 1|qJGI5:<e >pIr:QJGW1>pY?<ED>>\AIc
I
6 F
O
y:
G ®£L$:<e >!NPEA =4[D\JO:<=E1F=Ifz5|EGF;4]XO_f=:<e E18:z'9|@XU_q>qEGh :QJG=F
:<e>fJO;W1EG?<=4:<e N Y?<E1YZE1IS>A%h] ¹ EG;JGFgzIS>>f>1c Wcf² ³ |@cstqe>xA >@:QJG=;I
EGL:<e>5sd p4
~ ºJG;W1EO?<=4:<eN±JO?<>5=Fm=W c&c ¹ EG:<=D>!:<eJO:#=F%=WcX&J
Y$JU?QJGNP>C:<>@ ? ¯j=I=F:S?<EA 8DC>\AR=FuEO?QA >C?2:<E5=NPY ?<EUi&>#:<e>Ir:QJGh =;=4:]pEGL
F
:<e>>Ir:<=N*JO:<>I5EOL O X_fe=DQeb=I5IS>C:5:<E 2 -°Çs 2 +
c GIS8$JG;;4] E± .
O
F
A E± IfJO?<>9
IS>C:5ISEm:<eJO:q:<e >C]jJO?<>8F =L0EG?<NP;4]jA =Ir:S?<= h8:<>\A
} fbJOF$?
EUi&>C?:<e>%A O JO:QJPISY$JOD>1cutqe >DEGNPY8 :QJU:<=E1Fg:<=NP>uL0EG?p:<e >%sd p1
~ JG;WGEG?<=4:<eN JU:5>\JOD@e*?<E18 F$AP=S
I ²%z 8 f|#_fe>C?<
> %=I!:<e>A =NP>F IS=E1F
EGL:<e>pA JO:QJJOF$X
A fb=Iq:<e>RF8 NhZ>C?!EG+
L =RJO8ISIS=JGFKA=Ir:S?<=h 8 :<=E1F Ic
^³´
; µ9 o .X% >Z©5# ¢
@ J ©B« ?-AC|DF#] G""HI3 "!#JCA
F
F
F
F
F
@ ©L ¤ E± E± E± n¡ E± ¡ E± 8 £ I¶"¶"¶S o ¢ ?
O
O
O
O
O
¤
V .£
@ J ©B« ¥ ?-¤ AC|W=
, ©5J ©5N4
Y «*3 "#$%CA
ZN)$"SG © V M M. [\
, «$SG ©^["HB© ¢
_ ©I* R @
'! 8 £ ¥ I¶"¶"S¶ o
@JI 6 F
@JI 6 F
@nI
E
E
E
@5F ¤
O @JI°6 F @ O @nI n¡ 6 F O
E
;
.
E
@
O £ ¤ µ ¢ · `i 6 E
°
n¡
@F
@JI 6 O F
@5F
O
O
E
E
E
O @F . £ ; ¢ O @JI 6 F h ; O @F
E
E
. £ ¤ @ F ; ¢3@ F O E
h ; O 4 @
O @F
¤E
E
E
. n O @JI 6 F
O @F £¸ O
@F
E
¡ O E . £ ; ¢ ¡ O E
h F ; @F O 4 @ @¯
@F
@
F
@
F
@
¤
E
. £ ¡ O E n O E O E O E ¯
¡ O
V .£ V h
¤
E
y¹= ^³´
6 F
E
O
@nI
¢
6 F
¢
h
µ ;
o
2.2.2
£`F%:<e >fFE1Non-Parametric
FnyY$JO?QJONP>C:S?<=Dfi&>C?<ISVersion
=E1F%_!>>NPY ;EU]JGI!JR[$F=4:<>fNP=4{:<8 ?<>
NPEA >C;+EUi&>@?x:<e >RDEGF:<=F8EG8IxA EGN*JG=FgJJº&@@ZC2
¾GS%\C
z&*0 v1|+.
,
»½¼ 6 ¾
O i
z&v O |%
z'&|
_fe>@?<> » =IxW1=i&>CF2Xvx. PZv 6 %7:7:7:T%'v W =I9DJG;;>\AKJ*IS>@:REGL¦$rGy1
¼Q¦ @QX z\:+Cv O |x=Ix:<e>ua&>C?<F>C;LM8 FDC:<=E1FBA>C[$F >\AgJGIRJX=RJO8ISIS=JGF
A >CFIS=4:`]¾ _f=:<epNP>JGFv O JGF$ARiGJO?<=JOFD>¼ N*JO:S?<=4{À¿. LRÁzFÂ 8 %7::7:T%LÂ 8 |
LMEO?qJYZE1IS=4:<=i&>fDE1F Ir:QJGF:NÂX&JGF$Auu=I#:<e>fA=NP>FIS=E1FmEGL+JpA JO:<8Ngc
tqe>mA =4w>C?<>CFD>uhZ>C:`_!>>Fg:<e >uYJO?QJONP>C:S?<=DJOF$AgFEGF nyY$JU?QJGNP>C:S?<=D
&i >C?<IS=EGFI=I:<eJO:+:<e>DE>C¶PDC=>CF:i&>DC:<EO?JOF$AR:<e>iGJO?<=JGF D>sN*JU:S?<=4{
LMEO?pJ%[$F =4:<>uNP=4{:<8 ?<>JU?<>miGJO?<=JOh;>m=Fg:<e >L0EG?<NP>C?9NPEA >;X$_fe =;>
:<e>@]lJU?<>R[{>\Aj=Fj:<e>p;JO:S:<>@?NPEA>;c
> =F:S?<EA8D>se>C?<>:<e>x¿À|Ã+ÄÃ'¿Z<ÄC@
'1M ¼9ÀR
M@QO
M|Ã5r1
¥ s
yG¼Q¦ sĦ&G
MCÅp1 &GQ
M0kLMEG?EGF ny;=F>q;>\JU?<F=FWY ?<EG:<EO:`]YZ>I#=F
:<e>fa&>@?<F>; NP={:<8?<>1c#tqe =Is=IshJGIS>\APE1
F =?QJOhZ>D1¡ I5JO;WGEG?<=4:<eN ² O³ c
EO?9JmW1=i&>FlAJO:QJmIS>\¨8>F D
> & @ .& 6 :<:7:'&A@ %[?<Ir:xA >@[$F>G
@
Å z&10 & @ | .
Æ
mz5>3%LÇZ|
Y
i
6
¾
z&& Æ |3%
_fe>@?<>Yuz5><%\>S| p. \ X Ymz5>3%LÇZ| }. \ z ?&| @nIÈ7I 6 L0EG?xÇmÉ>® JOF$A
@
x
u
=IqJuA=ISDE18 F:<=F WuLMJGDC:<EO?\c ¹ EG:<>f:<e$JU: w i 6 Ymz5>3%\Ç$|+.
Æ
@
eEG;}AIc¢9>F D> Å z&10 & |s=IfJ_q>=W1e:<>\AjIS8NEOL z&& Æ |9zFÇ .
%:7:7:T%\><|b_fe >C?<>v:<e>_q>=W1e:BhZ>DEGNP>I^;JO?<WG>3JG¾ IUÇT=FD@?<>\JGIS>Ic
@
¹ >C{:xA >C[F>9:<e >RI<¨8$JU?<>p>C?S?<EG?xEGL;,z&*0 v&|s:<E Å z&*0 & |!h]
z
@
ª 8 z vm!& |+.
,
8
Å z&10 & |
@
&|
&10 v
3. EXPERIMENTAL RESULTS
3.1
;=>\A3dN*JO?S:@Intrusion
d=L}:<>C?u:<El:<e>jDetection
AJU:QJGIS>C:u ¤!8 Y µGµ1µ3² ³
¥ >*JOYY Network
Y ?<>CY$JO?<>AL0EG?PF >C:`_!EG?<av=F:S?<8IS=EGF°A>C:<>DC:<=E1F+ctqe >lY8?<YZE1IS>jEGL
:<e>x>C{YZ>C?<=NP>F:_5JOI!:<EuA >C:<>D@:5JGIsN*JGF]%=F:S?<8IS=EGFIqJOI!YZEGISIS=h ;>
=FBJGFBE1F ny;=F>uIS>C:S:<=FW*_f=4:<eE18:pN*JGa=FWP8 IS>EOLs:<e >m;JGhZ>C;Icux;4n
:<eEG8WGe=x
F ¯¤!8Y µ1µGµ:<e>5A JO:QJ9;JOhZ>;I_!>C?<>q8IS>Am=F:S?QJG=Fn
=FWxLMEG?IS8 YZ>C?<i=IS>Am=F:S?<8IS=E1FmA >C:<>CDC:<=E1F2XG_q>q8 IS>\Au:<e >NTEGF;4]LMEO?
:<e>>iGJG;8$JU:<=EGFlEOLddZc¢9>F D>RJOF]*IS8 YZ>C?<i=IS>\AbJOYY?<E&JGDQeb:<Eu:<e>
AJU:QJGIS>C:x=IxFEG:5LMJG=4?<;4]gDEGNPY$JU?QJGh;>R_f=4:<e^d dc
&42
EG?sJRF>C_V=FY 8 :&A@ 6 X1:<e >xdCG,JO;W1EG?<=4:<e N 8 YAJU:<>IJ9Y ?<EO:<EGn
:]YZ>(v E @F =F:<Ev E @F pv E @5F h]mD@e EE1IS=FW uv E @F ISEp:<eJO:Eª 8 zv E @F
@5F
pv E
& @ & @ 6<|R=ImNP=F =N*JO;8F$A>C?p:<e>PDCE1F$A=4:<=EGF:<e$JU:+ª 8 zv
A
@
&
|#=I!NP=F=NP= >\Auhu
] vD.v E @F 2tqe>xA >@:QJG=;IqJO?<>xISeE\_fFP=F*=W c c
 % » W1=i&>F$|
{
z%L;
@ - ©B« ?AC|DF#$ G""H63 "!#1CA
F
@ ©L ¤ l E± 8 £ I¶"¶"¶S N¢ [!|)3N )© qJ©Sz$#$ '!,G *]"[ $z]J©5*/?
O
¤
V .£
@ - ©B« ¥ ¤ AC|W !! !«s©|Y+«*3"#]%CA
ZN)$"GS© V M M. [,«$GS©(["HB© ¢
_ ©I*aR ` @
'9!NG"G "O ? \Co °¢
v
I
@F
@F
j
E
. £ ; 4 b @ 6 l ` E ¢ ©'ª«
v
¢
`
v
I
@F
@F
E
E
V
·
6
fl
l ` ¢ ©'ª«
v
¢
O i
O
@F
@F
E
©IJ
© l ` E * ©5#$!¼ J ©5[^ ) © )qd5!
, «!# ©5#^!' l `
¶¢
!#"$ & *%+ -$'$ )& & #( ' ,( *+ ) ,( ,. '
$ )& #( -$ v 3& ,( v
/ '0 . j 0 $ )2& ,(1 -$ 3& ,(1 + $v )5& #(4 -$ 3& ,(4
@ !G > ( ) G""# I 56}z3 "!#/. · 0 / '0 87 l '0
' *+
o 6¶"¶"¶ g 6¶"¶"¶ 9 '!xG"G "O l 20
. l '0 h 7 l 20
V . V h
9
;=
: {a
i
]
E
@F
Z©
y£
]
`
©
@ 6 F S E ¤
£
£
©
F
]
E
I
E
8
+©
C@£ F
£
I
E
]
¤
]
S @F¢
E
]
E
F
`
E
`
@F
x¢
¤
G ®tqe >KDE1NPY 8 :QJO:<=EGFk:<=NP>lLMEO?b:<e >KdC+GJG;W1EO?<=:<e NÉJU:
>JGDQe°?<E18 F$Ak=Is²%z 8 » 8 |m_fe>@?<>=IP:<e >^A =NP>F IS=EGF°EOLuAJO:QJ
JOF$A » =IR:<e>uF8 NhZ>C?9EGL!Y ?<EG:<EO:`]YZ>Icmtqe>%dCG JG;W1EO?<=4:<eN
DCE1=FD=A>IR_f=4:<e =?QJOhZ>D1¡ IJG;WGEG?<=4:<eN.² U³ =F^:<e >mD\JOIS>m_fe >C?<>u_!>
;>C(
: mhZ>9:<=NP>pA >YZ>CF$A >CF:5JG(
I . } >Cc
tqe >gFEGF nyY$JU?QJGNP>C:S?<=Dji&>C?<IS=E1FVEGLpddvD\JOF°hZ>b:<e E18 W1e:%EOLpJGI%J
iGJO?<=JOF:REGL1!8 ?<WG>PJGFAdeE\_5ntJ];EO?\¡ IpY ?<E1WO?QJGN ² ³ IS=F D>:<e >C]
JU?<>^hZEG:<ekh$JGIS>AkE1F=?QJGhZ>DG¡ IjJO;WGEG?<=4:<eNgchgJZ`EG?lA =4w>C?<>F D>I
hZ>@:`_q>C>Fl:<e>CN JO?<> |5NP>@:<eEA I5EOLA =ISDEG8F:<=FWYJGIr:x>C{ JGNPY ;>I
JOF$A^G|qNP>C:<eEAIqEGLISDEO?<>pD\JG;D8 ;JO:<=E1F+c
2.3
Score Calculation
s>;EU_¬_q>pWG=i&>JNP>C:<e EAjEOL#D\JG;D8 ;JO:<=FW*JISDCEG?<>pLMEO?9JAJO:<8 Ngc
C> :, E @F z$+%-&#|phZ>*:<e >rE1=F:PA=Ir:S?<=h 8 :<=E1FEGh :QJO=F >\AJO:u:<=NP>N>CX
@F
@F
@F
=c >1cX , E z$%'&|4., E z$|/, E z&*0 $|@c*=9=i&>CF^JGFg=F Y8 :uz$ @ %\& @ |fJU:
:<=NPy
> >@X _!>A >C[F>R=4:<I CM
M@9C<GSJOI
#
?>
`
@
@
¢T£
;
¤8
=<
5@BA DC
¬
E
@F
`
¢
C
8
E
@JI
6 F
`
¢ ±
9
_ e>@?<>Nl=IJ^A=ISDE18 F:<=F WgY$JU?QJGNP>C:<>C?_fe >C?<>P_q>*IS>C:u . c
f
£F:<8=4:<=i&>;4]X:<e=I%ISDEO?<>lNP>\JOIS8 ?<>I%e E\_ ;JO?<W1>b:<e>gA=Ir:S?<=h 8 :<=E1F
@F
, E
eJGIfNPEUi&>\APL0?<EGN , E @JI 6 F JOL}:<>C?9;>\JU?<F=FWmL0?<E1N z$ @ %\& @ |@c
¥ >JG;ISE*A >@[$F>RJGFEO:<e>C?fISDCEG?<>D\JG;;>\Al:<e >%<&GQ
M0
mG<!JGI
FE
z$A@'%'&9@`|._b;E1WA,
E
@JI
6 F
z$A@r|;EGW9,
E
HG
@nI
6 F
JI
LK
M
I
© ª!«
¢ '
@ F
E
]
£
@F
~JGDQe^AJU:<8Nº=FX±¤!8Y µGµ1µ=IfISYZ>D=4[$>Abh]j JU:S:S?<=h8 :<>CI
z'GDE1F:<=F8E18 I5JGF"
A D\JO:<>WGEG?<=D\JO;0|fJGFAbJm;}JOhZ>;+A >ISD@?<=h =FWPJU:Sn
:QJGDQa,:`]YZ>3zy13a=FA IVFEO?<N*JG;XRhJGDQaZXRh8w>C? EOi1>C?'$E\_pXR>@:<D1c |
_fe>@?<>KJG;;9;JGhZ>C;Ij>C{D>Y: `F EG?<N*JG; =F$A=D\JO:<>KJOF¯JO:S:QJOD@aZc ¥ >
8IS>A°LME18?lEOL:<e>KEG?<=W1=FJG;p JU:S:S?<=h 8 :<>IBzIS>C?<i=D>1XA 8?QJO:<=E1F+X
Ir?<D h]:<>IX+AIr: h]:<>IQ|5hZ>D\JG8 IS>:<e>CIS>uL0E18 ?9_q>C?<>:<e E18 W1e:REOLqJOI
:<e>NPE1Ir:!h$JGIS=DpJU:S:S?<=h8 :<>CIcs79F;4] IS>C?<i=D>1¡=I5D\JO:<>WGEG?<=D\JO;'c!tqe>
F8NmhZ>C?EGLfIS>C?<i=D>*a=F$A Iu=Im XJOF$A_!>jDC;}JOISIS=4[$>\Av:<e>CN =F:<E
PUe:S:<Y+XISNm:<Y+X1L0:<Y+X&L0:<Y
A JO:QJXEO:<e>C?<I W csd=FDC>f:<e >DCE1F:<=F8 E18 I!JU:Sn
:S?<=h8:<>uiGJG;8 >I_!>C?<>mDCE1FDC>F:S?QJO:<>\A^JU?<E18F
A XZ_!>u:S?QJOFIrLMEO?<NP>\A
>\JOD@egiGJG;8 >R=F:<E%Ji1JO;8>9LMJO?xL0?<E1
N X$h] x.¯;EGW+z p
C2 |@c
¢
N
tqe>EO?<=WG=F$JG;A JO:QJOIS>C:DEGF:QJG=FI2 X ¸1µG¸X & AJU:QJXO=FD;8A =FWfX µ1X
JO:S:QJOD@aIbz'¸ c %|@ctqe =Iu?QJO:<>bEGLJO:S:QJOD@aI=Iu:<EE;JO?<WG>bL0EG?%Ir:QJUn
:<=Ir:<=D\JG;pEG8 :<;=>C?KA >@:<>DC:<=E1F+ctqe >C?<>CLMEO?<>1X9_!>Y?<EA 8 D>\A¯JIS8hn
AJU:QJGIS>C:*d HDCE1FIS=Ir:<=FWBEGL9µ X !AJU:QJX=FD;8A =FWX !JU:Sn
:QJGDQaIsz c |2h]9Y =DQa=FW58Y:<e>AJU:QJ!_feE1IS>sJO:S:S?<=h 8 :<>f<\S
M
=IqYZE1IS=4:<=i&>1csq:S:QJGDQaIs:<eJO:qIS8 DD>ISIrL08;;4]B<\<
MJO?<>9DJG;;>\AB
M
Q<
'O<c ¥ >#LM8?S:<e>C?2Y ?<EA8D>ApL}?<E1NTd *:`_qEfa=F$AI2EOL$A JO:QJGIS>@:<I
d ^JGFAvd gh]B?QJOF$AE1N I<JGNPY ;=F W X2_fe>C?<>bd lDEGFIS=Ir:<I
EG
L !
EGLRd !XJOF$AVd DEGFIS=Ir:<I%EOL EOLd !c#EG?jd JGFAPd X&:<e >5[?<Ir:s¸X !
AJO:QJpJOF$Am:<e >q[?<Ir:s X uAJU:QJ9_q>C?<>
?<>ISYZ>D@:<=i1>;4]vFEO:ISDCEG?<>\Ah8:u8IS>\AvEGF;4]L0EG?u:S?QJG=F=FWKhZ>DJG8IS>
:<e>9NPEA >;_qEG8;AlFEO:fhZ>R_q>;;4n':S?QJG=F>Al=Fl:<e>R>JO?<;4]lIr:QJOW1>Ic
> W1>CF>C?QJU:<>\Ag:`_qEld GIh]lN*JGa=FWjA =4w>C?<>CF:x?QJGFA EGNoI<JON%n
¥ u
Y;=FWGIc5EO?x>\JGDQegEGL#:<e >NgX_q>R?QJGFlhZEG:<egYJO?QJGNP>@:S?<=DJOF$AlF E1Fn
Y$JU?QJGNP>C:S?<=Dji&>C?<IS=E1F I%EGL9d dv_fe >C?<>*:<e>*LMEG?<NP>@?%=I%A>FEO:<>\Ah]
dd%_fe=;>9:<e >;JO:S:<>@?fh]*dd &ctqe>RYJO?QJONP>C:<>C?<IqEOLddPJU?<>RIS>C:q:<E
N.
C2 !
& % X.
C2 !
1s
%3f.±s %5¯ . s 2 X+_fe=;>m:<e E1IS>EOLfd d
JO?<>IS>C:f:<E .
s2 1s % p.
s2 !
GC
% » . s%5Â.b
C2 cfdd*Y ?<EOn
D>ISIS>Avµ X AJU:QJl=FO¸c lIS>DEGF$A IX_fe=;>jdd *A =A=F3U1c ¸
IS>DEGF$AIcptJOh;> ISeE\_fIx:<e>uF8 NhZ>C?xEOL!=F:S?<8IS=E1F Ipd d+z G|fA >@n
:<>DC:<>Aj_fe>@?<>R:<e>R;E1W1JO?<=4:<eNP=Dp;E1ISI5_qJGIx8IS>\AbJGIxJmISDEO?<>1cs¢9>C?<>
<G§G@S5=I!:<e >x?QJU:<=EEGL+:<e>xF8NmhZ>C?!EOLA>C:<>DC:<>A*=F:S?<8IS=EGFI!:<E
:<e$JU:!EOL=F:S?<8IS=EGFI=FP:<e >A JO:QJOIS>C:!:<eJO:qdd+z O|ISDCEG?<>\Acsdd=I!IS8n
YZ>C?<=EG?5:<Edd 9hZEG:<e*=FlJODD8 ?QJODC]jJGFAjDCE1NPY8:QJO:<=E1FP:<=NP>1ctqe =I
=NPY;=>I5:<e$JU:x:<e >C
d R1
~ JG;WGEG?<=4:<eN _f=4:<eKN
J =RJG8 ISIS=JGF^NP=4{:<8 ?<>
_qEO?<aIhZ>C:S:<>C?u:<e$JO
F =?QJGhZ>D1¡ IJG;W1EO?<=:<e N»8 IS=F WBJKa1>C?<F>;sNP=4{n
:<8 ?<>GX _fe =DQel=IJG;ISE*JhJGIS=IfEGL#:<e>9Y ?<E1WO?QJGN®=F² ³ c
-O
-O
-O
O
O
%O
PK
> JG;ISEgW1>CF>C?QJU:<>\ABL0E18 ?md!
OIuh]KN*JOa=F WlA=w>@?<>F:R?QJGFA E1N
¥ %
I<JGNPY ;=F W1I2EG?28IS=FWfJOFmJGAA=:<=EGF$JG;1D\JO:<>WGEG?<=D\JO;i1JU?<=}JOh;> Y?<EG:<EDEG;4n
:`]YZ>1¡UEOL ?QJOFWG(
> Pq:<DCY2XO8$AY*XG=NPDY W ctJGh ;>5fISe EU_fI:<e >!F8NmhZ>C?
EGL+=F:S?<8IS=E1F Iqd dA >@:<>DC:<>\A=F%:<e >qLME18?fd
!
GIc x>N*JU?<a1JOh;4]X1dd
_5JOIlJOh;>^:<EA >@:<>DC:b¸&!
=F:S?<8IS=EGFIj=Fk:<e>g:<E1b
Y AJU:QJvEGL
e=WGe>Ir:xISDEO?<>Ic
RQ
z&A@<0 $A@r|32
?<E1N :<e>i=>C_fYZEG=F:uEOL5=F LMEO?<N*JO:<=E1F:<e>EO?S]X2:<e >%;E1W&JU?<=4:<eNP=D
;EGISIxDJGFlhZ>x:<eEG8W1e:5EOLJGIq:<e >9DEA>;>FWO:<el?<>\¨8=4?<>\AP:<E>CFDEA>
z $A@ %\&9@|*8 F$A>C?b:<e >BJGISIS8NPY:<=E1F°:<eJO:lJVA JO:<8 N =IjW1>F >C?QJO:<>A
@nI
F
JODDEO?QA =FW%:<EPJmY ?<E1hJGh =;=4:`]lA >CFIS=4:`p
] , E 6 c
3.2
Pathology
8 Ir:S?QJGOutliers
;=J¡ I#¢9>JG;4:<emin
£FISMedical
8?QJGFDC>q¤!EGNP
NP=ISIS=EGFbz¢£S¤5Data
|2JGA NP=F=Ir:<>C?<I
Q
:<e>8F=i&>@?<I<JG;e>\JO;4:<ev=FIS8 ?QJOFD>ISD@e >NP>aFE\_fFJGIul>\A =D\JU?<>1X
=FEGYZ>C?QJO:<=E1FIS=F D> µ cb¤5d£ x7 8Ir:S?QJO;=}Jb=Ip_!EG?<a=FWb_f=4:<e
:<e>9¢9£S¤°:<E%>@{ Y ;EG?<>9:<e >p8 :<=;d= JO:<=E1F^EOL#Y$JU:<eE1;EGWG]bIS>C?<i=DC>Ic
!«
\3 "!
P
P
¥
x
¤
P
¤
¥¥x ¥
¥u ¤
¥ ¤ ¤ p
¤ ¤
¢
¢
¢
¢
¢
¤
d5!6>Z©5\%©
@]@ C
p
¤ x ¤ ¥ P u
¤ ¥ ¢
¢
¢
¢
¢
:<e>uA JO:QJX$hZEG:<eg:<e ?<EG8WGeg:<e>=A >F:<=4[$D\JU:<=E1FKEGL>C?S?<EGF>EG8IRA JO:QJ
JGFAB:<e?<E18WGe:<e >%=A >F:<=4[$D\JU:<=E1FvEOL5>F:<=4:<=>CI:<eJO:N*J]^?<>\¨8=4?<>
LM8?S:<e>C?x=Fi&>Ir:<=W&JU:<=E1F2c
¢
¤ 5¥
¤ p
¥u ¥
¤
¢
¢
¢
4.
tqe=IpCONCLUSION
YJGYZ>C?eJGIpY ?<EGYZE1IS>\AdN*JU?S:@d=4L0:<>C?pJGIJbY?<E1WO?QJGN LMEO?E1Fn
¢
¤
~ "!6"!U"#%$&
P
¥ ¤ ¥¥x
¢
¤
¥
u
¥
¢
¥ ¤ ¥ x
!«
\3 "!
¥ x
¤ !'="#} z$[ "!#$[ "#$d5G"z$*©5*
@$@
¤
!'="#} z$[ "!#$[ "#$d5G"z$*©5* d5!6>Z©5\%© ¢
[-©5>]"dB©
[-©5>]"dB©%'«]! !pd5!G «s©
u
¥ P
¤ ¥
¤ x
¢
¢
¢
¢
¤
¢
¤ P ¤ ¤ ¤
P ( ¤ ¤ u
¢
¢
¢
¤
/¥
¤
p5¥ x
¤ ¤ ¤
P ¤ x
¢
¢
¢
¢
¤
¢
¢
¢
¢
¬¹= "!6"!U"#*)+&
ºAJO:QJOIS>C:mDEUi&>C?<=FWKb]&>\JO?<Ip_f=4:<eEUi&>C?m&lNP=;;=EGFvY$JU:<eEG;EGWG]
:S?QJOFI<JODC:<=E1FIK=I^:<e>h$JGIS=IKEGLm:<e>vIr:<8A]co~JGDQeH:S?QJGF I<JGDC:<=EGF
?<>CDEG?QAI*:<e >l:`]YZ>bEGLpNP>\A=D\JG;5:<>Ir:*YZ>C?SL0EG?<NP>\AX5JOF°>F DC?S]Y :<>\A
=A>F:<=[>C?9L0EG?R:<e >u?<>CF$A >@?<=F WjA EDC:<EO?\XZ:<e>u;}JOhZEG?QJU:<EG?S]KYZ>C?SL0EG?<N%n
=F W:<e>g:<>Ir:\X5JGF$AV:<e>^AEDC:<EG?*_feE?<>\¨8>Ir:<>\A3:<e>g:<>Ir:\X5JGF$A
EO:<e>C?=F L0EG?<N*JU:<=EGF%?<>;JO:<=FWR:<ER:<e >!:`]YZ>qEOL+A EDC:<EO?qJOF$AYJO:<=>F:\c
dN*JO?S:@d=L}:<>C?ue$JOIuhZ>C>F8 IS>\AE1F:<e=IAJU:QJGIS>C:uLMEO?u:_qEKA=Ir:<=F DC:
L08F DC:<=E1FIctqe>m[?<Ir:p8 IS>\Ad d^:<Ej=A >F:<=4L0]B>C?S?<EO?<Ip=FB:<e >%AJU:QJc
xFH=F =:<=JO;JOYY;=D\JU:<=EGFT:<Ek:<e >vEG?<=WG=FJG;:S?QJGF I<JGDC:<=E1F AJO:QJOIS>C:
=A>F:<=[>\Av:S?QJGF I<JGDC:<=E1F I:<e$JU:_!>C?<>l8 F8 IS8$JO;-,°E18:<;=>@?<Ic gJGF]
EOLR:<e>j:S?QJGF I<JGDC:<=E1F I*=}A>F:<=4[$>\A3e$JGAV=Fi1JO;=}AVAJU:QJ=4:<>NPIgz'AE1;4n
;JU?%JONPE18F:<IReJ1A>@{:S?Q
J >C?<EGIXJGW1>CIuEOLfY$JU:<=>CF:<Ip_!>C?<>PWG?<>\JU:<>C?
:<eJGF !
*]&>\JO?<IX>C:<DGc |@c9tqe>mAJU:QJGIS>C:9LMEG?pJGF$JO;4] IS=IRDJGF^:<e8IxhZ>
DC;>JGFIS>AgEGL:<e >IS>R?<>DEO?QA Ic
tqe >fY ?<=N*JO?S]mY8?<YZE1IS>5EGL2d dm=I:<Ep>@{ Y ;EG?<>fi1JU?<=E18I:S?QJGF IrLMEO?<N*JOn
:<=EGFIxEGL:<e>R:S?QJOFI<JGD@:<=EGFBAJO:QJOIS>C:\cftqe >IS>=F D;8$A>JGW1WO?<>W&JU:<=FW
AEDC:<EG?<Ijzy! X ^>F:<=4:<=>IQ|@XYJO:<=>F:<I*z X !
X !
B>CF:<=4:<=>IQ|@XJGF$A
;JOhZEG?QJO:<EO?<=>Iz !
f>F:<=4:<=>CIQ|@cdd9_5JOIJGh ;>:<E=A>F:<=L}]XULMEG?>@{JON%n
Y ;>1X;JGhZEG?QJU:<EG?<=>Iq:<eJO:se$J\i&>fY$JU:S:<>C?<FIsEGL+hZ>e$J\i=EG?s:<e$JO:!JO?<>xE18:
EOLq:<e>mEG?QA=FJO?S]c%79F>PA JO:QJOIS>C:8IS>\AKDEGFIS=Ir:<>\AEO9
L r8 Iru
: jiGJO?<=4n
JOh;>ILMEG?!>\JGDQeP;JGhZEO?QJO:<EG?S]X=F D;8$A =F WpYZ>C?<D>F:QJGWG>xA =Ir:S?<=h8 :<=EGFI
EUi&>@?9[$i1>:<>CIr:RD\JU:<>W1EO?<=>CIPz>1c W cX¤!e>NP=D\JO;:<>Ir:<I9
X l=DC?<E1h =EG;E1WG]
:<>CIr:<IX#£`NPNm8FEG;E1WG]l:<>Ir:<IX#>C:<D1c |@X2:<e>%F8NmhZ>C?pEOLfA =4w>C?<>F:YJOn
:<=>F:<IjA >JG;4:*_f=:<e°h]3:<e >g;JGhZEG?QJU:<EG?S]XxJOF$Ak:<e >lL0?<>\¨8 >FDC]VEOL
:<>CIr:<IPYZ>C?SLMEO?<NP>\A¬z'tJGh;>l&|@c,ddv=A >F:<=4[$>\A3;JGhZEO?QJO:<EG?<=>I 1µX
X$JOF$A 1 m_f=:<ejDEGFIS=Ir:<>F:<;4]be =W1ebA =Ir:QJGF D>RISDEO?<>Icqt!_!EEOL
:<e >IS>;JGhZEG?QJU:<EG?<=>IRISYZ>CD=JG;= >\A^=F^tq=ISIS8p
> #JO:<e E1;E1WO]z GµPJGF$A
E l=DC?<E1h =E1;E1WO]bF EG?qtq=ISIS8 > #JU:<eE1;4n
G &|!JGFAP:<e >EO:<e>C?qA E>IsFu
EGWG]lz |@cstqe> `F EG?<N*JG; pIS=4:<8$JU:<=E1FPLMEO?!:<e=IsAJU:QJGIS>C:s=F$A =D\JU:<>I
:<eJO:#YJO:<e E1;E1WO]mY?<EUi=A>C?<IW1>CF>C?QJO;;4]uYZ>C?SL0EG?<NJxISY ?<>\JGAuEOL:<>Ir:<Ic
8 ?S:<e >C?9JGF$JO;4] IS>CI9_f=4:<eB:<e >m¢;0¤HJO?<>=FKY ?<EGWG?<>ISIX2>NPY ;E\]=FW
G
K P
$&32
M
6
¤
P& ? ¤¤
P
$3
$9¤ 6
¤¤
¤¤ $<
¤¤ ;+:
¥
¤
JI
M
P&"4-73¤ 7
P ? ¤
&
P ?P
P&
P
¤
P ? ¤
0 =>=
:
*
M
P& ? P
P ?P
¥
P&"4-737
P ?P
¤
"? ¥
M0/
P& ? P
¤
P ? Z¥
P& ? P ? P ?
P$ ? P P ? P$ ? P P ?P
P ? ¤
¤
P ? PP
P ? P
P& ? ¥
P ?
M.
P& ? P
8
P& ?
&
P ?P
¤
A@
1
&"4 28:
P ? P$ ? P ? &"4 787
P ? ¤@
1
6
P $ ? ¥
P ? P ? ¥
CB &
¤
ED
8
P&5? 4 P 68 7
P ?P P&5? 4 P 73&
¤
P ?
P ? ¤
$
P ?P
¤
J _f=A >bi1JU?<=>C:`]EGLf:<>DQeF=¨8>CIA?QJ\_fFL}?<E1N.AJO:QJ^NP=F=F WKJGF$A
g
Ir:QJU:<=Ir:<=DCIP=F3WG>F>C?QJO;cVtqe>l8 IS>bEOLpd dvY ?<EUi=}A>I=F IS=WGe:<I%=F:<E
;=F>^8F IS8YZ>C?<i=IS>\A3E18:<;=>C?bA>C:<>DC:<=E1F+c ¥ >lW&J\i&>^JIr:QJU:<=Ir:<=DJG;
:<e>CEG?S]LMEO?ldd3JGF$AVA >CNPE1FIr:S?QJU:<>\A3=:<IP>@w>DC:<=i&>F >ISIP=FV:<>C?<NPI
EGL5JGDD8?QJGDC]JGFADEGNPY8:QJO:<=E1FB:<=NP>m:<e ?<E18 W1eB:<e>:_qEl>@{ YZ>@?Sn
=NP>F:<ITF >C:`_!EG?<a¬=F:S?<8 IS=E1F±A >@:<>DC:<=E1F L0EGH
? y ¤!8Y µ1µ1µ
JGFA*?QJU?<>p>i&>F:fA>C:<>DC:<=EGFjL0EG?f:<e>e>\JO;:<eb=FIS8 ?QJOFD>9Y$JO:<e E1;E1WO]
AJU:QJGIS>C:uY?<EOi=A >ABh]B8 Ir:S?QJG;=JGF¢9>\JO;:<e£`F IS8 ?QJGF D>*¤!EGNPNP=Irn
IS=E1F+cf£:=I>C{YZ>DC:<>\Aj:<e$JO:x:<e>RL}?QJGNP>C_!EG?<agEOLE1F ny;=F>8F IS8YZ>C?Sn
i=IS>\A°E18:<;=>@?lA>C:<>DC:<=EGF,8IS=FWdd3_!E18 ;}AVhZ>gLM8?S:<e>C?jJOYY;=>\A
=F:<E^Jb_f=A >PiGJO?<=>C:]EOLfAJU:QJlNP=F=FWb=ISIS8>IuEG:<e >C?p:<e$JOFL0?QJO8$A
A >@:<>DC:<=E1F+XIS8 D@elJGIf:S?<>F$AbA >C:<>D@:<=EGF2X:<E1Y =Dp=A>F:<=[D\JO:<=EGF2c
FHGIKJ @8LM B ? J ¤ D tqe >^JG8:<eEO?<I%IS=FD>C?<>C;]3>@{ Y?<>ISI%:<e>C=?
WG?QJU:<=4:<8$A >%:<E)9?\c N!EGISe=4LM8 NP=ON!JGN*JONPEG:<EbEGL ¹ ~s¤ £`FLMEG?<N*JU:<=E1F
d]Ir:<>NPIsLMEG?x_5?<=4:<=FW%:<e>9DEA >I5L0EG?RdN*JO?S:@d=4L0:<>C?\c
5. ADDITIONAL AUTHORS
]* *$ "!#$Gz] )$!6.W;©L-©5I? P+"G"#© (Q @ D _OR PJ3 )©5,-3 "d6G$#$*ÀDF#]'! e
,-3 "!# @ d5S©5#$dB©5[6g0S^W RUT ! ª g Q # C©5 \ QWV¥ P g z$[ \G"]g
¤
©5,-"GfY
. X
Z[
Z\Y]^+_a`ab9Zc9dfe_g0]hdg9_\9i"](jk ¢ ?
6.l REFERENCES
#©L ^
#$* V ? K ©LZN"[6grqstu vwaxnyzv{}|8t(~tvyftvf~up~t(~g+!)$#
@
"GS© >' !#][6g ?
l ¥ c ? T !#$d\)$fg c +
? S^¤ #$#$!fgS|?PJ"#©L !$g#$*
|?$W;©5*©5[d\)]fg m dIG[ [ dI3 "!# J[ ©5*+
, ©L)$!}*$!G"!% '9!|«]G#$#$"#$%-z$*] e
[ \3J ©I%S ©5[x"#'\z$** ©LJ ©IdL "!#/g"}
# xhar%h
g
g ?
««/. a
¤
l W=? T ¤ z$% ©S
#]
* ¤ $? @ )IZ e V ]G"!I+g
1©LJ ©IdL "#$%Bd ©5G"G"z$G'9z$*-z$["#]%
m *7 «] Z
> ©(«]! ! «s©5[6g"}
# OxhaEz*z93xh~9n<waypt(0xh~s
pwat(watv{~
{3AvyH~{3~a9w wa{+t9
g ««/. a g ?
¤
l W=? Q )$#J#$* @ ? @ !G '9!$g V !6Z *q[dIG $SG ©S¤SG ©I #$
"#$%|ZN )
m #$!# z$#] '9! , d5G[[x#$*adI![ *$"[ $zp"!#$[I. dI-[ ©S[z]* "#
e
e
dIJ ©5*$ Nd6 *a'\z$** ©LJ ©IdL "!#/g"}
# xhar%h
¡g
^^ D e W J ©5[[6!g ««/. ¢ ?
l V ? c IZBBd ©LS#$* c ¤ ?]W ¤ !6>![ I¤ g d5 >p a,!#] ! "#$%$.=#$!"d5"#$%
m "#}J ©5- ©5[ "#$%d\)#]% ©I[x"# s©5)5>]"!Ig"}
# xhar%h
g
?
««/. a¥ g
l D\8
? S^\ s©5dg ¤ @ ©5G ' e !%#$"HI3 "!#q!K
' ¢4©5z$ !#$[N* ©5[d5 s©5* -) ©
m ,-< ª]",|z$, ©5#} ! « «]"#$d5S «$SG ©8
g
A
£
vu
vf~uO¤K¥9¦waxn{3watvy=>!Gf? g
e
P ?
««/. P a9 P g
l )}- «i. AA §p*$*i? "dI¤ [I? z$d5f? ©5*$zA3*3 -[ ©5[\A §p*$*]dI
z « A §p*$*]d6z « ? ) ,G
l m
? Pm? ª(#$!N#$* _ ? V +? ¢x%$g G"%! )$,['!B,"#$"#$%
+
m©¨*$"[ #$Bd © -[ ©5*+!zpG"S ©5[N"#G% ©S*3-[ ©L [6g"
# Oxhar%tw
e
«¬ t®"¯5£°¤K{anwaxhwa{3fwI
g ««i. ¥a9 P g ?
l ? K © ©g @ +
? $? @ !G '!$g#$}
* ª? ? P+! §g ¤ P+"#$"#$%|"#+|*$3\ e ± !6Z
m ©I#>p"!#$
, ©5#6A
. ©'ª«s©5S ©5#$Bd ©"#a# ©5FZ! §"#} z$[ "!#a* ©5J ©5dL"!#/g"#
Oxhar%%
g ««/. ¥ g ?
l
* S|? ? ¤¤ "#} ¤ !#/g ¤ >]S ©LZ!' ) © P«G"%! )$,
P _ ? Pm+? ¢4©IG#]M
¤
m )3E
²z$[ ©5[x"#]dIJ ©5
, ¨ ©I#Gfg$-[ «$-[ ©g$#$*q! ) ©5N>¨ #[Ig$'- «/. AA
'J «/? d5[6? !!#!$? ©5*$z<A «$z A3*]'9! *A6Z Z Z(<A «]z $G""dI3"!#][6? ),G
?
l
@¤ ? _ ![-[ ©LIgY+? P+z$*/g +? ¢4©5z$,-#]#/<g ³|?$DF*#/g#]M
* S|?$WX"# §[Ig
¤¤nm
^"[d5!6Z
> ©5 a!''\z$*z]SG ¨©I[B'!B- ©5SG ©5d5!,,z$#$"dI3 "!#$[ e d\)G"SG ©5#$% ©5[
#$*q[ !G"z]"!#][6g"
# Oxhr%zh9!g ««/. P a9 g ?
nmpo
¤
?
T
5
.
¤
¤
© Copyright 2026 Paperzz