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BK�;2 +�M +H�bbB7B2/ BMiQ QM2 Q7 i?2 7QHHQrBM; bBt +�i2;Q`B2b, i?2 TB;K2Mi M2irQ`F �ii`B#mi2-

i?2 M2;�iBp2 M2irQ`F �ii`B#mi2- i?2 bi`2�Fb �ii`B#mi2- i?2 KBHB�@HBF2 +vbib �ii`B#mi2- i?2 ;HQ#@

mH2b �ii`B#mi2- �M/ i?2 #�+F;`QmM/- r?B+? #�bB+�HHv K2�Mb i?2 TBt2H #2HQM;b iQ MQM2 Q7 i?2

7Bp2 �ii`B#mi2bX

A MQiB+2/ i?�i � HQi Q7 �ii`B#mi2 K�bF BK�;2b �`2 2KTiv BM i?2 /�i�b2i Uh?2 K�bF BK�;2

Bb +QMbBbi2/ Q7 TBt2Hb rBi? �HH x2`Q p�Hm2bVX h?Bb BKTHB2b bQK2 Q7 i?2 �ii`B#mi2b K�v MQi

T`2b2Mi BM bQK2 /2`KQb+QTB+ BK�;2bX h?2 2t�KTH2b �`2 b?QrM BM 6B;m`2 jXkX 6Q` BK�;2 �-

i?2 M2;�iBp2 M2irQ`F- i?2 bi`2�Fb- i?2 KBHB�@HBF2 +vbib- �M/ ;HQ#mH2b �ii`B#mi2b K�bF BK�;2b

�`2 �HH 2KTiv- r?B+? K2�M i?Qb2 �ii`B#mi2b /Q MQi T`2b2Mi BM i?2 BK�;2X

A �M�Hvx2/ i?2 r?QH2 /�i�b2i iQ +QmMi i?2 MmK#2` Q7 MQM@2KTiv K�bF BK�;2b 7Q` 2�+?

�ii`B#mi2- �M/ ?Qr Q7i2M i?2v T`2b2Mi �+`Qbb i?2 /�i�b2iX h?2 `2bmHi Bb b?QrM BM h�#H2 jXRX

h�#H2 jXR, h?2 �M�HvbBb Q7 i?2 7Bp2 �ii`B#mi2b T`2b2M+2 BM i?2 /�i�b2i

jXRX .�i� RR

6B;m`2 jXk, h?2 2t�KTH2b Q7 /2`KQb+QTB+ BK�;2b �M/ +Q``2bTQM/BM; �ii`B#mi2bX q2 +�M b22bQK2 �ii`B#mi2b �`2 2KTiv 7Q` bQK2 /2`KQb+QTB+ BK�;2b- r?B+? K2�M bm+? �ii`B#mi2b /Q MQiT`2b2Mi BM i?2 BK�;2bX

Rk *?�Ti2` jX J2i?Q/b

6B;m`2 jXj, L2irQ`F bi`m+im`2 mbBM; BM l@L2i #�b2/ �TT`Q�+?X h?2 2M+Q/2` T�ì Q7 i?2l@L2i Bb `2TH�+2/ rBi? � T`2i`�BM2/ o::Re M2irQ`F (8) X irQ +H�bbB7B+�iBQM ?2�/b �`2 �//2/iQ i?2 M2irQ`F- r?2`2 QM2 Bb �//2/ iQ i?2 KB//H2 H�v2` rBi? R R +QMpQHmiBQM �M/ ;HQ#�H�p2`�;2 TQQHBM; H�v2`b �M/ i?2 Qi?2` Bb �//2/ iQ i?2 H�bi H�v2` rBi? � ;HQ#�H K�t TQQHBM;H�v2`X

jXk JmHiB@i�bF l@L2i JQ/2H

h?2 l@L2i (j9) Bb 2KTHQv2/ iQ /Q i?2 b2;K2Mi�iBQM i�bFX h?2 �`+?Bi2+im`2 Q7 i?2 M2irQ`F Bb

b?QrM BM 6B;m`2 jXjX h?2 o::Re (8) Bb mb2/ �b i?2 2M+Q/2` T�ì bQ i?�i A +�M mb2 T`2@i`�BM2/

r2B;?ib iQ #QQbi i?2 T2`7Q`K�M+2X AM i?2 /2+Q/2` T�ì- i`�MbTQb2/ +QMpQHmiBQM Bb mb2/ iQ

mTb�KTH2 i?2 72�im`2 iQ i?2 Bib Q`B;BM�H bBx2X AM i?2 bFBT +QMM2+iBQMb- i?2 72�im`2 K�Tb 7`QK

i?2 2M+Q/2` T�ì �`2 +QM+�i2M�i2/ rBi? i?2 +Q``2bTQM/BM; 72�im`2 K�Tb BM i?2 /2+Q/2` T�ìX

h?2 bQ7iK�t 7mM+iBQM (8R) Bb mb2/ �b i?2 �+iBp�iBQM 7mM+iBQM BM i?2 H�bi H�v2` iQ ;2M2`�i2

i?2 �ii`B#mi2 K�bF BK�;2bX h?2M � +miQ77 Q7 yXj Bb mb2/ iQ i`�Mb7Q`K T`2/B+i2/ T`Q#�#BHBiv

BMiQ #BM�`v K�bFX h?2 /2`KQb+QTB+ BK�;2 Bb 722/ BMiQ i?2 M2irQ`F �M/ i?2 QmiTmi Q7 i?2

M2irQ`F Bb � 7Bp2 +?�MM2H BK�;2 K�bF- �M/ 2�+? +?�MM2H +Q``2bTQM/b iQ QM2 �ii`B#mi2X h?2

;2M2`�i2/ �ii`B#mi2 BK�;2 K�bFb �`2 i?2M +QKT�`2/ rBi? +Q``2bTQM/BM; ;`QmM/ i`mi? BK�;2

K�bF T`QpB/2/ BM i?2 /�i�b2iX h?2 #BM�`v +`Qbb 2Mi`QTv HQbb L1 Bb i?2M +QKTmi2/ #2ir22M

jXkX JmHiB@i�bF l@L2i JQ/2H Rj

i?2 M2irQ`F QmiTmi �M/ i?2 ;`QmM/ i`mi?,

L1 = −n∑

i=0

5∑

k=0

yik HQ;2 yik

r?2`2 M Bb i?2 MmK#2` Q7 TBt2Hb BM i?2 BK�;2- F Bb i?2 i?2 +H�bbB7B+�iBQM Q7 i?2 TBt2HX yik Bb i?2

i`m2 �ii`B#mi2 +H�bb Q7 i?2 BK�;2 TBt2H i r?BH2 1 /2MQi2b T`2b2Mi �M/ 0 /2MQi2b MQM@T`2b2Mi-

�M/ yik Bb i?2 T`2/B+i2/ T`Q#�#BHBiv p�Hm2 Q7 +H�bb k 7Q` BK�;2 TBt2H iX

hQ 7Q`+2 i?2 M2irQ`F QmiTmi iQ �TT`Q�+? i?2 ;`QmM/ i`mi?- i?2 C�++�`/ BM/2t UCV (8k) Bb

+�H+mH�i2/ #2ir22M i?2 M2irQ`F QmiTmi �M/ i?2 ;`QmM/ i`mi?X h?2 +Q``2bTQM/BM; HQbb Bb

?2M+27Q`i? +�H+mH�i2/ �b,

L2 =

∑ni=0

∑5k=0 y

ik ∗ yik∑n

i=0

∑5k=0 y

ik +

∑ni=0

∑5k=0 y

ik −

∑ni=0

∑5k=0 y

ik ∗ yik

r?2`2 M Bb i?2 MmK#2` Q7 TBt2Hb BM i?2 BK�;2- F Bb i?2 i?2 +H�bbB7B+�iBQM Q7 i?2 TBt2HX yik Bb i?2

i`m2 �ii`B#mi2 +H�bb Q7 i?2 BK�;2 TBt2H i r?BH2 1 /2MQi2b T`2b2Mi �M/ 0 /2MQi2b MQM@T`2b2Mi-

�M/ yik Bb i?2 T`2/B+i2/ T`Q#�#BHBiv p�Hm2 Q7 +H�bb k 7Q` BK�;2 TBt2H iX

�b �7Q`2K2MiBQM2/- QM2 BKTQ`i�Mi Q#b2`p�iBQM Bb i?�i �HH i?2 7Bp2 H2bBQM �ii`B#mi2b /Q MQi

T`2b2Mi BM 2�+? bFBM /2`KQb+QTB+ BK�;2X h?2`27Q`2- irQ +H�bbB7B+�iBQM ?2�/b �`2 �//2/ iQ

+H�bbB7v 2�+? /2`KQb+QTB+ BK�;2 #�b2/ QM i?2 �ii`B#mi2b Bi `2�HHv TQbb2bb2bX PM2 +H�bbB7B+�iBQM

?2�/ Bb �7i2` i?2 H�bi H�v2` Q7 i?2 l@L2i M2irQ`FX � ;HQ#�H K�t TQQHBM; H�v2` Bb �TTHB2/ iQ

i?2 H�bi +QMpQHmiBQM�H H�v2` iQ +H�bbB7v i?2 T`2b2Mi �ii`B#mi2b �M/ i?2 �#b2Mi �ii`B#mi2bX h?2

QmiTmi Q7 i?2 +H�bbB7B+�iBQM H�v2` Bb � p2+iQ` rBi? 7Bp2 2Mi`B2bX 1�+? 2Mi`v ?�b i?2 p�Hm2

7`QK x2`Q iQ QM2- `2T`2b2MiBM; i?2 HBF2HB?QQ/ Q7 i?2 T`2b2M+2 Q7 2�+? Q7 i?2 7Bp2 �ii`B#mi2bX

h?2 +H�bbB7B+�iBQM `2bmHi 7`QK i?2 M2irQ`F Bb i?2M +QKT�`2/ rBi? i?2 ;`QmM/ i`mi?- r?B+?

BM/B+�i2b i?2 `2�H T`2b2M+2 Q7 2�+? �ii`B#mi2X h?2 +`Qbb 2Mi`QTv HQbb Bb +�H+mH�i2/ #v i?2

R9 *?�Ti2` jX J2i?Q/b

+QKT�`BbQM �b,

L3 =5∑

k=0

ck HQ;2 ck

r?2`2 ck Bb i?2 i`m2 T`2b2Mi �ii`B#mi2b BM i?2 BK�;2- �M/ ck Bb i?2 T`2/B+i2/ T`2b2Mi �ii`B#mi2b

BM i?2 BK�;2X

PM2 /2`KQb+QTB+ BK�;2 rBHH ?�p2 �M 2KTiv �ii`B#mi2 K�bF BK�;2 B7 i?2 �ii`B#mi2 /Q2b MQi

T`2b2Mi BM i?2 /2`KQb+QTB+ BK�;2X h?2 +H�bbB7B+�iBQM HQbb +�M 7Q`+2 i?2 M2irQ`F iQ T`2/B+i �M

2KTiv K�bF BK�;2 7Q` i?2 �#b2Mi �ii`B#mi2 #2+�mb2 Qi?2`rBb2 �7i2` ;HQ#�H K�t TQQHBM;- i?2

+H�bbB7B+�iBQM HQbb rBHH #2 H�`;2X �b � `2bmHi- i?2 +H�bbB7B+�iBQM HQbb �+ib �b � `2;mH�`Bx2` iQ 7Q`+2

i?2 M2irQ`F iQ T`2/B+i �M 2KTiv �ii`B#mi2 K�bF BK�;2 B7 i?2 +Q``2bTQM/BM; ;`QmM/ i`mi?

�ii`B#mi2 K�bF BK�;2 Bb 2KTivX �b BMbTB`2/ #v i?2 B/2� mb2/ BM BM+2TiBQM M2m`�H M2irQ`F

(8j)(89)(jy) - �MQi?2` +H�bbB7B+�iBQM H�v2` r�b �//2/ iQ #QiiQK Q7 i?2 lL2iX h?2 H�v2` Bb

+QMbBbi2/ Q7 � R R +QMpQHmiBQM�H H�v2` �M/ � ;HQ#�H �p2`�;2 TQQHBM; H�v2`X h?2 QmiTmi Q7

i?2 H�v2` Bb �HbQ � p2+iQ` rBi? 7Bp2 2Mi`B2b- `�M;BM; 7`QK x2`Q iQ QM2X h?2 +`Qbb 2Mi`QTv HQbb

Bb +�H+mH�i2/ i?2M #v +QKT�`BM; i?2 K�bF +H�bbB7B+�iBQM rBi? i?2 ;`QmM/ i`mi?,

L4 =5∑

k=0

ck HQ;2 ck

r?2`2 ck Bb i?2 i`m2 T`2b2Mi �ii`B#mi2b BM i?2 BK�;2- �M/ ck Bb i?2 T`2/B+i2/ T`2b2Mi �ii`B#mi2b

BM i?2 BK�;2X aBKBH�` iQ i?2 7mM+iBQM Q7 i?2 +H�bbB7B+�iBQM H�v2` �i i?2 2M/ Q7 i?2 M2m`�H

M2irQ`F- i?2 +H�bbB7B+�iBQM H�v2` �i i?2 #QiiQK +�M 7Q`+2 i?2 M2irQ`F iQ H2�`M i?2 BM7Q`K�iBQM

�#Qmi r?2i?2` �M �ii`B#mi2 T`2b2Mib Q` MQiX

h?2 7BM�H HQbb Bb � +QK#BM�iBQM Q7 TBt2H@rBb2 b2;K2Mi�iBQM HQbb2b loss1 �M/ loss2- +H�bbB7B+�iBQM

HQbb2b loss3 �M/ loss4X A �bbB;M2/ r2B;?ib yX8 iQ i?2 H�bi irQ HQbb2bX

loss = L1 + L2 + 0.5ƓL3 + 0.5ƓL4

jXjX JQ/2H i`�BMBM; R8

jXj JQ/2H i`�BMBM;

h?2 r?QH2 /�i�b2i �`2 /BpB/2/ BMiQ i`�BMBM;- p�HB/�iBQM- �M/ i2bi /�i�b2i- rBi? R88e /2`KQ@

b+QTB+ BK�;2b- k8N /2`KQb+QTB+ BK�;2b- �M/ ddN /2`KQb+QTB+ BK�;2b b2T�`�i2Hv Uh�#H2 jXkVX

.m2 iQ i?2 `2H�iBp2Hv bK�HH /�i�b2i Uk8N9 /�i� Q#D2+ib BM i?2 /�i�b2i BM iQi�HV- � p�`B2iv Q7

i`�BMBM; bi`�i2;B2b �`2 mb2/ iQ Qp2`+QK2 i?2 Qp2`7BiiBM; �M/ #QQbi i?2 ;2M2`�HBx�iBQM �#BHBivX

h�#H2 jXk, h?2 bTHBi Q7 i?2 /�i�b2i BMiQ i`�BMBM;- p�HB/�iBQM- �M/ i2bi /�i�b2iX

S`2T`Q+2bbBM;, �b i?2 T`2T`Q+2bbBM;- A 7B`bi `2bBx2 �HH i?2 /2`KQb+QTB+ BK�;2b �M/ K�bF

BK�;2b BMiQ 8Rk 8RkX h?2M �HH i?2 /2`KQb+QTB+ BK�;2b �`2 MQ`K�HBx2/ BMiQ i?2 `�M;2 7`QK

x2`Q iQ QM2X 6Q` 2�+? /2`KQb+QTB+ BK�;2- i?2 7Bp2 �ii`B#mi2b K�bF BK�;2b �`2 +QM+�i2M�i2/

BMiQ � 7Bp2@+?�MM2H K�bF BK�;2 iQ #2 +QKT�`2/ rBi? i?2 QmiTmi Q7 M2m`�H M2irQ`FX

AK�;2 �m;K2Mi�iBQM, AK�;2 �m;K2Mi�iBQM Bb 2KTHQv2/ QM i?2 7Hv #27Q`2 722/BM; �M BK�;2

BMiQ i?2 M2irQ`FX hQ BM+`2�b2 i?2 `Q#mbiM2bb iQ ;2QK2i`B+ i`�Mb7Q`K�iBQM �M/ TBt2H p�Hm2

p�`B�iBQMb- A T`BK�`BHv 7Q+mb2/ QM irQ ivT2b Q7 BK�;2 i`�Mb7Q`K�iBQMb, ;2QK2i`B+ i`�Mb7Q`@

K�iBQM �M/ TBt2H p�Hm2 i`�Mb7Q`K�iBQMX �b 7Q` ;2QK2i`B+ i`�Mb7Q`K�iBQM- 2�+? BK�;2 rBHH ;Q

i?`Qm;? ?Q`BxQMi�H 7HBTTBM; rBi? i?2 T`Q#�#BHBiv Q7 yX8 �M/ p2`iB+�H 7HBTTBM; rBi? i?2 T`Q#�@

#BHBiv Q7 yX8X h?2M � `Qi�iBQM rBHH #2 �TTHB2/ iQ i?2 BK�;2 #v θ /2;`22- r?2`2 θ Bb `�M/QKHv

;2M2`�i2/ 7`QK @Ny /2;`22 iQ Ny /2;`22 #v � mMB7Q`K /Bbi`B#miBQMX h?2 b+�HBM; rBHH #2 �TTHB2/

iQ i?2 BK�;2 BM #Qi? /BK2MbBQMb rBi? i?2 b+�HBM; 7�+iQ` `�M/QKHv b2H2+i2/ 7`QK yXd iQ RXj

rBi? � :�mbbB�M /Bbi`B#miBQMX �b 7Q` TBt2H p�Hm2 i`�Mb7Q`K�iBQM- A 7B`bi �/Dmbi i?2 BK�;2

#`B;?iM2bb #v �// � MmK#2` iQ �HH i?2 BK�;2 TBt2Hb r?B+? Bb `�M/QKHv +?Qb2M 7`QK @yXj �M/

Re *?�Ti2` jX J2i?Q/b

yXjX h?2M A �/Dmbi i?2 BK�;2 +QMi`�bi #v KmHiBTHvBM; 2p2`v BK�;2 TBt2H #v � 7�+iQ` `�M/QKHv

+?Qb2M 7`QK yXd iQ RXjX aBM+2 i?2 BK�;2 i`�Mb7Q`K�iBQMb QMHv `2[mB`2 � HBiiH2 +QKTmi�iBQM�H

+Qbi- �HH i?2 i`�Mb7Q`K�iBQMb �`2 /QM2 QM i?2 7Hv rBi?BM 2�+? Bi2`�iBQMX

PTiBKBx2` �M/ H2�`MBM; `�i2, �/�K QTiBKBx2` Bb mb2/ iQ QTiBKBx2 i?2 HQbb 7mM+iBQMX

�/�TiBp2 H2�`MBM; `�i2 i2+?MB[m2 Bb 2KTHQv2/X h?2 BMBiB�H H2�`MBM; `�i2 Bb b2i iQ #2 yXyR �M/

i?2 KQK2MimK Bb b2i iQ #2 yXNX h?2 H2�`MBM; `�i2 Bb b2i iQ /2+`2�b2 #v � 7�+iQ` Q7 yX3 B7 i?2

HQbb /B/ MQi /2+`2�b2 BM 8 2TQ+?bX

S`2@i`�BM2/ r2B;?i �M/ 2M+Q/2` 7`22xBM;, h?2 T`2i`�BM2/ o::Re (8) r2B;?i QM AK�@

;2L2i (88) Bb HQ�/2/ BMiQ i?2 2M+Q/2` T�ìX 6Q` i?2 7B`bi 8y 2TQ+?b- i?2 i?2 2M+Q/2` T�ì Bb

7`Qx2M �M/ QMHv /2+Q/2` T�ì Bb mM/2` i`�BMBM;X h?2 iQi�H i`�BMBM; 2TQ+?b Bb b2i iQ #2 k8yX

�b b?QrM BM 6B;m`2 9XR- i?2 HQbb #2+QK2b �HKQbi 7H�i �7i2` kyy 2TQ+?bX

jX9 1p�Hm�iBQM

�b bT2+B7B2/ #v i?2 Aa"A +?�HH2M;2 kyR3 (8e)- i?2 C�++�`/ BM/2t Bb mb2/ �b i?2 2p�Hm�iBQM Q7

i?2 �H;Q`Bi?KX C�++�`/ BM/2t Bb +�H+mH�i2/ #v i?2 /BpBbBQM Q7 i?2 BMi2`b2+iBQM �`2� �M/ mMBQM

�`2� #2ir22M T`2/B+iBQM BK�;2 K�bFb �M/ ;`QmM/ i`mi? BK�;2 K�bFbX h?2 +�H+mH�iBQM Bb

/QM2 �+`Qbb �HH i?2 7Bp2 �ii`B#mi2b �M/ i?2 2MiB`2 BK�;2b BM i?2 /�i�b2i UMQi BK�;2@#v@BK�;2-

�b bQK2 BK�;2b K�v ?�p2 MQ TQbBiBp2 BMbi�M+2b Q7 � /2`K�b+QTB+ �ii`B#mi2VX

JaccardIndex =

∑x

∑ni=0

∑5k=0 y

ix,k ∗ yix,k∑

x

∑ni=0

∑5k=0 y

ix,k +

∑x

∑ni=0

∑5k=0 y

ix,k −

∑x

∑ni=0

∑5k=0 y

ix,k ∗ yix,k

r?2`2 x /2MQi2b 2�+? BK�;2 BM i?2 /�i�b2i- n Bb i?2 MmK#2` Q7 TBt2Hb BM i?2 BK�;2- k Bb i?2

+H�bbB7B+�iBQM Q7 i?2 TBt2HX yix,k Bb i?2 i`m2 �ii`B#mi2 +H�bb p�Hm2 Q7 i?2 �ii`B#mi2 k Q7 i?2

BK�;2 TBt2H i Q7 i?2 BK�;2 x r?BH2 1 /2MQi2b T`2b2Mi �M/ 0 /2MQi2b MQM@T`2b2Mi- �M/ yix,k Bb

jX8X AKTH2K2Mi�iBQM Rd

i?2 T`2/B+i2/ T`Q#�#BHBiv p�Hm2 Q7 i?2 �ii`B#mi2 +H�bb k Q7 i?2 BK�;2 TBt2H i Q7 i?2 BK�;2 xX

jX8 AKTH2K2Mi�iBQM

h?2 �H;Q`Bi?K r�b BKTH2K2Mi2/ BM Svi?QM #�b2/ QM SvhQ`+? (8d)X h?2 #�i+? bBx2 r�b b2i

iQ #2 kX h?2 i`�BMBM; r�b /QM2 QM � T2`bQM rQ`Fbi�iBQM rBi? AMi2H *Q`2 B8@d9yy *Sl �M/

Re:" _�JX � :Sl +�`/ ULpB/B� :hs hBi�M sV �++2H2`�i2/ i?2 i`�BMBM; T`Q+2bbX �HH i?2

+QMpQHmiBQM �M/ /2+QMpQHmiBQM 7BHi2`b r2`2 BMBiB�HBx2/ rBi? `�M/QK :�mbbB�M /Bbi`B#miBQMb

rBi? x2`Q K2�M �M/ yXyR bi�M/�`/ /2pB�iBQMX

*?�Ti2` 9

_2bmHib

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