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HD
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K
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w
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s
:
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o
llab
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ativ
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f
ilter
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Hier
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ch
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ity
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ased
s
p
atial
clu
s
ter
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Scalab
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Sin
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d
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m
p
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itio
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Sp
ar
s
ity
T
h
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s
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a
rticle
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CC
BY
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C
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t Fatwa
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Her
to
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Dep
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tm
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t o
f
Ma
th
em
atics,
Facu
lty
o
f
Ma
th
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m
atics a
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d
Na
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Scien
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s
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Un
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ca
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s
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s
p
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an
d
s
ca
lab
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[
1
]
.
Sp
a
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ity
is
a
p
r
o
b
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in
s
ea
r
ch
in
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f
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'
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lack
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[
2
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.
Scalab
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th
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in
cr
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tatio
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wh
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r
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m
m
en
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n
f
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m
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p
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ce
s
s
[
3
]
.
T
h
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two
p
r
o
b
lem
s
ar
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q
u
ite
co
m
m
o
n
i
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m
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ased
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m
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ca
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tr
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s
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in
clu
d
es
m
o
v
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r
ec
o
m
m
e
n
d
atio
n
[
4
]
–
[
1
4
]
,
f
o
o
d
r
ec
o
m
m
e
n
d
ati
o
n
s
[
1
5
]
,
m
e
d
ical
p
u
r
p
o
s
es
s
u
ch
as
d
ia
b
etes
d
i
ag
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o
s
is
[
1
6
]
,
m
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s
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m
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,
a
n
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ar
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Evaluation Warning : The document was created with Spire.PDF for Python.
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tif
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tell
,
Vo
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14
,
No
.
6
,
Dec
em
b
er
2
0
2
5
:
4
8
6
5
-
4
8
7
7
4866
ac
q
u
is
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co
m
p
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y
[
1
7
]
.
A
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r
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m
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ased
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m
p
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co
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o
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ativ
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f
ilter
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el
in
co
p
in
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with
s
p
ar
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a
n
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la
b
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p
r
o
b
lem
.
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r
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m
m
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m
m
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f
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a
p
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d
u
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s
p
r
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ce
s
to
u
s
er
s
.
I
n
th
is
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ase,
th
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p
r
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d
u
ct
is
a
b
o
o
k
,
an
d
th
e
u
s
er
s
will
b
e
th
e
cu
s
to
m
er
b
u
y
i
n
g
th
at
b
o
o
k
.
So
m
e
r
elate
d
wo
r
k
s
s
u
c
h
as
ef
f
icien
t
d
ee
p
m
atr
i
x
f
ac
t
o
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(
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DM
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with
r
ev
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f
ea
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r
e
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n
i
n
g
f
o
r
in
d
u
s
tr
ial
r
ec
o
m
m
e
n
d
er
s
y
s
tem
[
1
8
]
,
co
n
f
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ce
-
awa
r
e
r
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o
m
m
e
n
d
er
m
o
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(
C
AR
M)
v
ia
r
ev
iew
r
ep
r
esen
tatio
n
lear
n
i
n
g
an
d
h
is
to
r
ical
r
atin
g
b
eh
av
i
o
r
in
t
h
e
o
n
lin
e
p
latf
o
r
m
s
[
1
9
]
,
a
n
d
m
u
lti
-
p
er
s
p
ec
tiv
e
s
o
cial
r
ec
o
m
m
en
d
atio
n
m
eth
o
d
with
g
r
ap
h
r
ep
r
esen
tatio
n
le
ar
n
in
g
[
2
0
]
ar
e
d
is
cu
s
s
ed
h
er
e.
T
h
e
r
ec
o
m
m
e
n
d
atio
n
s
y
s
tem
is
ca
teg
o
r
ized
in
to
two
ty
p
es
o
f
f
ilter
in
g
:
co
n
ten
t
-
b
ased
an
d
CF
.
C
o
n
ten
t
-
b
ased
f
ilter
in
g
f
o
c
u
s
es
o
n
u
s
er
p
r
o
f
ile
p
r
ef
er
e
n
ce
s
(
e.
g
.
,
b
o
o
k
s
)
a
n
d
item
d
escr
ip
ti
o
n
s
to
r
ec
o
m
m
en
d
item
s
th
at
ar
e
m
o
s
t
co
r
r
elate
d
with
o
th
e
r
item
s
th
at
u
s
er
s
h
av
e
h
ig
h
ly
r
ated
in
th
e
p
a
s
t.
Me
an
wh
ile,
CF
co
n
s
id
er
s
v
ar
iatio
n
s
in
cr
iter
ia
s
u
ch
as
u
s
er
p
r
ef
er
en
ce
s
,
ac
tiv
ities
,
an
d
h
ab
its
,
th
en
r
ec
o
m
m
en
d
s
an
o
b
ject
b
ased
o
n
s
im
ilar
ity
r
elatio
n
s
w
ith
o
th
er
u
s
er
s
[
4
]
.
CF
is
d
iv
id
ed
in
to
two
ca
teg
o
r
ies:
m
em
o
r
y
-
b
ased
a
n
d
m
o
d
el
-
b
ased
.
Me
m
o
r
y
-
b
ased
is
a
h
eu
r
is
tic
ap
p
r
o
ac
h
,
s
u
ch
as
co
r
r
elatio
n
an
aly
s
is
an
d
v
ec
to
r
s
im
ilar
ity
,
th
at
lo
o
k
s
f
o
r
u
s
er
p
r
o
f
iles
th
at
r
esem
b
le
ac
tiv
e
u
s
er
p
r
o
f
iles
s
o
th
at
a
r
ec
o
m
m
en
d
atio
n
ca
n
b
e
d
eter
m
i
n
ed
.
T
h
e
m
o
d
el
-
b
ased
ap
p
r
o
ac
h
u
s
es
a
lear
n
in
g
m
o
d
el
b
y
u
tili
zin
g
d
ata
co
n
tain
in
g
r
ec
o
m
m
en
d
atio
n
ass
ess
m
en
t
p
ar
am
eter
s
,
wh
ich
ar
e
th
e
n
ap
p
lied
to
p
r
o
v
id
e
r
ec
o
m
m
en
d
atio
n
p
r
ed
ictio
n
s
[
5
]
.
Me
m
o
r
y
-
b
ased
a
n
d
m
o
d
el
-
b
ased
f
ilter
in
g
m
eth
o
d
s
ca
n
b
e
co
m
b
i
n
ed
to
g
en
er
ate
r
ec
o
m
m
en
d
atio
n
s
b
a
s
ed
o
n
u
s
er
r
atin
g
p
r
e
d
ictio
n
s
f
o
r
b
o
o
k
s
.
I
n
th
is
ca
s
e,
m
em
o
r
y
-
b
ased
f
ilter
in
g
ca
lcu
lates
th
e
weig
h
tin
g
o
f
a
co
r
r
elatio
n
v
alu
e
b
etwe
en
u
s
er
s
u
s
in
g
Pear
s
o
n
co
r
r
elatio
n
weig
h
tin
g
,
a
n
d
m
o
d
el
-
b
ased
f
ilter
in
g
m
o
d
if
ie
s
th
e
d
ataset
with
t
h
e
HDBS
C
AN
an
d
R
SVD
m
o
d
els.
T
h
i
s
co
m
b
in
atio
n
will
esti
m
ate
th
e
r
atin
g
o
f
a
b
o
o
k
t
h
at
u
s
er
s
ar
e
ex
p
ec
te
d
to
ap
p
r
ec
iate.
W
e
p
r
o
p
o
s
e
a
m
eth
o
d
o
f
b
o
o
k
r
ec
o
m
m
en
d
atio
n
s
y
s
tem
th
at
s
o
lv
es
s
p
ar
s
ity
an
d
s
ca
lab
ili
ty
p
r
o
b
lem
s
in
C
F
ap
p
lied
to
th
e
elec
tr
o
n
ic
b
o
o
k
tr
ad
in
g
d
atasets
an
d
c
o
n
tr
ib
u
tes
to
CF
liter
ac
y
in
th
e
f
o
r
m
o
f
HDBS
C
A
N
an
d
R
SVD.
T
h
e
p
r
o
p
o
s
ed
HDBS
C
AN
-
R
SVD
-
C
F
h
y
b
r
id
m
o
d
el
is
th
e
f
ir
s
t
ap
p
r
o
ac
h
th
at
in
teg
r
ates
HDBS
C
AN
clu
s
ter
in
g
an
d
R
SVD
with
in
a
CF
f
r
am
ew
o
r
k
to
ad
d
r
ess
s
ca
lab
ilit
y
an
d
s
p
ar
s
ity
is
s
u
es
in
lar
g
e
-
s
ca
le
r
ec
o
m
m
en
d
er
s
y
s
tem
s
.
T
h
is
r
esear
ch
also
aim
s
t
o
d
eter
m
i
n
e
th
e
p
er
f
o
r
m
a
n
ce
o
f
HDBS
C
AN
an
d
R
SVD
in
C
F
wh
en
co
m
p
ar
ed
to
HDBS
C
AN
-
C
F,
R
SV
D
-
C
F
,
an
d
s
in
g
le
C
F.
T
h
e
m
o
d
el'
s
p
er
f
o
r
m
a
n
ce
will b
e
ev
alu
ated
u
s
in
g
d
en
s
ity
-
b
ased
clu
s
ter
v
alid
atio
n
(
DB
C
V)
an
d
r
o
o
t
m
ea
n
s
q
u
ar
ed
er
r
o
r
(
R
MSE
)
to
d
eter
m
in
e
th
e
o
p
tim
al
n
u
m
b
e
r
o
f
clu
s
ter
s
f
r
o
m
th
e
HDBS
C
A
N
m
eth
o
d
.
T
h
is
r
esear
ch
u
s
es
a
d
atas
et
p
r
o
v
i
d
ed
b
y
th
e
Kag
g
le
s
ite
[
2
1
]
wh
ic
h
co
n
s
is
ts
o
f
b
o
o
k
in
f
o
r
m
atio
n
an
d
r
atin
g
s
f
r
o
m
th
e
Go
o
d
R
ea
d
s
d
ataset.
T
h
e
r
est
o
f
th
e
p
ap
er
is
d
iv
id
ed
in
to
th
e
f
o
llo
win
g
s
ec
tio
n
s
:
s
ec
tio
n
2
p
r
o
v
id
es
th
e
liter
atu
r
e
r
ev
iew.
Sectio
n
3
p
r
esen
ts
th
e
p
r
o
p
o
s
ed
m
eth
o
d
.
S
ec
tio
n
4
p
r
esen
ts
th
e
r
esu
lts
an
d
d
is
cu
s
s
io
n
.
Fin
a
lly
,
th
e
p
ap
e
r
en
d
s
with
a
co
n
clu
s
io
n
is
s
ec
tio
n
5
.
2.
L
I
T
E
R
AT
U
RE
R
E
VI
E
W
T
h
e
r
esear
ch
o
f
r
ec
o
m
m
en
d
atio
n
s
y
s
tem
is
q
u
ite
b
r
o
a
d
.
T
o
ea
s
ily
r
elate
to
c
u
r
r
en
t
s
tu
d
y
,
th
e
liter
atu
r
e
will
th
en
b
e
g
r
o
u
p
e
d
at
t
h
eir
f
o
cu
s
f
o
r
o
v
er
co
m
i
n
g
p
r
o
b
lem
s
in
r
ec
o
m
m
en
d
ati
o
n
s
y
s
tem
.
T
h
er
e
is
r
esear
ch
th
at
f
o
cu
s
es
o
n
o
v
er
c
o
m
in
g
s
p
ar
s
ity
,
s
u
c
h
as
[
8
]
,
[
9
]
,
[
1
5
]
.
Oth
er
r
esear
ch
f
o
cu
s
es
o
n
im
p
r
o
v
i
n
g
CF
p
er
f
o
r
m
an
ce
b
y
en
h
an
cin
g
th
e
s
im
ilar
ity
m
eth
o
d
,
s
u
ch
as
[
1
0
]
–
[
1
3
]
,
[
2
2
]
,
[
2
3
]
.
T
h
er
e
i
s
also
r
esear
ch
th
at
f
o
cu
s
es
o
n
u
s
in
g
a
clu
s
ter
in
g
o
r
m
atr
ix
d
ec
o
m
p
o
s
itio
n
m
eth
o
d
to
im
p
r
o
v
e
CF
p
er
f
o
r
m
an
ce
,
s
u
ch
as
[
1
]
,
[
1
4
]
,
[
1
7
]
.
Fin
ally
,
th
e
r
e
is
also
s
o
m
e
r
esear
ch
f
o
cu
s
ed
o
n
im
p
r
o
v
in
g
t
h
e
co
n
t
r
ib
u
tio
n
to
CF
[
1
8
]
–
[
2
0
]
.
Yet,
th
e
r
esear
c
h
jo
u
r
n
e
y
to
o
v
er
co
m
e
is
s
u
es
o
f
s
p
ar
s
ity
an
d
s
ca
lab
ilit
y
u
s
in
g
clu
s
ter
in
g
(
a
g
r
o
u
p
in
g
m
eth
o
d
)
o
r
m
atr
ix
d
ec
o
m
p
o
s
itio
n
in
CF
m
o
d
els
was
u
n
d
er
tak
en
in
ea
r
l
y
2
0
1
8
.
T
h
o
s
e
s
tu
d
ies
s
h
o
wed
a
p
r
o
m
is
in
g
r
esu
lt
in
o
v
er
c
o
m
in
g
th
e
s
p
a
r
s
ity
an
d
s
ca
lab
ilit
y
i
s
s
u
es
r
eg
ar
d
in
g
th
e
CF
r
ec
o
m
m
en
d
atio
n
s
y
s
tem
s
m
o
d
el.
I
n
itial
s
tu
d
ies
s
u
ch
a
s
th
e
k
-
m
ea
n
s
clu
s
ter
an
d
SVD
d
im
en
s
io
n
r
ed
u
ctio
n
m
eth
o
d
s
ar
e
u
s
ed
o
n
a
co
m
b
in
ed
m
em
o
r
y
-
m
o
d
el
-
b
as
ed
CF
(
h
y
b
r
id
)
[
4
]
.
I
n
th
is
r
esear
ch
,
th
e
co
s
in
e
s
im
ilar
ity
m
eth
o
d
ca
lcu
lates
d
ata
s
im
ilar
ity
ca
lcu
latio
n
s
f
o
r
Mo
v
ieL
en
s
1
M
a
n
d
Mo
v
ieL
e
n
s
1
0
M
f
ilm
d
ata
.
T
h
is
r
esear
c
h
h
as
an
in
c
r
ea
s
ed
R
MSE
o
f
±
2
0
%
c
o
m
p
ar
e
d
t
o
m
em
o
r
y
-
b
ased
CF
with
th
e
k
-
n
ea
r
est
n
ei
g
h
b
o
r
s
(
k
-
NN)
m
eth
o
d
.
T
h
e
o
th
er
h
y
b
r
id
CF
m
o
d
el
in
2
0
1
8
u
s
es
th
e
o
n
to
lo
g
y
m
et
h
o
d
ap
p
r
o
ac
h
a
n
d
s
in
g
u
lar
v
alu
e
d
ec
o
m
p
o
s
itio
n
(
SVD)
d
im
en
s
io
n
r
ed
u
ctio
n
,
a
p
p
lied
to
Mo
v
ieL
e
n
s
an
d
Yah
o
o
!
W
eb
s
co
p
e
[
5
]
.
T
h
e
r
esu
lts
s
h
o
w
th
at
th
e
p
r
o
p
o
s
ed
m
eth
o
d
o
v
e
r
co
m
es
s
p
ar
s
ity
an
d
s
ca
lab
ilit
y
p
r
o
b
lem
s
in
f
ilm
d
ata.
T
h
e
r
esu
lts
f
r
o
m
ap
p
ly
in
g
SVD,
ex
p
ec
tatio
n
m
ax
im
izatio
n
,
an
d
o
n
to
lo
g
y
p
r
o
v
id
e
m
ea
n
a
b
s
o
lu
te
er
r
o
r
(
MA
E
)
±
1
3
%
b
ett
er
p
er
f
o
r
m
an
ce
th
an
CF
with
Pear
s
o
n
n
ea
r
est.
I
n
2
0
2
0
,
b
o
t
h
th
e
DB
SC
AN
clu
s
ter
in
g
ap
p
r
o
ac
h
a
n
d
lin
ea
r
d
is
cr
im
in
an
t
an
aly
s
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Ar
tif
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9
3
8
S
o
lvin
g
s
p
a
r
s
ity
a
n
d
s
ca
la
b
ilit
y
p
r
o
b
lems fo
r
b
o
o
k
r
ec
o
mme
n
d
a
tio
n
s
o
n
…
(
Mu
h
a
mma
d
I
c
h
s
a
n
u
d
in
)
4867
(
L
DA)
d
im
en
s
io
n
r
e
d
u
ctio
n
w
er
e
u
s
ed
f
o
r
m
em
o
r
y
-
m
o
d
e
l
-
b
ased
CF
o
n
clo
u
d
s
y
s
tem
s
to
c
r
ea
te
a
clo
u
d
r
ec
o
m
m
en
d
er
s
y
s
tem
with
th
e
Mo
v
ieL
en
s
d
ataset
[
6
]
.
H
y
b
r
id
CF
b
y
co
m
b
in
in
g
th
e
cl
u
s
ter
in
g
m
eth
o
d
with
Slo
p
e
On
e
alg
o
r
ith
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en
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a
n
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ictio
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it
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k
-
m
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n
s
u
s
in
g
th
e
Mo
v
ieL
en
s
1
M
d
ataset
[
7
]
.
B
ased
o
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th
e
ex
c
ellen
t
p
er
f
o
r
m
a
n
ce
o
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id
m
eth
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f
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o
m
p
r
ev
io
u
s
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esear
ch
,
a
m
eth
o
d
ca
lled
HDBS
C
AN
-
R
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-
C
F
is
in
tr
o
d
u
ce
d
to
ad
d
r
ess
s
p
ar
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ity
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d
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lab
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u
es,
in
clu
d
in
g
HDBS
C
AN,
wh
ich
is
in
s
p
ir
ed
b
y
DB
SC
A
N
[
6
]
an
d
R
SVD
th
at
is
in
s
p
ir
ed
b
y
SVD
in
[
4
]
,
[
5
]
.
3.
M
E
T
H
O
D
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
,
w
h
ich
co
m
b
in
es
HDBS
C
AN
an
d
R
SVD
m
eth
o
d
s
,
will
p
r
o
v
id
e
b
o
o
k
r
ec
o
m
m
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s
to
b
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e
r
s
b
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f
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t
ap
p
ly
in
g
th
e
H
DB
SC
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clu
s
ter
in
g
tech
n
iq
u
e
t
o
g
r
o
u
p
d
ata
with
p
ar
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o
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tim
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DB
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f
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llo
wed
b
y
th
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R
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m
eth
o
d
to
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ed
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ce
th
e
lar
g
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d
ata
in
to
s
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aller
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d
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T
h
e
Pear
s
o
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co
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elatio
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m
eth
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d
is
ap
p
lied
to
th
e
r
ed
u
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m
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.
T
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r
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r
ev
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a
le
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f
s
im
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ity
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etwe
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m
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d
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s
.
T
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e
m
o
d
el
w
o
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f
l
o
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is
s
h
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wn
in
Fig
u
r
e
1
.
Fig
u
r
e
1
.
HDBS
C
AN
-
R
SVD
-
C
F
r
ec
o
m
m
en
d
atio
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s
tem
m
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3
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1
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Da
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h
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m
Kag
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le
f
o
r
elec
tr
o
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o
o
k
tr
ad
in
g
[
2
1
]
.
Data
co
llectio
n
is
f
r
o
m
2
0
0
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2
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2
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an
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o
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2
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A
c
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to
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ta
t
i
o
n
b
y
M
c
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s
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l
.
[
2
4
]
,
th
e
t
wo
p
r
i
m
a
r
y
p
ar
a
m
e
t
e
r
s
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ly
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m
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c
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s
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in
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[
2
4
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.
T
h
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m
i
n
_
c
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_
s
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D
B
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A
N
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e
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u
l
t.
Fig
u
r
e
2
.
HDBS
C
AN
m
o
d
el
wo
r
k
f
lo
w
I
n
HDBS
C
A
N,
clu
s
ter
s
ar
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d
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id
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in
to
two
g
r
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s
:
n
o
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e
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d
clu
s
ter
s
b
ased
o
n
d
en
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ity
f
r
o
m
t
h
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b
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ix
.
A
clu
s
ter
with
a
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e
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with
m
em
b
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th
at
a
r
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s
id
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ed
n
o
is
e
[
2
4
]
.
T
h
e
cl
u
s
ter
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f
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-
1
ca
n
b
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lled
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u
s
er
s
s
in
ce
th
e
clu
s
ter
c
o
n
tain
s
h
alf
m
o
r
e
d
ata.
I
t
is
also
a
v
alu
ab
le
s
o
u
r
ce
to
s
ee
h
o
w
w
ell
th
e
HDBS
C
AN
-
R
SVD
-
C
F
h
elp
s
th
e
HDBS
C
AN
m
o
d
el
to
c
o
r
r
elate
u
s
er
s
with
lo
w
s
im
ilar
ity
o
f
in
ter
est in
th
e
k
in
d
o
f
b
o
o
k
s
.
T
h
e
clu
s
ter
in
g
p
r
o
c
ess
r
ep
lace
s
em
p
ty
v
alu
es
with
a
ze
r
o
v
alu
e
as
a
n
eu
tr
al
v
alu
e
f
r
o
m
th
e
d
ata
d
is
tr
ib
u
tio
n
.
T
h
is
s
tep
is
im
p
o
r
tan
t
s
in
ce
th
e
HDBS
C
AN
a
lg
o
r
ith
m
ca
n
n
o
t
weig
h
t
cl
u
s
ter
s
with
g
ap
s
in
th
e
d
ata,
esp
ec
ially
in
th
e
Py
th
o
n
p
r
o
g
r
am
with
th
e
HDBS
C
AN
lib
r
ar
y
[
2
5
]
,
an
d
r
e
g
ar
d
i
n
g
HDBS
C
AN
[
2
4
]
.
T
h
e
DB
C
V
we
ig
h
s
th
e
p
ar
am
eter
s
b
ased
o
n
th
e
d
en
s
ity
o
f
th
e
HDBS
C
AN
m
o
d
el
an
d
g
iv
es
it
a
s
co
r
e
f
r
o
m
-
1
to
1
,
wh
ich
is
ap
p
r
o
p
r
iate
to
th
e
g
o
o
d
n
ess
o
f
th
e
clu
s
ter
r
esu
lt.
T
h
e
h
ig
h
er
th
e
DB
C
V
s
co
r
e,
th
e
b
etter
th
e
clu
s
ter
in
g
r
esu
lt.
C
lu
s
ter
in
g
r
esu
lts
in
g
r
o
u
p
s
o
f
u
s
er
s
with
s
im
ilar
b
o
o
k
in
ter
e
s
ts
,
allo
win
g
th
e
r
ec
o
m
m
en
d
atio
n
s
y
s
tem
to
r
e
d
u
ce
co
m
p
u
tatio
n
b
y
c
o
n
s
id
er
in
g
o
n
l
y
u
s
er
s
with
in
th
e
s
am
e
clu
s
ter
in
s
tead
o
f
all
u
s
er
s
.
Mo
r
e
d
etails o
n
DB
C
V
ca
n
b
e
f
o
u
n
d
in
[
2
6
]
.
3
.
3
.
Ra
nd
o
m
ized
s
ing
ula
r
v
a
lue dec
o
m
po
s
it
io
n
T
h
e
p
u
r
p
o
s
e
o
f
R
SVD
is
f
o
r
m
atr
ix
r
ed
u
ctio
n
,
wh
e
r
e
a
co
m
p
ar
is
o
n
will
b
e
ca
r
r
ied
o
u
t
to
s
elec
t
th
e
b
est
n
-
co
m
p
o
n
en
t
h
y
p
er
p
ar
am
eter
s
.
T
h
is
n
-
co
m
p
o
n
en
t
will
af
f
ec
t
th
e
ac
cu
r
ac
y
o
f
R
MSE
an
d
r
u
n
tim
e
o
f
th
e
m
o
d
el.
T
h
e
R
SVD
m
o
d
el
wo
r
k
f
lo
w
is
in
Fig
u
r
e
3
.
T
h
e
p
r
o
c
ess
is
a
s
f
o
llo
ws:
i)
R
SVD
i
s
a
r
an
d
o
m
ized
m
eth
o
d
to
r
ec
o
n
s
tr
u
ct
h
ig
h
-
d
im
en
s
io
n
al
m
atr
ices in
to
s
m
aller
m
atr
ices,
f
o
llo
wed
b
y
th
e
SVD
p
r
o
ce
s
s
,
wh
ich
s
p
lits
a
m
atr
ix
in
to
th
r
ee
m
at
r
ix
co
m
p
o
n
e
n
ts
.
T
h
e
r
esu
lt
is
th
r
ee
m
atr
ix
co
m
p
o
n
en
ts
f
r
o
m
th
e
m
ain
m
atr
ix
A
m×n
,
s
o
th
at
A
m×n
=
U
m
×
k
×
Σ
k
×
k
×
T
k
×
n
,
wh
er
e
U
a
n
d
V
ar
e
o
r
th
o
n
o
r
m
al
m
atr
ices,
a
n
d
Σ
is
a
d
iag
o
n
al
a
n
d
n
o
n
-
n
eg
ativ
e
m
atr
ix
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2
2
5
2
-
8
9
3
8
S
o
lvin
g
s
p
a
r
s
ity
a
n
d
s
ca
la
b
ilit
y
p
r
o
b
lems fo
r
b
o
o
k
r
ec
o
mme
n
d
a
tio
n
s
o
n
…
(
Mu
h
a
mma
d
I
c
h
s
a
n
u
d
in
)
4869
ii)
T
h
e
R
SVD
p
r
o
ce
s
s
ca
n
b
e
ap
p
lied
if
m
atr
ix
A
h
as
a
lo
w
-
r
an
k
s
tr
u
ctu
r
e,
an
d
it
is
a
v
er
y
ef
f
icien
t
m
atr
ix
d
ec
o
m
p
o
s
itio
n
alg
o
r
ith
m
b
ase
d
o
n
r
an
d
o
m
s
am
p
lin
g
th
eo
r
y
.
I
t
is
also
ca
lled
th
e
r
a
n
d
o
m
iz
ed
n
u
m
e
r
ical
m
eth
o
d
[
2
7
]
.
T
h
e
k
v
alu
es f
o
r
Σ
,
in
d
icate
s
th
e
eig
en
v
alu
es f
r
o
m
m
atr
ix
A.
iii)
T
h
e
U
m
atr
ix
b
u
ild
s
a
r
ec
o
m
m
en
d
atio
n
s
y
s
tem
,
an
d
th
e
m
a
tr
ix
d
im
en
s
io
n
s
ar
e
r
e
d
u
ce
d
a
cc
o
r
d
in
g
t
o
th
e
n
u
m
b
er
o
f
n
-
co
m
p
o
n
e
n
t v
alu
e
s
(
s
in
g
u
lar
v
alu
es)
s
elec
ted
f
r
o
m
th
e
k
v
alu
es o
f
Σ
,
s
o
th
e
r
ec
o
m
m
en
d
atio
n
s
y
s
tem
d
o
es n
o
t u
s
e
to
o
m
u
ch
wo
r
k
in
p
r
o
g
r
ess
[
2
8
]
.
iv
)
C
o
n
s
id
er
th
e
m
atr
ix
A
m×n
=
U
m×k
×
Σ
k
×k
×
V
T
k
×n
.
T
h
en
,
f
o
r
a
s
elec
tio
n
o
f
th
e
n
u
m
b
e
r
o
f
n
-
c
o
m
p
o
n
en
t
v
alu
es
r
ep
r
esen
te
d
as
t
i
n
Σ
k
×k
,
wh
er
e
t
< k
an
d
k
r
ep
r
esen
ts
th
e
r
an
k
v
alu
e
o
f
th
e
m
atr
ix
A
m×n
.
T
h
er
ef
o
r
e,
th
e
n
-
co
m
p
o
n
e
n
t
(
t
)
v
alu
e
is
b
etwe
en
0
—
r
an
k
o
f
th
e
m
atr
ix
,
o
r
th
e
s
m
allest
r
o
w/co
lu
m
n
s
ize
in
th
e
m
atr
ix
A
m×n
.
T
h
e
r
an
k
o
f
m
atr
ix
A
is
th
e
n
u
m
b
er
o
f
lin
ea
r
ly
in
d
ep
en
d
en
t
co
l
u
m
n
s
p
ac
es.
T
h
e
m
atr
ix
U
m×k
will
ex
p
er
ien
ce
a
d
im
en
s
io
n
r
e
d
u
ctio
n
,
f
r
o
m
U
m×k
b
ec
o
m
es
th
e
r
ed
u
ce
d
m
at
r
ix
U
m×t
,
s
ee
Fig
u
r
e
4
.
v)
I
n
th
e
r
e
d
u
ce
d
m
atr
ix
U
,
t
h
e
r
o
ws
r
ep
r
esen
t
u
s
er
s
with
in
t
h
e
s
am
e
clu
s
ter
,
wh
ile
th
e
co
lu
m
n
s
r
ep
r
esen
t
an
ag
g
r
e
g
atio
n
o
f
b
o
o
k
s
,
f
o
cu
s
in
g
o
n
ly
o
n
th
e
m
o
s
t d
o
m
in
a
n
t p
ar
ts
.
T
h
e
elem
e
n
t
u
p,
t
r
ep
r
esen
ts
th
e
b
o
o
k
r
atin
g
b
y
u
s
er
p
f
o
r
t
h
e
t
-
th
a
g
g
r
eg
ated
b
o
o
k
s
.
Fig
u
r
e
3
.
R
SVD
m
o
d
el
wo
r
k
f
l
o
w
Fig
u
r
e
4
.
I
ll
u
s
tr
atio
n
o
f
t
h
e
r
e
d
u
ce
d
m
atr
i
x
U
T
h
e
d
eter
m
in
atio
n
o
f
p
ar
am
et
er
s
in
v
o
lv
es
th
e
n
-
co
m
p
o
n
en
t
,
wh
ich
is
s
et
to
5
0
%,
6
0
%
t
o
1
0
0
%
o
f
th
e
r
an
k
f
r
o
m
ea
c
h
clu
s
ter
ed
u
s
er
-
b
o
o
k
m
atr
ix
.
T
h
is
co
r
r
esp
o
n
d
s
to
th
e
ac
tiv
e
u
s
er
’
s
clu
s
ter
.
T
h
e
n
-
co
m
p
o
n
en
t
r
etr
iev
al
is
ap
p
li
ed
o
n
l
y
wh
e
n
th
er
e
ar
e
at
least
1
0
u
s
er
s
in
a
clu
s
ter
;
o
th
e
r
wis
e,
all
u
s
er
s
in
th
e
clu
s
ter
ar
e
in
clu
d
ed
.
3
.
4
.
Sp
litt
ing
d
a
t
a
T
h
e
tr
ain
in
g
an
d
test
in
g
d
ata
d
iv
is
io
n
was
ca
r
r
ied
o
u
t
with
an
8
0
:2
0
d
iv
is
io
n
s
eq
u
en
tia
lly
o
n
th
e
u
s
er
-
b
o
o
k
s
m
atr
ix
.
User
s
in
t
h
e
test
in
g
d
ata
ar
e
ca
lled
ac
ti
v
e
u
s
er
s
,
as
th
e
y
will
r
ec
eiv
e
r
ec
o
m
m
e
n
d
atio
n
s
f
r
o
m
t
h
e
m
o
d
el.
Me
an
wh
ile,
t
h
e
tr
ain
in
g
d
ata
c
o
n
s
is
ts
o
f
in
ac
tiv
e
u
s
er
s
wh
o
g
en
er
ate
p
r
e
d
icted
b
o
o
k
r
atin
g
s
.
T
h
e
p
r
o
ce
s
s
was c
ar
r
ied
o
u
t f
i
v
e
tim
es seq
u
en
tially
,
o
r
5
-
f
o
ld
cr
o
s
s
-
v
alid
atio
n
.
3
.
5
.
P
e
a
rso
n
co
rr
ela
t
io
n c
o
e
f
f
icient
a
nd
ind
ex
equa
liza
t
i
o
n
T
h
e
P
e
ar
s
o
n
c
o
r
r
e
l
a
t
io
n
c
o
e
f
f
i
c
i
e
n
t
(
P
C
C
)
m
e
t
h
o
d
i
s
a
p
p
li
e
d
t
o
u
s
e
r
s
in
t
h
e
i
n
d
ex
(
r
o
w
)
o
f
t
h
e
m
a
t
r
i
x
U
t
o
o
b
t
a
in
th
e
u
s
er
s
’
s
i
m
i
l
ar
i
t
y
m
a
t
r
i
x
.
B
a
s
ed
o
n
t
h
i
s
m
a
tr
i
x
,
th
e
P
ea
r
s
o
n
c
o
r
r
e
l
a
t
i
o
n
m
e
th
o
d
i
s
a
l
s
o
a
p
p
l
i
e
d
b
e
t
we
e
n
a
c
t
i
v
e
u
s
e
r
s
(
u
s
er
s
f
r
o
m
te
s
t
i
n
g
d
a
t
a)
a
n
d
in
a
c
t
iv
e
u
s
e
r
s
(
tr
a
i
n
in
g
d
a
t
a
)
t
o
g
en
e
r
a
t
e
th
e
i
n
d
ex
e
d
s
i
m
i
la
r
i
ty
m
a
t
r
ix
.
F
i
n
a
l
l
y
,
a
c
t
i
v
e
u
s
e
r
s
c
an
b
e
i
d
e
n
t
if
i
e
d
f
r
o
m
th
i
s
m
a
t
r
i
x
t
o
h
a
v
e
b
o
o
k
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
14
,
No
.
6
,
Dec
em
b
er
2
0
2
5
:
4
8
6
5
-
4
8
7
7
4870
r
e
c
o
m
m
en
d
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t
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th
a
t
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t
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r
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g
h
th
e
p
r
e
d
i
c
t
ed
b
o
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i
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s
.
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t
i
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ed
m
a
t
r
ic
e
s
U
o
n
a
g
i
v
en
c
lu
s
t
e
r
c
r
e
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te
d
b
y
t
h
e
R
S
V
D
p
r
o
c
e
s
s
.
U
s
e
P
C
C
d
e
f
in
e
d
in
(
1
)
b
e
t
w
e
en
a
c
t
iv
e
u
s
e
r
(
u
)
an
d
an
o
th
e
r
u
s
e
r
(
u
’
)
f
r
o
m
t
h
e
s
a
m
e
c
l
u
s
t
er
a
s
f
o
l
lo
w
s
:
PC
C
(
u,
u
'
)
=
∑
(
r
,i
-
̅
)(
r
′
,i
-
̅
′
)
i
∈
I
√
∑
(
r
u,
i
-
̅
)
2
i
∈
I
×
√
∑
(
r
′
,i
-
̅
′
)
2
i
∈
I
(
1
)
W
h
e
r
e
r
u,
i
an
d
r
u'
,
i
T
h
e
b
o
o
k
r
a
t
in
g
g
iv
e
n
b
y
t
wo
u
s
e
r
s
u
an
d
u'
t
o
t
h
e
i
-
t
h
b
o
o
k
,
c
o
r
r
e
s
p
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n
d
i
n
g
l
y
.
T
h
e
̅
a
n
d
̅
′
d
en
o
t
e
s
th
e
a
v
er
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g
e
b
o
o
k
r
a
t
in
g
b
y
u
s
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r
s
u
an
d
u'
,
a
n
d
=
I
u
∩
I
u'
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o
t
e
s
th
e
b
o
o
k
s
r
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ted
b
y
u
s
e
r
u
an
d
u’
,
r
e
s
p
e
c
t
iv
el
y
.
T
h
e
v
a
l
u
e
PC
C
(
u,
u
'
)
∈
[
-
1
,
1
]
s
h
o
w
s
t
h
e
s
im
i
l
a
r
i
t
y
v
a
l
u
e
b
e
t
w
e
en
u
s
e
r
s
u
an
d
u
'
c
o
r
r
e
s
p
o
n
d
in
g
ly
.
W
h
e
n
t
h
e
v
a
lu
e
o
f
P
C
C
i
s
c
l
o
s
e
t
o
1
o
r
-
1
,
t
h
e
u
s
e
r
s
s
h
o
w
a
h
ig
h
p
o
s
i
t
i
v
e
o
r
n
e
g
a
t
iv
e
c
o
r
r
e
l
a
t
io
n
.
Af
ter
o
b
tain
in
g
th
e
u
s
er
s
’
s
i
m
ilar
ity
m
atr
ix
,
th
e
in
d
ex
eq
u
aliza
tio
n
p
r
o
ce
s
s
eq
u
ates
th
e
u
s
er
'
s
"I
D"
in
d
ex
f
r
o
m
th
e
u
s
er
s
im
ilar
ity
m
atr
ix
with
th
e
tr
ain
in
g
d
ata
with
th
e
s
am
e
in
d
ex
(
th
e
u
s
er
'
s
"I
D")
.
T
h
is
p
r
o
ce
s
s
r
em
o
v
es
r
o
ws
f
r
o
m
th
e
u
s
er
"I
Ds"
n
o
t
in
th
e
tr
ai
n
in
g
d
ata
a
n
d
will
n
o
t
a
p
p
ea
r
in
th
e
r
esu
lts
.
I
t
is
im
p
o
r
tan
t
n
o
t
to
d
elete
th
e
u
s
er
"I
D"
in
th
e
m
atr
ix
co
lu
m
n
b
ec
au
s
e
th
is
co
lu
m
n
,
wh
ich
s
till
co
n
tain
s
th
e
u
s
er
"I
D"
f
r
o
m
th
e
test
in
g
d
ata,
will
b
e
u
s
ed
as
a
r
e
f
er
en
ce
f
o
r
i
n
ac
tiv
e
u
s
er
s
with
s
im
ilar
ity
t
o
ac
tiv
e
u
s
er
s
th
at
will r
ec
eiv
e
r
ec
o
m
m
en
d
atio
n
s
.
3
.
6
.
Sim
ila
ri
t
y
t
hresh
o
ld
T
h
e
s
im
ilar
ity
th
r
esh
o
ld
will
p
r
o
v
id
e
a
lis
t
o
f
p
e
o
p
le
with
s
im
ilar
in
ter
ests
o
r
n
o
t.
Af
ter
g
ettin
g
th
e
in
d
ex
ed
u
s
er
s
'
s
im
ilar
ity
m
atr
ix
,
th
e
PC
C
v
alu
e
will
b
e
s
et
with
a
th
r
esh
o
ld
to
d
ete
r
m
in
e
if
th
e
u
s
er
h
as
a
v
alu
e
ab
o
v
e
th
e
lim
it,
in
wh
ic
h
ca
s
e
it
m
atch
es
ac
tiv
e
u
s
er
s
.
T
h
e
m
atr
ix
is
ca
lled
th
e
in
d
ex
ed
u
s
er
s
’
s
im
ilar
ity
th
r
esh
o
ld
m
atr
ix
.
E
s
tab
lis
h
in
g
a
s
im
ilar
ity
v
alu
e
th
r
esh
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ld
is
im
p
o
r
tan
t
in
in
c
r
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s
in
g
p
r
e
d
ictio
n
ac
cu
r
ac
y
f
o
r
an
ac
tiv
e
u
s
er
.
T
h
e
h
ig
h
er
th
e
r
estrictio
n
v
alu
e,
th
e
h
ig
h
e
r
th
e
ac
cu
r
ac
y
[
2
9
]
.
3
.
7
.
B
o
o
k
r
a
t
ing
predict
io
n
T
h
e
p
r
ed
ictio
n
s
f
o
r
ac
tiv
e
u
s
e
r
s
u
tili
ze
th
r
ee
m
ain
m
atr
ices:
th
e
u
s
er
s
im
ilar
ity
,
th
e
ac
tiv
e
u
s
er
-
b
o
o
k
,
an
d
th
e
in
ac
tiv
e
u
s
er
-
b
o
o
k
m
atr
ix
.
T
h
e
p
r
ed
ictio
n
p
r
o
ce
s
s
is
ca
r
r
ied
o
u
t
iter
ativ
ely
,
o
n
e
b
y
o
n
e
,
f
o
r
ea
c
h
ac
tiv
e
u
s
er
o
n
test
in
g
d
ata
u
s
in
g
(
2
)
.
r
̂
a,
i
=
̅
+
∑
(
P
C
C
a,
u
×
|
r
u,
i
-
̅
|
)
n
u
∑
P
C
C
a,
u
n
u
(
2
)
W
h
er
e
̂
,
is
th
e
p
r
ed
icted
r
atin
g
o
f
th
e
i
-
t
h
b
o
o
k
b
y
th
e
a
-
th
a
ctiv
e
u
s
er
,
̅
is
th
e
av
er
ag
e
r
ati
n
g
o
f
th
e
b
o
o
k
r
ated
b
y
t
h
e
a
-
th
ac
tiv
e
u
s
er
,
P
C
C
a,
u
is
th
e
Pear
s
o
n
co
r
r
elatio
n
ass
ess
m
en
t
o
f
th
e
a
-
th
ac
tiv
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u
s
er
to
t
h
e
u
-
th
in
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tiv
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u
s
er
,
r
u,
i
is
th
e
as
s
ess
m
e
n
t
b
y
th
e
u
-
th
in
ac
tiv
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er
o
f
th
e
i
-
th
b
o
o
k
,
a
n
d
̅
is
th
e
av
e
r
ag
e
r
atin
g
o
f
th
e
b
o
o
k
f
r
o
m
u
-
th
in
ac
tiv
e
u
s
er
s
[
3
0
]
.
Af
ter
o
b
tain
i
n
g
t
h
e
p
r
e
d
icted
v
alu
es,
th
e
av
er
ag
e
v
alu
es
will
b
e
ca
lcu
lated
to
d
eter
m
i
n
e
th
e
R
MSE
o
f
th
e
m
o
d
el.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
W
e
p
r
esen
t
th
e
r
esu
lts
an
d
d
i
s
cu
s
s
io
n
o
f
th
e
im
p
lem
e
n
tatio
n
o
f
th
e
HDBS
C
A
N
-
R
S
VD
-
C
F
m
o
d
el.
T
h
e
R
MSE
v
alu
es
ar
e
th
e
a
v
e
r
ag
e
o
f
f
iv
e
q
u
in
tile
r
esu
lts
f
r
o
m
th
e
m
o
d
el'
s
r
atin
g
p
r
e
d
ictio
n
s
f
o
r
ac
tiv
e
u
s
er
s
,
co
m
p
ar
ed
to
th
e
ac
t
u
al
b
o
o
k
r
atin
g
s
th
ey
h
av
e
r
ated
.
T
h
e
m
o
d
el
r
ec
o
r
d
s
th
e
r
u
n
n
in
g
tim
e
v
alu
es a
f
ter
f
o
r
m
in
g
th
e
u
s
er
-
b
o
o
k
s
m
atr
ix
a
n
d
d
iv
i
d
in
g
th
e
d
ataset
in
to
f
iv
e
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u
in
t
iles
.
T
h
e
im
p
lem
en
tatio
n
o
f
H
DB
S
C
AN
s
elec
ts
s
ev
er
al
i
m
p
o
r
tan
t
p
ar
a
m
eter
s
in
th
e
f
o
r
m
o
f
m
in
_
clu
s
ter
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s
ize
an
d
m
i
n
_
s
am
p
les
to
o
b
tain
clu
s
ter
ed
d
ata
[
2
4
]
.
T
h
e
p
r
o
ce
s
s
in
v
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lv
es
h
ier
a
r
ch
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y
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ized
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eq
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en
tially
r
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im
u
ltan
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ly
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.
T
h
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q
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ality
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Acc
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d
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DB
C
V,
th
e
v
alu
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to
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T
h
e
HDBS
C
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p
ar
am
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et
with
a
v
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f
m
in
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ter
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ize
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2
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d
m
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p
les
o
f
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n
th
e
p
r
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ce
s
s
,
th
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e
is
a
clu
s
ter
with
th
e
v
alu
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f
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d
icatin
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n
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id
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wh
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in
clu
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in
p
r
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r
atin
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v
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ac
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Min
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DB
C
V
s
co
r
e
(
th
e
n
atu
r
e
DB
C
V
v
alu
e
is
in
[
-
1
,
1
]
)
,
wh
ich
in
d
icate
s
th
e
d
at
a
is
v
er
y
s
p
ar
s
e.
T
h
e
m
in
_
cl
u
s
ter
_
s
ize
o
f
2
w
ill
th
en
b
e
ca
r
r
ied
t
o
f
in
d
th
e
b
est
m
in
_
s
am
p
les
b
y
th
e
h
ier
ar
ch
ical
h
y
p
er
p
ar
am
eter
tu
n
in
g
m
eth
o
d
th
at
s
eq
u
en
tially
o
p
tim
ized
ea
ch
p
ar
am
eter
,
r
esu
lts
in
m
in
_
s
am
p
les
is
1
.
Min
_
s
am
p
les
is
th
e
m
in
im
u
m
p
o
in
t
i
n
th
e
c
o
r
e
p
o
in
t
o
f
s
o
m
e
en
v
ir
o
n
m
en
t
(
g
r
o
u
p
)
,
wh
er
e
th
e
v
al
u
e
is
a
n
in
teg
er
n
u
m
b
er
in
[
1
,
in
f
)
.
F
r
o
m
T
ab
le
2
,
th
e
iter
atio
n
p
r
o
ce
s
s
s
h
o
ws
th
at
th
e
h
ig
h
er
th
e
m
in
_
s
am
p
les,
th
e
m
o
r
e
th
e
r
esu
lt
o
f
DB
C
V
s
co
r
e
an
d
n
u
m
b
er
o
f
cl
u
s
ter
s
will
d
ec
ay
.
T
h
is
r
esu
lt
s
h
o
ws
th
at
ch
o
o
s
in
g
m
o
r
e
co
r
e
p
o
in
ts
f
o
r
th
e
m
o
d
el
will
r
esu
lt
in
h
ig
h
er
d
is
tan
ce
s
ca
lcu
lated
b
y
th
e
n
ea
r
est
n
eig
h
b
o
r
alg
o
r
ith
m
b
etwe
en
p
o
in
ts
,
wh
ich
in
d
icate
s
th
e
in
c
r
ea
s
in
g
n
u
m
b
er
o
f
o
u
tlier
s
in
s
o
m
e
g
r
o
u
p
s
o
f
clu
s
ter
s
.
T
h
e
r
esu
lts
o
f
T
ab
les
1
an
d
2
s
h
o
w
th
at
th
e
m
o
d
el
f
ac
in
g
th
e
d
ata
is
to
o
s
p
ar
s
e
to
b
e
g
r
o
u
p
e
d
.
T
h
e
b
est
DB
C
V
ev
alu
atio
n
s
h
o
ws
a
lo
w
s
co
r
e
(
0
.
0
8
5
1
)
,
wh
ich
m
ig
h
t
in
d
icate
in
s
u
f
f
icien
t
p
er
f
o
r
m
an
ce
wh
en
h
an
d
lin
g
th
e
s
p
ar
s
ity
a
n
d
s
ca
lab
ilit
y
p
r
o
b
lem
.
T
o
ad
d
r
ess
th
is
is
s
u
e,
R
SVD
i
s
ap
p
lied
to
ea
ch
cl
u
s
ter
to
s
u
p
p
r
ess
n
o
is
e
an
d
f
ac
ilit
ate
th
e
s
elec
tio
n
o
f
th
e
m
o
s
t r
ep
r
ese
n
tativ
e
co
m
p
o
n
en
t f
o
r
m
o
d
eli
n
g
.
T
ab
le
1
.
Par
am
eter
iter
atio
n
ta
b
le
o
f
m
in
_
clu
s
ter
_
s
ize
I
t
e
r
a
t
i
o
n
mi
n
_
c
l
u
st
e
r
_
si
z
e
D
B
C
V
N
u
mb
e
r
o
f
c
l
u
s
t
e
r
s
1
2
0
.
0
5
5
0
82
5
6
0
.
0
3
8
5
15
10
15
0
.
0
0
8
8
5
11
20
0
.
0
3
12
30
0
.
0
1
T
ab
le
2
.
Par
am
eter
iter
atio
n
ta
b
le
o
f
m
in
_
s
am
p
les with
m
in
_
clu
s
ter
_
s
ize
eq
u
al
2
I
t
e
r
a
t
i
o
n
mi
n
_
sa
mp
l
e
s
D
B
C
V
N
u
mb
e
r
o
f
c
l
u
s
t
e
r
s
1
1
0
.
0
8
5
1
1
7
1
5
5
0
.
0
2
4
0
25
10
10
0
.
0
1
1
2
11
11
15
0
.
0
0
8
8
7
12
20
0
.
0
0
2
1
5
13
30
0
.
0
4
4
.
1
.
M
a
t
rix
r
educt
io
n us
ing
ra
nd
o
m
ized
s
ing
ula
r
v
a
lue dec
o
m
po
s
it
io
n
T
h
e
R
SVD
alg
o
r
ith
m
is
ap
p
lied
to
a
clu
s
ter
ed
u
s
er
-
b
o
o
k
m
at
r
ix
o
v
er
a
p
ar
ticu
lar
clu
s
ter
f
o
r
d
im
en
s
io
n
r
ed
u
ctio
n
.
T
h
e
s
elec
tio
n
o
f
R
SVD
p
ar
am
eter
s
is
p
er
f
o
r
m
ed
b
y
s
elec
tin
g
th
e
n
u
m
b
er
o
f
n
-
co
m
p
o
n
en
ts
in
th
e
s
in
g
u
lar
m
atr
ix
,
wh
ich
r
e
d
u
ce
s
th
e
m
atr
ix
d
im
en
s
io
n
ality
ac
c
o
r
d
in
g
to
th
e
s
elec
ted
n
-
co
m
p
o
n
en
t
v
alu
e
with
a
v
alu
e
s
m
aller
th
an
o
r
eq
u
al
to
th
e
s
m
allest
r
o
w/co
lu
m
n
s
ize
(
r
an
k
o
f
th
e
m
atr
ix
)
.
T
h
e
s
elec
tio
n
is
p
er
f
o
r
m
e
d
th
r
o
u
g
h
iter
ativ
e
ex
p
er
im
en
ts
b
y
co
m
p
ar
in
g
th
e
r
atin
g
v
alu
e
p
r
ed
ictio
n
at
th
e
f
in
al
s
tag
e
o
f
th
e
HDBS
C
AN
-
R
SV
D
-
C
F a
lg
o
r
ith
m
.
4
.
2
.
I
m
ple
m
ent
a
t
io
n o
f
s
im
ila
rit
y
a
nd
ind
ex
equa
liza
t
io
n
Af
ter
o
b
tain
in
g
th
e
U
m
atr
ix
,
th
e
v
alu
es
i
n
th
e
U
m
atr
ix
a
r
e
ap
p
lied
with
th
e
Pear
s
o
n
c
o
r
r
elatio
n
m
eth
o
d
co
n
ce
r
n
in
g
th
e
in
d
ex
/
r
o
w,
wh
ich
is
th
e
“I
D”
o
f
th
e
u
s
er
will
b
e
tr
an
s
f
o
r
m
ed
in
to
a
u
s
er
s
im
ilar
ity
m
atr
ix
.
T
h
e
p
r
o
ce
s
s
is
co
n
tin
u
ed
b
y
r
e
p
lacin
g
t
h
e
NaN
d
at
a
with
ze
r
o
.
Nex
t,
t
h
e
p
r
o
ce
s
s
o
f
eq
u
alizin
g
th
e
u
s
er
“I
D”
in
d
ex
in
th
e
s
im
il
ar
ity
m
atr
ix
with
th
e
t
r
ain
in
g
d
ata
is
im
p
lem
en
ted
.
T
h
is
eq
u
aliza
tio
n
p
r
o
ce
s
s
r
em
o
v
es a
ll u
s
er
“I
D”
v
alu
es th
at
ar
e
n
o
t
p
r
esen
t in
th
e
tr
ain
i
n
g
d
ata.
4
.
3
.
E
v
a
lua
t
i
o
n o
f
s
im
ila
rit
y
t
hresh
o
ld
T
h
e
av
er
a
g
e
m
eth
o
d
was
u
s
ed
to
o
b
tain
s
im
ilar
ity
th
r
es
h
o
ld
v
al
u
es
with
r
esp
ec
t
to
R
MSE
an
d
co
m
p
u
tin
g
tim
e.
T
h
e
clo
s
est
v
alu
e
to
th
e
av
er
a
g
e
R
MSE
an
d
co
m
p
u
tin
g
tim
e
is
s
elec
ted
as
th
e
s
im
ilar
ity
th
r
esh
o
ld
.
T
h
is
th
r
esh
o
ld
will
b
e
u
s
ed
in
t
h
e
n
e
x
t
p
r
o
ce
s
s
.
T
h
e
av
er
a
g
e
R
MSE
v
alu
e
in
T
ab
le
3
is
0
.
8
5
3
7
,
wh
ile
th
e
av
er
ag
e
w
o
r
k
in
g
m
o
d
el
is
3
8
3
1
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8
6
s
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o
n
d
s
.
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ased
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b
o
t
h
av
er
a
g
es,
th
e
clo
s
est s
im
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ity
th
r
esh
o
ld
v
alu
e
is
0
.
4
(
th
e
s
im
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ity
lim
it p
ar
am
eter
is
0
.
4
)
.
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4
.
HDBS
C
AN
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R
SVD
-
C
F m
o
d
el
ev
alu
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m
p
ar
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s
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M
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l
H
D
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S
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A
N
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R
S
V
D
(
5
0
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D
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A
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R
S
V
D
(
6
0
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CF
H
D
B
S
C
A
N
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R
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V
D
(
7
0
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CF
H
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C
A
N
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D
(
8
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(
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0
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C
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N
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N
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V
D
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C
A
N
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R
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V
D
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CF
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C
A
N
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R
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V
D
(
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0
%)
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CF
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D
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C
A
N
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R
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V
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0
0
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n
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m
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n
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t f
r
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ly
.
T
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le
6
.
R
SVD
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C
F
m
o
d
el
ev
alu
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n
co
m
p
ar
is
o
n
M
o
d
e
l
R
S
V
D
(
5
0
%)
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CF
R
S
V
D
(
6
0
%)
-
CF
R
S
V
D
(
7
0
%)
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CF
R
S
V
D
(
8
0
%)
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CF
R
S
V
D
(
9
0
%)
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CF
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S
V
D
(
1
0
0
%)
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CF
A
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e
r
a
g
e
R
M
S
E
0
.
5
3
8
8
0
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5
3
5
0
5
0
.
4
9
0
2
0
.
3
3
4
2
0
.
1
5
7
0
1
N
a
N
Ti
me
(
S
e
c
o
n
d
s)
4
7
4
.
5
9
1
3
3
.
3
8
1
3
9
.
8
3
1
1
9
.
8
8
1
1
0
.
9
6
1
0
7
.
2
2
T
ab
le
7
.
T
h
e
n
u
m
b
er
o
f
ac
tiv
e
u
s
er
s
r
ec
o
m
m
en
d
ed
b
y
R
SVD
-
CF
M
o
d
e
l
R
S
V
D
(
5
0
%)
-
CF
R
S
V
D
(
6
0
%)
-
CF
R
S
V
D
(
7
0
%)
-
CF
R
S
V
D
(
8
0
%)
-
CF
R
S
V
D
(
9
0
%)
-
CF
R
S
V
D
(
1
0
0
%)
-
CF
N
u
mb
e
r
o
f
a
c
t
i
v
e
u
sers
g
e
t
r
e
c
o
m
me
n
d
a
t
i
o
n
s
1
,
5
7
6
1
,
2
8
5
1
,
0
2
7
5
0
1
57
0
4
.
6
.
E
v
a
lua
t
i
o
n o
f
c
o
m
pa
ra
t
iv
e
re
s
ults
o
f
H
DB
SCAN
-
R
S
VD
-
CF
,
RSVD
-
CF
,
H
DB
SC
AN
-
CF
,
a
nd
CF
T
ab
le
8
p
r
esen
ts
th
e
p
er
f
o
r
m
an
ce
s
o
f
th
e
HDBS
C
A
N
-
R
S
VD
-
C
F,
R
SVD
-
C
F,
HD
B
S
C
AN
-
C
F,
an
d
s
in
g
le
C
F
m
o
d
els.
T
h
e
av
er
ag
e
R
MSE
i
s
ca
lcu
lated
b
y
av
er
ag
in
g
th
e
R
MSE
v
alu
es
o
f
a
g
r
o
u
p
o
f
ac
tiv
e
u
s
er
s
(
test
in
g
d
ata)
an
d
co
m
p
ar
in
g
th
e
p
r
ed
icted
b
o
o
k
r
atin
g
s
with
th
eir
ac
tu
al
r
atin
g
s
f
o
r
th
e
s
am
e
b
o
o
k
.
I
n
th
is
r
esear
ch
,
s
im
p
le
C
F
i
s
th
e
b
as
e
m
o
d
el
th
at
will
b
e
im
p
r
o
v
e
d
with
p
r
o
p
o
s
ed
m
eth
o
d
s
ca
lled
HDBS
C
AN
an
d
R
SVD.
T
ab
le
8
s
h
o
ws
th
at
C
F
f
ails
to
p
er
f
o
r
m
well
wh
en
attem
p
tin
g
to
o
v
er
co
m
e
s
p
ar
s
ity
an
d
s
ca
lab
ilit
y
with
R
MSE
an
d
r
u
n
n
i
n
g
tim
e
o
f
0
.
8
5
1
2
8
a
n
d
3
9
4
0
.
5
2
,
r
e
s
p
ec
tiv
ely
.
T
h
e
c
o
m
p
ar
is
o
n
b
etwe
en
all
p
o
s
s
ib
le
m
o
d
els
co
m
p
ar
ed
to
s
im
p
le
C
F
as
th
e
b
ase
m
o
d
el
ca
n
b
e
s
o
r
ted
as
f
o
llo
ws:
HDBS
C
A
N
-
C
F
is
in
f
er
io
r
to
s
im
p
le
C
F
,
wi
th
R
MSE
an
d
r
u
n
n
in
g
tim
e
b
ei
n
g
2
7
.
4
2
% a
n
d
1
2
.
4
6
% wo
r
s
e
,
r
esp
ec
tiv
el
y
; H
DB
S
C
AN
-
R
SVD
-
C
F
h
as
a
2
1
.
8
3
%
lo
we
r
R
MSE
an
d
2
6
8
4
.
4
8
%
f
aster
co
m
p
u
tin
g
tim
e;
R
SVD
-
C
F
h
as
a
6
0
.
7
4
%
lo
wer
R
MSE
an
d
3
2
8
7
.
0
5
% f
aster
co
m
p
u
tin
g
tim
e.
T
ab
le
8
s
h
o
ws
th
at
C
F
f
ai
l
s
to
p
er
f
o
r
m
well.
Nev
er
th
eless
,
HD
B
S
C
AN
-
C
F
h
ad
a
n
in
f
er
io
r
p
er
f
o
r
m
an
ce
to
C
F
with
R
MSE
,
an
d
th
eir
r
u
n
n
in
g
tim
es
a
r
e
2
7
.
4
2
%
an
d
1
2
.
4
6
%
wo
r
s
e,
r
e
s
p
ec
tiv
ely
,
r
elativ
e
to
th
e
C
F
m
o
d
el.
Ho
wev
er
,
th
e
C
F
m
o
d
el
with
th
e
R
S
VD
m
eth
o
d
o
u
t
p
er
f
o
r
m
ed
th
e
C
F
m
o
d
el.
T
h
e
HDBS
C
AN
-
R
SVD
-
C
F
h
as
a
2
1
.
8
3
%
lo
wer
R
MSE
an
d
a
2
6
8
4
.
4
8
%
f
aster
co
m
p
u
tin
g
tim
e
co
m
p
ar
e
d
to
th
e
C
F
m
o
d
el.
Fin
ally
,
R
SVD
-
C
F
h
as
a
6
0
.
7
4
%
lo
wer
R
MSE
a
n
d
a
9
6
.
9
5
%
co
m
p
u
tin
g
tim
e
co
m
p
ar
ed
to
t
h
e
C
F
m
o
d
el
s
ee
Fig
u
r
es 7
a
n
d
8
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
14
,
No
.
6
,
Dec
em
b
er
2
0
2
5
:
4
8
6
5
-
4
8
7
7
4874
T
ab
le
8
.
HDBS
C
AN
-
R
SVD
-
C
F
m
o
d
el
ev
alu
atio
n
co
m
p
ar
a
tiv
e
M
o
d
e
l
H
D
B
S
C
A
N
-
R
S
V
D
(
9
0
%)
-
CF
R
S
V
D
(
8
0
%)
-
CF
H
D
B
S
C
A
N
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CF
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v
e
r
a
g
e
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M
S
E
0
.
6
6
5
4
0
.
3
3
4
2
1
.
0
8
4
7
0
.
8
5
1
2
8
Ti
me
(
S
e
c
o
n
d
s)
1
4
6
.
7
8
1
1
9
.
8
8
4
4
3
1
.
7
9
3
9
4
0
.
5
2
Fig
u
r
e
7
.
C
o
m
p
a
r
is
o
n
o
f
av
er
a
g
e
R
MSE
am
o
n
g
th
e
C
F m
o
d
els
Fig
u
r
e
8
.
C
o
m
p
a
r
is
o
n
o
f
co
m
p
u
tin
g
tim
e
am
o
n
g
th
e
CF
m
o
d
els
5.
CO
NCLU
SI
O
N
T
h
e
HDBS
C
AN
-
R
SVD
-
C
F
m
o
d
el
d
em
o
n
s
t
r
a
tes
e
x
c
ell
e
n
t
p
e
r
f
o
r
m
a
n
ce
in
ad
d
r
ess
i
n
g
s
p
a
r
s
it
y
a
n
d
s
ca
l
ab
ilit
y
is
s
u
es
.
T
h
is
is
ev
id
en
t
f
r
o
m
t
h
e
co
m
p
a
r
is
o
n
b
e
t
wee
n
t
h
e
HDBS
C
A
N
-
R
SV
D
-
C
F
a
n
d
C
F
m
o
d
els
,
wh
i
ch
s
h
o
ws
a
n
i
m
p
r
o
v
em
e
n
t
o
f
2
1
.
8
3
%
in
R
MS
E
e
v
a
lu
a
ti
o
n
a
n
d
a
r
e
d
u
ct
io
n
o
f
3
7
9
3
.
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3
s
e
co
n
d
s
in
co
m
p
u
ti
n
g
ti
m
e
c
o
m
p
a
r
e
d
to
t
h
e
s
i
m
p
le
C
F
m
o
d
el
.
F
u
r
t
h
e
r
m
o
r
e
,
t
h
e
a
p
p
li
ca
ti
o
n
o
f
t
h
e
H
DB
SC
AN
m
et
h
o
d
i
n
th
e
HDBS
C
AN
-
R
SVD
-
C
F
m
o
d
el
r
eso
lv
es
t
h
e
li
m
i
tati
o
n
o
f
th
e
R
SVD
-
C
F
m
o
d
el
b
y
r
e
tr
i
ev
i
n
g
th
e
n
u
m
b
e
r
o
f
n
-
c
o
m
p
o
n
e
n
ts
f
r
o
m
t
h
e
r
a
n
k
m
at
r
i
x
o
f
cl
u
s
t
er
e
d
u
s
e
r
-
b
o
o
k
s
.
T
h
e
R
SVD
-
C
F
m
o
d
el
is
r
o
b
u
s
t
a
n
d
f
i
ts
es
p
e
ci
all
y
well
f
o
r
CF
m
o
d
el
b
y
g
iv
in
g
t
h
e
ab
s
o
l
u
t
e
b
est
p
er
f
o
r
m
a
n
c
e
c
o
m
p
ar
ed
to
o
t
h
er
m
o
d
els
.
E
v
e
n
t
h
o
u
g
h
R
SVD
-
C
F
is
s
u
p
e
r
i
o
r
,
R
SVD
-
C
F
r
e
q
u
ir
e
s
m
o
r
e
a
tte
n
t
io
n
i
n
t
ak
in
g
th
e
n
u
m
b
e
r
o
f
n
-
c
o
m
p
o
n
e
n
ts
d
u
e
to
its
l
im
ita
ti
o
n
s
i
n
p
r
o
v
i
d
i
n
g
s
i
m
il
ar
u
s
e
r
r
e
co
m
m
e
n
d
ati
o
n
s
t
o
ac
ti
v
e
u
s
e
r
s
.
On
t
h
e
o
th
er
h
an
d
,
t
h
e
HDB
SC
AN
-
C
F
m
o
d
el
is
ill
-
s
u
i
te
d
t
o
d
ea
l
in
g
wit
h
s
p
a
r
s
i
ty
an
d
s
ca
la
b
il
it
y
p
r
o
b
l
em
s
,
w
h
e
r
e
its
p
er
f
o
r
m
a
n
ce
is
we
a
k
es
t.
T
h
e
H
DB
SC
AN
-
R
SVD
-
C
F
m
o
d
el
is
a
f
u
s
io
n
o
f
t
h
e
HDBS
C
A
N
a
n
d
R
SV
D
m
et
h
o
d
s
.
I
t
w
o
r
k
s
b
y
f
i
r
s
t
g
r
o
u
p
i
n
g
u
s
er
s
wi
th
t
h
e
s
am
e
cl
u
s
te
r
i
n
t
o
a
s
i
n
g
le
m
at
r
ix
,
f
o
ll
o
w
e
d
b
y
d
im
en
s
io
n
r
e
d
u
ct
io
n
u
s
i
n
g
R
SV
D
b
y
t
ak
in
g
th
e
m
o
s
t
d
o
m
i
n
a
n
t
p
a
r
t
o
f
th
e
m
at
r
i
x
.
E
v
en
t
h
o
u
g
h
HB
DSC
AN
-
R
SVD
-
C
F
h
as
a
n
in
f
e
r
i
o
r
R
MS
E
co
m
p
a
r
e
d
t
o
R
SVD
-
C
F,
th
is
m
o
d
el
ca
n
s
til
l
d
ea
l
w
it
h
s
p
a
r
s
i
ty
a
n
d
s
c
ala
b
i
lit
y
p
r
o
b
l
em
s
q
u
it
e
s
a
tis
f
a
ct
o
r
i
ly
,
wit
h
a
r
el
ati
v
el
y
wi
d
er
Evaluation Warning : The document was created with Spire.PDF for Python.