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jo
u
nal
ho
me
p
ag
e:
www.in l.else ie heal
h.com/jou nals/cmpb
In eg a ing
biological
knowledge
based
on
unc ional
anno a ions
o
biclus e ing
o
gene
exp ession
da a
Juan
A.
Nepomucenoa,∗,
Alicia
T oncosob,
Isabel
A.
Nepomuceno-Chamo oa,
Jesús
S.
Aguila -Ruizb
aDepa amen o
de
Lenguajes
y
Sis emas
In o má icos,
Uni e sidad
de
Se illa,
A d.
Reina
Me cedes
s/n,
41012
Se ille,
Spain
bDepa men
o
Compu e
Enginee ing,
Pablo
de
Ola ide
Uni e si y,
C a.
U e a
km.
1,
41013
Se ille,
Spain
a
i
c
l
e
i
n
o
A icle
his o y:
Recei ed
22
July
2014
Recei ed
in
e ised
o m
17
Feb ua y
2015
Accep ed
27
Feb ua y
2015
Keywo ds:
Biclus e ing
o
gene
exp ession
da a
In eg a ion
o
biological
knowledge
Sca e
sea ch
a
b
s
a
c
Gene
exp ession
da a
analysis
is
based
on
he
assump ion
ha
co-exp essed
genes
imply
co- egula ed
genes.
This
assump ion
is
being
e o mula ed
because
he
co-exp ession
o
a
g oup
o
genes
may
be
he
esul
o
an
independen
ac i a ion
wi h
espec
o
he
same
expe imen al
condi ion
and
no
due
o
he
same
egula o y
egime.
Fo
his
eason,
adi-
ional
echniques
a e
ecen ly
being
imp o ed
wi h
he
use
o
p io
biological
knowledge
om
open-access
eposi o ies
oge he
wi h
gene
exp ession
da a.
Biclus e ing
is
an
unsupe ised
machine
lea ning
echnique
ha
sea ches
pa e ns
in
gene
exp ession
da a
ma ices.
A
sca e
sea ch-based
biclus e ing
algo i hm
ha
in eg a es
biological
in o ma ion
is
p oposed
in
his
pape .
In
addi ion
o
he
gene
exp ession
da a
ma ix,
he
inpu
o
he
algo i hm
is
only
a
di ec
anno a ion
file
ha
ela es
each
gene
o
a
se
o
e ms
om
a
biological
eposi o y
whe e
genes
a e
anno a ed.
Two
di e en
biolog-
ical
measu es,
F acGO
and
SimNTO,
a e
p oposed
o
in eg a e
his
in o ma ion
by
means
o
i s
addi ion
o-be-op imized
fi ness
unc ion
in
he
sca e
sea ch
scheme.
The
measu e
F acGO
is
based
on
he
biological
en ichmen
and
SimNTO
is
based
on
he
o e lapping
among
GO
anno a ions
o
pai s
o
genes.
Expe imen al
esul s
e alua e
he
p oposed
algo-
i hm
o
wo
da ase s
and
show
he
algo i hm
pe o ms
be e
when
biological
knowledge
is
in eg a ed.
Mo eo e ,
he
analysis
and
compa ison
be ween
he
wo
di e en
biological
measu es
is
p esen ed
and
i
is
concluded
ha
he
di e ences
depend
on
bo h
he
da a
sou ce
and
how
he
anno a ion
file
has
been
buil
in
he
case
GO
is
used.
I
is
also
shown
ha
he
p oposed
algo i hm
ob ains
a
g ea e
numbe
o
en iched
biclus e s
han
o he
classical
biclus e ing
algo i hms
ypically
used
as
benchma k
and
an
analysis
o
he
o e -
lapping
among
biclus e s
e eals
ha
he
biclus e s
ob ained
p esen
a
low
o e lapping.
The
p oposed
me hodology
is
a
gene al-pu pose
algo i hm
which
allows
he
in eg a ion
o
biological
in o ma ion
om
se e al
sou ces
and
can
be
ex ended
o
o he
biclus e ing
algo i hms
based
on
he
op imiza ion
o
a
me i
unc ion.
©
2015
Else ie
I eland
L d.
All
igh s
ese ed.
∗Co esponding
au ho .
Tel.:
+34
954559769.
E-mail
add ess:
[email p o ec ed]
(J.A.
Nepomuceno).
h p://dx.doi.o g/10.1016/j.cmpb.2015.02.010
0169-2607/©
2015
Else ie
I eland
L d.
All
igh s
ese ed.
164
c
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o
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i
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163–180
1.
In oduc ion
Gene
exp ession
da a
ma ices
show
he
exp ession
p ofile
o
housands
o
genes
along
dozens
o
samples,
which
a e
s ud-
ied
in
di e en
mic oa ay
expe imen s.
Each
alue
in
hese
ma ices
is
a
nume ical
alue
ha
ep esen s
he
exp ession
alue
o
a
gene
in
a
specific
sample.
I
is
assumed
ha
g oups
o
genes
ha
sha e
a
simila
exp ession
p ofile
also
sha e
he
same
egula o y
egime
and
hence
he
same
unc ionali ies.
This
assump ion
is
called
he
guil -by-associa ion
heu is ic
[1].
I
is
la ely
being
e o mula ed
because
o
he
co-exp ession
o
a
g oup
o
genes
may
be
he
esul
o
an
independen
ac i a-
ion
wi h
espec
o
he
same
expe imen al
condi ion
and
no
due
o
he
same
egula o y
egime
is
cap u ed.
Biclus e ing
o
gene
exp ession
da a
is
an
unsupe ised
machine
lea n-
ing
echnique
ha
sea ches
g oups
o
genes
wi h
a
simila
exp ession
p ofile
unde
a
subse
o
condi ions.
Recen ly,
in e-
g a ion
me hods
based
on
he
combina ion
o
mul iple
sou ces
om
open-access
da a
ha e
been
p oposed
in
o he
fields
as
clus e ing
o
classifica ion.
These
app oaches
can
ou pe o m
he
adi ional
algo i hms
and
inc ease
he
possibili ies
o
co -
ec ing
he
spu ious
in o ma ion
exis ing
in
high- h oughpu
echnology
da a
as
gene
exp ession
da a
o
o he
“omic”
da a.
The
mos
impo an
di e ence
o
biclus e ing
wi h
espec
o
adi ional
clus e ing
is
ha
biclus e ing
aims
o
clus e
simul aneously
genes
as
well
as
condi ions,
a he
han
ocus-
ing
solely
on
ei he
one.
Clus e ing
echniques
spli
he
da a
ma ix
in o
g oups
o
co-exp essed
genes
along
all
samples
in
he
ma ix
such
ha
he
union
o
all
he
clus e s
cons i u es
he
comple e
ma ix
and
all
o
hem
a e
disjoin .
Howe e ,
biclus e ing
finds
co-exp essed
genes
only
unde
a
subse
o
samples.
The e o e,
he
o e lapping
among
esul s
is
consid-
e ed
and
he
mo i a ion
is
o
disco e
hidden
pa e ns
mo e
han
o
desc ibe
he
gene
exp ession
ma ix.
No e
ha
some
ecen ly
published
adi ional
clus e ing
algo i hms
allow
he
o e lapping
be ween
clus e s
[2,3].
The
goal
o
biclus e ing
is
o
sea ch
g oups
o
locally
co-exp essed
genes
mo e
han
o
desc ibe
he
gene
exp ession
ma ix.
The
mo i a ion
is
o
find
hidden
pa e ns
o
disco e
po en ial
bioma ke s
o
o mu-
la e
new
hypo hesis.
Al hough
biclus e ing
was
s udied
fi s ly
in
he
1960s
[4]
when
i
was
p o ed
o
be
a
NP-ha d
p oblem,
in
he
con ex
o
gene
exp ession
da a
i
was
fi s ly
in oduced
by
Cheng
and
Chu ch
[5].
In
he
con ex
o
biclus e ing,
public
da abases
and
eposi-
o ies
such
as
he
Gene
On ology
p ojec
(GO)
o
Kyo o
Encyclopedia
o
Genes
and
Genomes
(KEGG)
ha e
been
commonly
used
o
alida e
he
quali y
o
biclus e s
om
a
biological
poin
o
iew.
Conc e ely,
he
en ichmen
analysis
o
a
se
o
genes
in
he
con ex
o
GO
is
usually
used
as
a
s anda d
amewo k
o
compa ison
among
biclus e ing
algo i hms
[6].
The
esul s
a e
compa ed
acco ding
o
a
anking
based
on
he
cha ac e -
iza ion
o
each
g oup
o
genes
belonging
o
a
biclus e
wi h
espec
he
in o ma ion
s o ed
in
GO.
GO
is
an
on ology
wi h
a
hie a chical
s uc u e
wi h
h ee
oo s
o
domains:
molecu-
la
unc ion,
biological
p ocess
and
cellula
componen .
Each
gene
is
ela ed
o
a
se
o
GO
anno a ions
wi h
di e en
le -
els
o
specifici y.
These
anno a ions
a e
e ms
in
he
on ology
which
a e
linked
wi h
g oups
o
genes.
These
genes
a e
anno-
a ed
in
he
e m.
Low-le el
e ms
in
he
ee
s uc u e
epo
mo e
de ailed
in o ma ion
han
high-le el
e ms
which
a e
mo e
gene al.
Func ional
anno a ion
files
a e
buil
such
ha
each
gene
is
associa ed
wi h
he
se
o
e ms
whe e
i
is
anno-
a ed.
These
open-access
biological
da a
a e
commonly
used
in
biclus e ing
li e a u e
o
alida e
esul s
and
hei
use
is
a
common
ac o
in
mos
o
he
pape s.
Many
biclus e -
ing
algo i hms
ha e
been
p oposed
using
di e en
heu is ic
s a egies
o
sea ch
c i e ia
o
find
biclus e s
[7–9].
Se e al
algo i hms
such
as
Cheng
and
Chu ch’s
algo i hm
(CC)
[5],
I e a i e
Signa u e
Algo i hm
(ISA)
[10],
O de -p ese ing
Sub-
ma ix
Algo i hm
(OPSM)
[11]
o
xMo i s
[12]
a e
usually
used
as
benchma k
algo i hms
in
o de
o
es ablish
a
compa ison
among
biclus e ing
algo i hms.
CC
was
he
ounda ional
algo-
i hm
and
i
is
based
on
a
de e minis ic
g eedy
i e a i e
sea ch
me hod.
This
me hod
finds
biclus e s
wi h
a
esidue
less
o
equal
han
a
h eshold
ha
is
gi en
as
an
inpu
pa ame e .
Al hough
he
esidue
is
a
measu e
usually
used
in
biclus e -
ing
[5],
i
canno
cap u e
cohe en
e olu ion
pa e ns
[13].
The
ISA
algo i hm
uses
a
nonde e minis ic
g eedy
algo i hm
ha
finds
up-
and
down- egula ed
pa e ns.
The
inpu
ma ix
is
eo de ed
o
find
blocks
o
cohe en
alues
wi h
espec
o
ows
and
columns
ha
a e
epo ed
as
biclus e s.
The
OPSM
algo i hm
sea ches
o
biclus e s
acco ding
o
a
model
based
on
linea
o de ing
among
ows.
This
algo i hm
sequen ially
finds
each
biclus e
and
al hough
cohe en
e olu ion
pa e ns
a e
cap u ed,
i
canno
find
in e se
cohe en
e olu ion
pa -
e ns.
The
xMo i s
algo i hm
i e a i ely
sea ches
he
la ges
biclus e
acco ding
o
some
cons ain s
by
emo ing
samples.
Di ec
and
in e se
cohe en
e olu ion
pa e ns
a e
cap u ed
by
his
algo i hm
and
a
huge
numbe
o
biclus e s
a e
usu-
ally
epo ed.
Mo eo e ,
i
is
impo an
o
highligh
he
amily
o
biclus e ing
algo i hms
based
on
e olu iona y
compu a ion
and
me aheu is ics
ha
op imize
a
ce ain
quali y
measu e
[14–17].
Likewise,
algo i hms
o
his
amily
ha
use
measu es
based
on
co ela ions
among
genes
as
a
mechanism
o
find
co-
exp essed
genes
ha e
been
ecen ly
published
in
li e a u es
[18–26].
All
he
abo e-men ioned
algo i hms
sea ch
biclus e s
com-
posed
o
co-exp essed
genes
and
he
biological
knowledge
is
only
used
as
a
pos e io i
c i e ion
o
de e mine
he
ele ance
o
he
biclus e s
ound.
Howe e ,
he
au ho
in
[27]
conside ed
ha
he
s udies
based
on
gene
exp ession
da a
had
some
lim-
i a ions.
In
pa icula ,
he
co-exp ession
o
a
g oup
o
genes
may
be
he
esul
o
a
pa allel
and
independen
ac i a ion
wi h
espec
o
he
same
expe imen al
condi ion
and
no
due
o
cap u e
he
same
biological
unc ionali y.
The e o e,
he
assump ion
ha
co-exp ession
means
co- egula ion
should
be
ein e p e ed.
Fo
his
eason,
he
biological
knowledge
has
been
inco po a ed
du ing
he
sea ch
p ocess
o
a oid
g oups
o
co-exp essed
genes
ha
do
no
show
biologically
ep esen-
a i e
connec ions.
Fo
example
in
he
field
o
clus e ing,
he
algo i hm
p esen ed
in
[28]
uses
he
K-means
algo i hm
and
in eg a es
gene
anno a ion
files
ex ac ed
om
GO
wi h
a
con-
cep
o
dis ance
based
on
he
co-exp ession
and
unc ional
simila i y.
A
GO-based
measu e
has
been
also
applied
as
pa
o
he
wo kflow
o
a
p edic i e
algo i hm
o
classi y
genes
in
[29].
Namely,
he
a e age
o
he
Pea son
co ela ion,
which
e alua es
simila i ies
among
gene
exp ession
p ofiles,
and
a
GO-based
measu e
a e
used
o
define
a
dis ance.
This
dis ance
c
o
m
p
u
e
m
e
h
o
d
s
a
n
d
p
o
g
a
m
s
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m
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163–180
165
is
used
o
clus e
genes
and
o
elabo a e
a
anking
o
candida e
genes.
A
gene
ea u e
selec ion
me hod
is
p esen ed
in
[30]
which
in eg a es
in o ma ion
om
KEGG
ins ead
o
om
GO.
This
algo i hm
is
a
KEGG-imp o ed
e olu iona y
s a egy
ha
shows
a
be e
pe o mance
o
selec ing
genes
han
classical
algo i hms.
Func ional
simila i y
measu es
based
on
GO
in ol e
a
concep
o
dis ance
be ween
wo
genes.
The e
a e
se e al
seman ic
simila i y
measu es
o
compa e
GO
e ms
o
which
genes
a e
anno a ed
[31].
They
can
be
basically
classified
in
wo
g oups:
edge-based
measu es
and
in o ma ion
con en
(IC)-based
measu es.
The
fi s
g oup
o
measu es
assumes
ha
he
specifici y
o
a
e m
can
be
di ec ly
in e ed
om
i s
dep h
in
he
GO
g aph
and
he
second
g oup
is
based
on
he
equency
o
a
e m
in
he
GO
g aph.
Howe e ,
a
gene
is
usually
anno a ed
in
se e al
e ms
and
no
in
only
one,
and
hence,
i
is
be e
o
use
simila i y
measu es
ha
compa e
se s
o
e ms
a he
han
single
e ms.
A
compa ison
among
his
kind
o
measu es
is
p esen ed
in
[31]
whe e
he
simGIC
measu e
shows
he
bes
pe o mance.
This
measu e
compu es
he
simila i y
be ween
wo
genes
using
he
IC
associa ed
o
each
e m
in
he
genes.
No e
ha
he
GO
g aph
s uc u e
is
needed
o
compu e
he
IC
in
addi ion
o
he
gene
anno a ion
file.
Also
he e
a e
o he
measu es
based
on
a
p ep ocessed
bina y
ma ix
ins ead
o
he
ee
s uc u e
o
GO.
This
ma ix
is
composed
o
genes
as
ows
and
GO
e ms
as
columns
and
he
elemen s
a e
1
o
0
depending
on
i
he
gene
is
o
is
no
anno a ed
in
he
GO
e m,
espec i ely.
These
measu es
a e
based
on
he
Vec o
Space
Model
(VSM)
o iginally
de eloped
in
he
con ex
o
in o ma ion
e ie al.
The
measu e
p esen ed
in
[32]
can
be
also
classified
as
a
seman ic
simila i y
measu e
bu
nei he
a
p ep ocessed
ma ix
no
he
GO
g aph
s uc u e
a e
necessa y.
This
measu e
is
based
on
he
o e lapping
among
gene
anno a ions
om
fla
GO
anno a ion
files
whe e
he
ee
s uc u e
o
GO
is
cap u ed.
In
pa icula ,
he
anno a ions
o
each
gene
a e
p opaga ed
o
uppe
le els
in
he
on ology
and
all
he
associa ed
pa en
e ms
a e
conside ed.
I
can
be
s ayed
ha
he
in eg a ion
o
biological
in o ma-
ion
om
di e en
sou ces
is
ac ually
one
o
he
challenges
and
esea ch
di ec ions
in
Bioin o ma ics
[33].
The e
a e
many
wo ks
ha
use
o he
da a
sou ces,
no
only
in o ma ion
om
GO
o
KEGG.
Fo
example,
se e al
da a
sou ces
can
be
me ged
o
in eg a e
biological
knowledge
as
p o ein–p o ein
in e ac-
ion
ne wo ks,
genome-wide
binding
da a
and
in o ma ion
om
he
li e a u e
and
no
only
in o ma ion
om
GO
[34].
The
COALESCE
algo i hm
[35]
uses
he
gene
exp ession
da a
oge he
wi h
DNA
sequence
da a
as
inpu
da a
and
o he
suppo ing
da a
as
addi ional
in o ma ion
du ing
he
p o-
cess
in
o de
o
disco e
egula o y
modules.
This
algo i hm
finds
biclus e s
ha
a e
used
as
a
guide
o
disco e
hese
modules.
The
p oposed
algo i hm
in
[36]
uses
p o ein–p o ein
in e ac ion
ne wo ks
and
gene
exp ession
da a
o
disco e
cance
bioma ke s,
which
a e
ound
h ough
he
disco e ing
o
g oups
o
genes
in
biclus e s
ha
a e
also
highly
connec ed
in
he
ne wo k.
Recen ly,
a
biclus e ing
algo i hm
[37],
which
wo ks
wi h
mic oRNA
and
a ge
genes
da a,
uses
GO
in o -
ma ion
o
do
a
anking
o
he
esul s.
F om
he
bes
o
ou
knowledge,
he
biological
in o ma-
ion
in eg a ion
in
biclus e ing
o
gene
exp ession
da a
has
no
been
s ill
in es iga ed.
The
aim
o
his
pape
is
o
in oduce
his
idea
in
he
biclus e ing
field
by
means
o
unc ional
anno-
a ion
files.
These
files
a e
fla
files
whe e
each
gene
is
linked
wi h
i s
co esponding
e ms
in
he
biological
eposi o y.
The
p oposed
algo i hm
is
a
sca e
sea ch-based
me aheu is ic
ha
op imizes
a
fi ness
unc ion
which
defines
a
c i e ion
o
e alua e
he
quali y
o
he
biclus e s.
This
algo i hm
is
based
on
he
algo i hm
p esen ed
in
[25]
and
al hough
se -
e al
p ocedu es
di e ,
he
mos
ele an
con ibu ion
is
he
fi ness
unc ion
defini ion
o
in eg a e
he
biological
in o -
ma ion.
This
unc ion
consis s
o
h ee
pa s:
he
fi s
one
is
a
e m
o
con ol
he
size
o
he
biclus e s;
he
second
one
is
he
co ela ion
among
genes
o
cap u e
co-exp essed
genes;
finally,
he
hi d
e m
is
an
addi ional
e m
o
in eg a e
he
biological
in o ma ion.
The
goal
is
o
es ablish
an
equi-
lib ium
in
he
fi ness
unc ion
o
find
biclus e s
composed
o
co-exp essed
genes
ha
cap u e
simila
biological
unc-
ionali ies.
Addi ionally,
wo
di e en
biological
in eg a ion
possibili ies
a e
expe imen ally
s udied:
fi s ly,
he
biological
in o ma ion
is
included
wi h
a
measu e
p oposed
he e
based
on
an
en ichmen
s udy
o
a
se
o
genes,
and
secondly,
wi h
a
GO-based
measu e
ha
compu es
he
o e lapping
among
he
anno a ed
e ms
o
a
g oup
o
genes.
Bo h
measu es
only
use
as
inpu
da a
o
in eg a e
he
unc ional
in o ma ion
an
anno-
a ion
file
ha
ela es
genes
and
biological
e ms.
The e o e,
he
inpu
da a
o
he
algo i hm
a e
only
he
gene
exp es-
sion
ma ix
and
a
unc ional
anno a ion
file.
The
p oposed
me hodology
is
a
gene al-pu pose
algo i hm
which
allows
he
in eg a ion
o
biological
in o ma ion
om
se e al
sou ces
such
as
GO,
pa hways
KEGG
o
any
biological
in o ma ion
p o-
ided
by
fla
anno a ion
files
and
can
be
ex ended
o
o he
biclus e ing
algo i hms
based
on
he
op imiza ion
o
a
me i
unc ion.
The
emainde
o
his
pape
is
o ganized
as
ollows.
Sec-
ion
2
p esen s
he
algo i hm
whe e
fi s ly
he
fi ness
unc ion
is
defined
and
secondly
he
sea ch
p ocedu e
is
desc ibed.
In
he
fi ness
unc ion
sec ion,
wo
di e en
biological
in e-
g a ion
measu es
a e
also
defined.
Expe imen s
a e
desc ibed
and
discussed
in
Sec ion
3.
Namely,
he
expe imen al
esul s
a e
analyzed
om
h ee
poin s
o
iew:
he
in eg a ion
o
biological
in o ma ion
imp o es
he
algo i hm
pe o mance;
he
pe o mance
o
ou
app oach
is
be e
han
ha
ob ained
by
se e al
benchma k
algo i hms;
and
he
esul s
om
he
wo
di e en
biological
in eg a ion
measu es
a e
dis-
cussed.
Finally,
Sec ion
4
is
de o ed
o
conclusions
and
u u e
wo k.
2.
Me hodology
The
p oposed
me hodology
is
di ided
in o
wo
phases
clea ly
di e en ia ed.
In
a
fi s
s ep,
a
fi ness
unc ion
in eg a ing
bio-
logical
knowledge
om
unc ional
anno a ion
files
is
designed
o
measu e
he
quali y
o
biclus e s
in
Sec ion
2.2.
A
sea ch
p ocess
based
on
a
sca e
sea ch
algo i hm
is
applied
by
minimizing
he
measu e
p o ided
by
his
fi ness
unc ion
in
Sec ion
2.3.
In
a
sense,
he
me hodology
sepa a es
he
sea ch-
ing
and
he
cha ac e iza ion
o
he
biclus e s
o
be
ound.
Tha
is,
he
sea ch
p ocess
is
independen
o
he
es ablished
c i e-
ion,
which
is
defined
by
he
fi ness
unc ion,
o
find
biclus e s.
166
c
o
m
p
u
e
m
e
h
o
d
s
a
n
d
p
o
g
a
m
s
i
n
b
i
o
m
e
d
i
c
i
n
e
1
1
9
(
2
0
1
5
)
163–180
2.1.
Inpu
da a
The
inpu
da a
o
he
algo i hm
a e
basically
he
gene
exp es-
sion
ma ix
and
a
di ec
anno a ion
file.
The
gene
exp ession
ma ix
is
composed
o
gene
exp ession
p ofiles
and
samples
ha
a e
ep esen ed
in
ows
and
columns,
espec i ely.
Each
elemen
in
he
ma ix
ep esen s
he
le el
o
exp ession
o
a
gene
unde
a
pa icula
sample
o
expe imen al
condi ion.
Di ec
anno a ion
files
a e
fla
files
whe e
each
line
is
cons i-
u ed
by
a
gene
wi h
a
se
o
e ms
om
a
biological
eposi o y.
These
e ms
a e
labels
o
a
de e mined
biological
unc ion-
ali y
whe e
he
gene
is
in ol ed.
Fo
example,
his
sen ence
TVP15
GO:0006810,GO:0016192
is
a
line
in
a
di ec
anno a ion
file
ex ac ed
om
GO,
whe e
TVP15
is
he
gene
name
and
GO:0006810
and
GO:0016192
a e
wo
GO
e ms
whe e
his
gene
is
anno a ed.
No e
ha
di ec
anno a ion
files
may
be
down-
loaded
om
eposi o ies
in
se e al
ways.
Ne e heless,
he
p oposed
me hodology
is
a
gene al-pu pose
algo i hm
which
allows
he
in eg a ion
o
biological
in o ma ion
om
se e al
sou ces
o
in o ma ion.
Addi ionally,
he
numbe
o
biclus e s
o
ob ain
is
also
p o ided
as
an
inpu
pa ame e .
2.2.
Fi ness
unc ion
The
main
goal
is
o
define
a
fi ness
unc ion
ha
in eg a es
biological
knowledge
o
find
biologically
ele an
biclus e s,
in
addi ion
o
o he
measu es
such
as
he
co ela ion
o
find
biclus e s
wi h
enclosed
in e es ing
pa e ns
and
he
olume
o
find
non- i ial
biclus e s.
The
gene
exp ession
ma ix
can
be
seen
as
a
nume ical
ma ix
D
whe e
an
elemen
(i,
j)
is
he
exp ession
le el
o
gene
i
unde
he
sample
o
condi ion
j.
A
biclus e
B
is
a
subma ix
o
D
wi h
N
genes
and
M
condi ions,
ha
is,
B
=
{(gi,
cj)}i,j whe e
i
∈
{1,
.
.
.,
N}
and
j
∈
{1,
.
.
.,
M}.
The
p oposed
fi ness
unc ion
o
e alua e
B
is
defined
as
ollows:
(B)
=
M1·
1(B)
+
M2·
2(B)
+
M3·
3(B)
(1)
whe e
1measu es
he
olume
o
he
biclus e ,
2 he
pa e ns
ound
in
he
biclus e
and
3 he
quali y
o
he
biclus e
om
a
biological
iew
poin ,
and
M1,
M2and
M3a e
pa ame e s
o
weigh
he
ele ance
o
he
measu es
1,
2and
3,
espec i ely.
The
measu e
1is
used
o
con ol
he
olume
o
biclus e .
I
is
defined
as
1(B)
=1
N
·
Q(2)
whe e
N
is
he
numbe
o
genes
and
Q
he
numbe
o
condi-
ions
in
he
biclus e
B.
This
e m
is
impo an
o
deal
wi h
he
size
o
biclus e s
du ing
he
sea ch
p ocess
and
o
a oid
i ele an
in o ma ion
[38].
I
is
used
o
a oid
finding
i ial
biclus e s
wi h
only
a
e y
low
numbe
o
genes
o
condi ions,
as
o
example
a
biclus e
wi h
only
wo
condi ions.
The
measu e
2is
based
on
he
a e age
co ela ion
among
he
genes
o
he
biclus e .
No e
ha
only
he
condi ions
in
he
biclus e
a e
conside ed
and
no
all
condi ions
in
he
gene
exp ession
ma ix.
This
e m
is
conside ed
in
o de
o
cap u e
mos
o
he
ele an
pa e ns
in
biclus e s
such
as
shi ing
and
scaling
pa e ns
[13]
o
ac i a ion-inhibi ion
pa e ns
[22].
The
co ela ion
has
been
p e iously
used
as
me i
unc ion
o
de e mine
co-exp essed
genes
and
i
e alua es
he
g ade
o
dependence
among
genes
[25].
I
is
defined
as
ollows:
co (B)
=1
N
2
N−1

i=1
N

j=i+1
|ij|
(3)
whe e
ij is
he
Pea son
co ela ion
coe ficien
be ween
he
genes
giand
gj.
No e
ha
only N
2elemen s
ha e
been
con-
empla ed
due
o
he
symme y
o
he
co ela ion
coe ficien .
The
absolu e
alue
is
conside ed
o
a oid
ha
g oups
o
genes
wi h
high
posi i e
co ela ion
alues
could
elimina e
he
e ec
o
g oups
o
genes
wi h
high
nega i e
co ela ion
alues.
I
is
no ewo hy
o
men ion,
he
a e age
co ela ion
e alua es
a
biclus e
conside ing
bo h
genes
and
condi ions,
ha
is,
wo
biclus e s
wi h
he
same
se
o
genes
bu
a
di e en
se
o
condi ions
p o ide
di e en
alues
o
he
co ela ion.
As
he
sca e
sea ch
is
applied
o
minimize
he
fi ness
unc ion
,
he
unc ion
2can
be
defined
as
2(B)
=
1
−
co (B)
(4)
The
measu e
3is
based
on
a
di ec
anno a ion
file
om
a
biological
knowledge
eposi o y,
and
hence,
i
de e mines
how
he
biological
in o ma ion
is
in eg a ed
in
he
p ocess.
No e
ha
he
e m
3(B)
e alua es
he
se
o
genes
o
he
biclus e
B
bu
no
he
condi ions,
ha
is,
3has
he
same
alue
o
wo
biclus e s
wi h
he
same
se
o
genes
and
di e en
se s
o
condi ions.
The e o e,
3e alua es
he
biological
ele ance
o
a
biclus e
bu
i
canno
find
in e es ing
pa e ns
in
a
biclus-
e
and
i
canno
di e en ia e
biclus e s
wi h
he
same
se
o
genes.
Two
di e en
unc ions,
which
use
only
as
biological
da a
sou ce
a
di ec
anno a ion
file
wi h
he
in o ma ion
o
he
genes
in
he
gene
exp ession
ma ix,
a e
p oposed
o
he
measu e
3in
he
ollowing
Sec ions
2.2.1
and
2.2.2.
2.2.1.
F ac ional
Gene
On ology
measu e
A
measu e
based
on
he
analysis
o
he
en ichmen
o
a
biclus-
e
[39]
is
p oposed
in
his
pape
o
measu e
he
biological
ele ance
o
a
biclus e .
The
measu e
is
he
p opo ion
o
ac-
ion
o
genes
in
a
biclus e
associa ed
o
en iched
GO
e ms,
he eina e
F acGO.
The
e ms
wi h
an
adjus ed
p- alue
unde
a
gi en
h eshold
a e
said
o
be
en iched
o
o e ep esen ed.
This
h eshold
is
known
as
significance
le el
and
is
usually
se
o
0.05.
The
adjus ed
p- alue
o
each
anno a ed
e m
in
he
anno a ion
file
is
compu ed
wi h
espec
o
he
g oup
o
genes
ha
belong
o
he
biclus e .
The
uni e se
o
genes
is
he
comple e
se
o
genes
in
he
gene
exp ession
ma ix.
Fishe ’s
exac
es
has
been
used
o
de e mine
s a is ically
o e ep e-
sen ed
e ms
and
Bon e oni
es
has
been
used
o
co ec
he
adjus ed
p- alues
o
mul iple
compa isons
as
he
numbe
o
c
o
m
p
u
e
m
e
h
o
d
s
a
n
d
p
o
g
a
m
s
i
n
b
i
o
m
e
d
i
c
i
n
e
1
1
9
(
2
0
1
5
)
163–180
167
hypo heses
es ed
is
he
numbe
o
e ms
in
he
anno a ion
file.
Thus,
F acGO
is
defined
as
ollows:
F acGO(B)
=⎧
⎪
⎨
⎪
⎩
0
i J
=
0
1
J
·
N
J

i=1
xii J
≥
1(5)
whe e
J
is
he
numbe
o
en iched
GO
e ms,
namely
he
num-
be
o
GO
e ms
wi h
an
adjus ed
p- alue
less
han
0.05,
N
is
he
numbe
o
genes
in
he
biclus e
and
xiis
he
numbe
o
genes
o
he
biclus e
ha
p esen s
he
GO
e m
i
in
he
anno-
a ion
file.
No e
ha
F acGO
is
equal
o
1
i
all
he
genes
o
he
biclus e
a e
associa ed
wi h
all
en iched
GO
e ms
(xi=
N,
∀i
=
{1,
.
.
.,
J})
and
0
when
he e
is
no
an
en iched
GO
e m.
I
can
be
concluded
ha
F acGO
has
a
alue
o
1
o
biologically
ele an
biclus e s
and
0
o he wise.
In
his
case,
he
p oposed
unc ion
3can
be
di ec ly
defined
as
3(B)
=
1
−
F acGO(B)
(6)
I
can
be
no ed
ha
he
biclus e
B
is
conside ed
a
high-
quali y
biclus e
i
3is
equal
o
0
and
a
bad
biclus e
i
i s
alue
is
se
o
1.
2.2.2.
No malize
e m
o e lap
measu e
Se e al
gene
pai wise
GO-based
measu es
ha e
been
p oposed
in
he
li e a u e.
These
measu es
compu e
he
simila i y
be ween
wo
genes
based
on
hei
GO
anno a ions.
The
sim-
NTO
measu e,
which
is
based
on
he
e m
o e lap
defined
in
[32],
only
uses
anno a ion
files
as
inpu .
This
measu e
is
as e
and
simple
han
o he
measu es
based
on
in o ma ion
con-
en
(IC).
These
IC-based
measu es
use
he
GO
ee
s uc u e
as
addi ional
in o ma ion
along
wi h
he
anno a ion
file.
Sim-
NTO
cap u es
he
GO
hie a chical
s uc u e
i
he
anno a ion
files
a e
buil
by
con aining
all
pa en
e ms
o
each
e m.
A
measu e
based
on
he
unc ional
simila i y
o
a
biclus e
using
simNTO
measu e
is
p oposed
as
a
measu e
o
e alua e
he
biological
ele ance
o
a
biclus e
in
his
wo k.
This
mea-
su e
is
defined
by
means
o
he
a e age
o e lapping
be ween
he
pai s
o
genes
o
a
biclus e
acco ding
o
he
in o ma ion
om
he
GO
anno a ion
file.
Tha
is,
SimNTO(B)
=1
N
2
N−1

i=1
N

j=i+1
simNTO(gi,
gj)
(7)
whe e
N
is
he
numbe
o
genes
in
he
biclus e
B
and
sim-
NTO
is
he
no malized
e m
o e lap
measu e
p oposed
in
[32].
In
pa icula ,
simNTO
measu es
he
o e lapping
be ween
wo
genes
g1and
g2wi h
espec
o
GO
e ms
and
is
defined
as
simNTO(g1,
g2)
=|anno g1∩
anno g2|
min(|anno g1|,
|anno g2|)(8)
whe e
anno giis
he
se
o
GO
e ms
associa ed
o
he
gene
gi
and
|
·
|
is
he
numbe
o
elemen s
o
a
se .
I
is
impo an
o
men ion
ha
he
di ec
anno a ion
file
mus
be
buil
by
p op-
aga ing
he
e ms
owa d
he
uppe
le els
in
he
on ology
o
compu e
his
measu e.
The e o e,
anno giis
defined
by
consid-
e ing
he
se
o
all
di ec
anno a ions
o
he
gene
giand
he
associa ed
pa en
e ms
in
he
on ology,
excluding
he
oo
o
he
hie a chy.
Acco dingly,
he
anno a ion
file
mus
cap u e
he
GO
ee
s uc u e.
No e
ha
he
simNTO
measu e
anges
om
0
o
1.
Two
genes
sha e
he
same
anno a ions
and
a e
e y
simila
in
he
on ology
i
simNTO
has
a
alue
o
1,
and
0
o he wise.
Mo eo e ,
i
one
gene
g
is
no
con empla ed
in
he
anno a ion
file
because
he e
is
no
any
in o ma ion
in
GO,
anno gis
he
emp y
se ,
and
in
his
case,
he
simNTO
measu e
is
di ec ly
se
o
0.
In
his
case,
he
p oposed
unc ion
3is
defined
as
ollows:
3(B)
=
1
−
SimNTO(B)
(9)
I
can
be
app ecia ed
ha
3(B)
=
0
when
B
is
composed
o
a
g oup
o
genes
ha
sha e
simila
biological
unc ionali ies
in
GO,
and
he e o e,
B
is
a
ele an
biclus e
acco ding
o
GO.
2.3.
Desc ip ion
o
he
algo i hm
An
algo i hm
based
on
a
me aheu is ic
scheme
has
been
con-
side ed
due
o
he
compu a ional
na u e
o
biclus e ing.
The
sea ch
scheme
de i es
om
he
algo i hm
p esen ed
in
[25]
whe e
a
sca e
sea ch
was
also
applied
in
biclus e ing
o
gene
exp ession
da a.
The
p oposed
algo i hm
is
a
sequen ial
co e -
ing
algo i hm,
namely,
each
biclus e
is
ob ained
by
applying
an
independen
sca e
sea ch
p ocedu e.
This
i e a i e
p o-
cess,
join ly
wi h
he
bias
in oduced
in
he
sea ch
h ough
he
fi ness
unc ion
defini ion,
con ols
he
non-de e minis ic
na u e
o
he
p ocess.
The
sca e
sea ch
is
a
popula ion-based
e olu iona y
me aheu is ic
whe e
a
popula ion
o
solu ions
e ol es
un il
an
op imal
solu ion
is
eached.
The
basic
idea
in
he
sca e
sea ch
is
o
pe o m
he
op imiza ion
wi h
a
small
se
o
solu ions,
called
he
e e ence
se ,
ins ead
o
a
comple e
popula ion
o
solu ions
as
in
o he
popula ion-based
me aheu is ics
[40].
The
e e ence
se
is
composed
o
he
bes
solu ions
acco ding
o
in ensifica ion
and
di e si y
s a egies.
Fig.
1
shows
he
basic
idea
behind
he
p oposed
algo i hm.
All
he
s eps
composing
his
algo i hm
a e
going
o
be
b iefly
desc ibed
in
Sec ions
2.3.1
and
2.3.2.
2.3.1.
Sca e
sea ch
A
solu ion
ep esen s
a
biclus e ,
which
is
codified
by
wo
bina y
s ings
whe e
he
bi s
indica e
i
he
gene
o
condi ion
is
p esen
o
no
in
he
biclus e .
Fi s ly,
an
ini ial
popula-
ion
is
gene a ed
by
he
di e sifica ion
gene a ion
me hod
and
is
composed
o
solu ions
as
sca e
as
possible,
which
a e
hen
imp o ed
by
a
local
sea ch
p ocedu e
ha
will
be
desc ibed
in
Sec ion
2.3.2.
Con a y
o
he
gene ic
algo i hms
he
ini-
ial
popula ion
is
buil
ollowing
a
mechanism
o
achie e
di e sifica ion
and
no
a
gene al
andomiza ion
p ocess.
The
di e sifica ion
gene a ion
me hod
gene a es
a
collec ion
o
solu-
ions
om
a
seed
solu ion.
I
x
is
a
bina y
s ing
used
as
seed,
a
new
s ing
xis
gene a ed
o
each
alue
o
an
in ege
h
=
1,
2,
3,
.
.
.,
hmax as
ollows:
x
1+kh =
1
−
x1+kh o
k
=
0,
1,
2,
3,
.
.
.,
n/h(10)

168
c
o
m
p
u
e
m
e
h
o
d
s
a
n
d
p
o
g
a
m
s
i
n
b
i
o
m
e
d
i
c
i
n
e
1
1
9
(
2
0
1
5
)
163–180
Fig.
1
–
The
p oposed
sca e
sea ch
o
biclus e ing.
whe e
x
=
(x1,
.
.
.,
xn),
n
is
he
numbe
o
bi s,
k
akes
al-
ues
om
0
o
he
la ges
in ege
sa is ying
k
≤
n/h.
Due
o
he
bina y
s ing
size
and
o
he
sca e
sea ch
li e a u e
ecom-
menda ions
[40],
he
maximum
alue
o
h
is
hmax =
n/5.
All
he
emaining
bi s
o
xa e
equal
o
hose
o
x.
A e
gene a ing
all
he
possible
solu ions
wi h
ha
seed,
i
mo e
solu ions
we e
needed
in
he
ini ial
popula ion,
he
ule
will
be
applied
again
using
he
las
solu ion
as
a
new
seed.
This
me hod
is
he
s an-
da d
p ocedu e
usually
used
in
sca e
sea ch
algo i hms
wi h
bina y
codifica ion
[40].
The
idea
o
sca e
be ween
wo
solu-
ions
is
in oduced
by
he
Hamming
dis ance.
The
Hamming
dis ance
be ween
wo
bina y
s ings
is
defined
as
he
num-
be
o
posi ions
a
which
he
co esponding
0’s
and
1’s
a e
di e en .
Once
he
ini ial
popula ion
is
gene a ed,
he
e e ence
se
is
buil
by
he
build
e e ence
se
me hod.
This
me hod
consis s
in
selec ing
he
fi e
bes
solu ions
and
he
fi e
mos
sca e ed
solu ions
wi h
espec
o
he
emaining
o
exis ing
solu ions
in
he
se
om
he
ini ial
popula ion.
The e o e,
he
e e ence
se
con ains
he
mos
ep esen a i e
solu ions
om
he
ini-
ial
popula ion
acco ding
o
quali y
and
di e si y
c i e ia.
The
sca e
solu ions
p o ide
di e si y
in
he
sea ch
p ocess
o
a oid
local
op ima.
This
di e si y
s a egy
plays
a
simila
ole
o
he
mu a ion
ope a o s
in
gene ic
algo i hms,
o
example.
On
he
o he
hand,
he
quali y
solu ions
a e
conside ed
as
mechanism
o
define
an
in ensifica ion
s a egy
in
he
sea ch.
I
is
impo an
o
upda e
he
ini ial
popula ion
by
emo ing
he
solu ions
selec ed
by
his
me hod.
The
e e ence
se
e ol es
by
using
he
subse
gene a ion
me hod,
he
solu ion
combina ion
me hod
and
he
e e ence
se
upda e
me hod
un il
he
e e ence
se
is
s able.
Once
he
e -
e ence
se
does
no
change,
he
e e ence
se
is
ebuil
wi h
he
fi e
bes
solu ions
om
he
p e ious
e e ence
se
and
he
fi e
mos
sca e ed
solu ions
wi h
espec
o
he
emaining
solu ions
in
he
se
om
he
ini ial
popula ion.
The
subse
gen-
e a ion
me hod
gene a es
subse s
o
pai s
o
solu ions
om
he
e e ence
se
o
be
combined
by
he
solu ion
combina ion
me hod
wi h
he
pu pose
o
c ea ing
new
solu ions.
Once
he
new
solu-
ions
a e
ob ained,
he
local
sea ch
p ocedu e
is
again
applied
o
imp o e
hem.
The
solu ion
combina ion
me hod
is
based
on
he
uni o m
c osso e
ope a o
commonly
used
in
e olu ion-
a y
compu a ion.
The
e e ence
se
upda e
me hod
consis s
in
choosing
he
10
bes
solu ions,
acco ding
o
he
fi ness
unc-
ion,
om
he
joining
o
he
solu ions
o
he
e e ence
se
and
he
new
solu ions
ob ained
by
he
solu ion
combina ion
me hod.
The
ou pu
is
he
bes
biclus e
in
he
las
e e ence
se .
The
whole
p ocess
is
epea ed
as
many
imes
as
numbe
o
biclus e s
o
be
ob ained,
which
is
an
inpu
pa ame e
o
he
algo i hm.
No
mechanism
o
edundancy
con ol
among
esul s
has
been
conside ed
and
i
could
be
hough
ha
he
same
biclus e
is
always
ound.
Se e al
wo ks
based
on
me a-
heu is ics
include
mechanisms
o
edundancy
con ol
bu
hese
algo i hms
usually
use
only
an
ini ial
popula ion
in
he
comple e
p ocess.
Conc e ely,
he
algo i hm
published
in
[41]
p esen s
an
addi ional
e m
in
he
fi ness
unc ion
o
con ol
he
edundancy
in
o de
o
a oid
simila i ies
among
biclus e s
and
o
find
epea edly
he
same
biclus e .
Howe e ,
i
a
di e -
en
ini ial
popula ion
is
buil
o
each
biclus e
ob ained
by
he
p oposed
algo i hm,
his
addi ional
e m
can
be
emo ed
and
i
is
enough
fil e ing
hose
highly
edundan
biclus e s.
Mo eo e ,
i
is
in e es ing
o
ob ain
biclus e s
sha ing
g oups
o
genes
om
a
biological
poin
o
iew
[2,3].
Consequen ly,
he
p oposed
algo i hm
does
no
con empla e
an
addi ional
e m
in
he
fi ness
unc ion
and
builds
an
ini ial
popula ion
c
o
m
p
u
e
m
e
h
o
d
s
a
n
d
p
o
g
a
m
s
i
n
b
i
o
m
e
d
i
c
i
n
e
1
1
9
(
2
0
1
5
)
163–180
169
o
each
ound
biclus e .
An
o e lapping
h eshold
o
30%
is
chosen
and
he
biclus e s
wi h
an
o e lapping
g ea e
han
his
h eshold
a e
emo ed.
The
pa ame e s
o
he
algo i hm
ha e
been
chosen
acco d-
ing
o
ecommenda ions
o
he
li e a u e
o
sca e
sea ch
[40]
and
p e ious
wo ks
[25].
In
pa icula ,
200
o
he
size
o
he
ini ial
popula ion,
10
o
he
size
o
he
e e ence
se
and
20
o
he
numbe
o
i e a ions
o
he
e olu iona y
p ocess
( he
inne
loop
in
Fig.
1).
2.3.2.
Imp o emen
me hod
The
imp o emen
me hod
is
a
local
sea ch
p ocedu e
designed
o
imp o e
he
quali y
o
solu ions
acco ding
o
he
fi ness
unc ion.
Namely,
gi en
a
biclus e
his
me hod
gene -
a es
a
new
biclus e
wi h
a
be e
alue
o
i s
fi ness
unc ion.
In
gene al,
he
imp o emen
me hod
in
a
sca e
sea ch
is
specifically
designed
o
each
p oblem
as
i
depends
on
he
na u e
o
he
fi ness
unc ion
[25].
Al hough
an
imp o emen
me hod
guided
by
a
heu is ic
is
be e
han
a
blind
imp o e-
men
me hod,
he
heu is ic
o
imp o e
he
quali y
o
biclus e s
is
ela ed
o
he
fi ness
unc ion
o
he
p oblem.
In
his
wo k,
se e al
di e en
fi ness
unc ions
a e
analyzed,
namely
one
o
each
measu e
p oposed
o
in eg a e
biological
knowledge,
and
he e o e,
he
same
heu is ic
is
no
good
o
all
he
fi -
ness
unc ions.
Fo
his
eason,
a
blind
imp o emen
me hod
is
p oposed
wi h
he
pu pose
o
being
used
wi h
all
hem.
This
independence
o
he
imp o emen
me hod
ega ding
he
fi -
ness
unc ion
mo i a es
a
blind
sea ch
among
solu ions
close
o
he
o iginal
solu ion.
Some imes
his
sea ch
does
no
find
a
be e
solu ion,
and
he e o e,
in
hese
cases
he
o iginal
solu-
ion
is
no
imp o ed.
This
me hod
plays
an
impo an
ole
o
speed
up
he
con e gence
o
he
sea ch.
The
imp o emen
me hod
aims
a
selec ing
he
bes
biclus-
e
om
a
ce ain
numbe
o
new
biclus e s
gene a ed
by
he
combina ion
o
di e en
bina y
s ings.
These
new
solu ions
a e
gene a ed
by
means
o
pe mu a ions
(see
Fig.
2)
in
o de
o
be
close
(in
he
sense
o
he
hamming
dis ance)
o
he
o iginal
biclus e /solu ion.
No e
ha
he
new
solu ions
mus
imp o e
he
o iginal
solu ion
bu
in
he
same
“neighbo hood”.
I
new
biclus e s
do
no
imp o e
he
sea ch,
he
ou pu
is
he
o iginal
biclus e .
Fig.
2
shows
how
bina y
s ings
a e
combined.
These
bina y
s ings
ha e
been
ob ained
om
he
bina y
s ings
o
he
o iginal
biclus e
o
be
imp o ed.
In
pa icula ,
each
bi
o
he
bina y
s ing
o
he
o iginal
biclus e
is
analyzed
and
i
he
bi
is
se
o
0
hen
he
bi
o
he
new
bina y
s ing
is
also
se
o
0
and
i
he
bi
is
1,
hen
he
ollowing
ou
cases
a e
conside ed:
•
Case
1:
The
nex
bi
is
changed
o
1
and
he
cu en
bi
does
no
change
i s
alue.
•
Case
2:
The
nex
bi
is
changed
o
1
and
he
cu en
bi
is
changed
o
0.
•
Case
3:
The
p e ious
bi
is
changed
o
1
and
he
cu en
bi
does
no
change
i s
alue.
•
Case
4:
The
p e ious
bi
is
changed
o
1
and
he
cu en
bi
is
changed
o
0.
Twel e
new
biclus e s
ha e
been
gene a ed
by
applying
his
me hod.
I
he
new
biclus e s
do
no
imp o e
he
alue
o
he
fi ness
unc ion
o
he
o iginal
biclus e ,
he
ou pu
o
he
imp o emen
me hod
is
he
o iginal
biclus e .
3.
Expe imen s
The
goal
o
he
expe imen s
is
o
analyze
how
he
in eg a ion
o
biological
in o ma ion
has
a
ele an
influence
on
he
pe -
o mance
o
he
p oposed
algo i hm.
In
pa icula ,
he
esul s
ob ained
om
F acGO
and
SimNTO
measu es
p oposed
he e
in
o de
o
in eg a e
he
biological
knowledge
a e
compa ed.
Finally,
he
esul s
ob ained
by
he
p oposed
algo i hm
a e
compa ed
wi h
hose
o
he
classical
biclus e ing
algo i hms
such
as
ChCh
[5],
ISA
[10],
OPSM
[11]
and
xMo i s
[12]
ypically
used
as
benchma k
in
he
li e a u e.
The
s anda d
compa ison
me hodology
among
biclus e ing
algo i hms
is
usually
based
on
he
gene
en ichmen
in
he
ob ained
biclus e s
[6].
In
his
wo k,
a
biclus e
is
said
o
be
en iched
i
a
leas
one
en iched
GO
e m
is
associa ed
o
i .
This
sec ion
p esen s
he
expe imen s
ca ied
ou
o
assess
he
pe o mance
o
he
p oposed
algo i hm
on
he
da ase s
desc ibed
in
Sec ion
3.1.
The
esul s
a e
ga he ed
in
Sec ion
3.2
and
a
discussion
can
be
ound
in
Sec ion
3.3.
3.1.
Da a
se s
Two
yeas
da ase s
wi h
accession
numbe s
GDS1116
and
GDS2914
om
he
GEO
eposi o y
[42]
ha e
been
used
in
he
expe imen a ion.
The
fi s
one
is
composed
o
7085
exp ession
p ofiles
and
131
samples
and
ecollec s
he
gene ic
a ia ion
in
he
gene
exp ession
be ween
pa en s
and
p ogenies
om
a
c oss
o
wo
di e en
kinds
o
yeas
s ains.
The
second
one
has
15,488
exp ession
p ofiles
and
36
samples
and
is
a
ime
cou se
expe imen
in
which
yeas
cells
deal
wi h
a
low
dose
o
ca eine
a e
analyzed.
The
aw
da a
ha e
been
p o-
cessed
wi h
he
Babelomics
web
ool
[43].
Fo
bo h
da ase s,
he
exp ession
p ofiles
wi h
mo e
han
a
30%
o
missing
al-
ues
ha e
been
fil e ed
and
he
emaining
missing
alues
ha e
been
eplaced
wi h
he
mean
o
he
alues
in
he
p ofile.
The
p ofiles,
which
appea
se e al
imes
bu
ep esen ing
he
same
gene,
ha e
been
summed
up
by
means
o
he
median
o
he
alues.
A e
p ocessing
he
aw
da a,
GDS1116
exp ession
ma ix
is
a
ma ix
composed
o
882
genes
and
131
samples
o
expe imen al
condi ions
and
GDS2914
a
ma ix
o
975
genes
and
36
condi ions.
Biological
in o ma ion
is
p o ided
by
a
di ec
anno a ion
file
om
biological
p ocess
domain
(BP)
o
Gene
On ology
(GO).
This
file
shows
he
GO
e ms
associa ed
wi h
each
gene
o
he
da a
se .
No e
ha
his
in o ma ion
could
be
downloaded
om
GO
in
di e en
ways.
In
his
wo k,
he
ee
s uc u e
o
GO
is
conside ed
and
he
anno a ion
file
has
been
ob ained
by
p op-
aga ing
he
anno a ions
o
he
uppe
le els
in
he
on ology.
Tha
is,
each
gene
is
also
ela ed
o
GO
e ms
co esponding
o
all
pa en
nodes
un il
he
oo
node.
The
anno a ion
files
o
bo h
da ase s
ha e
been
gene a ed
by
he
Babelomics
ool
wi h
de aul
op ions.
Fo
GDS1116
da a
se ,
632
genes
a e
anno a ed
in
he
file
om
he
882
genes
o
he
exp ession
ma ix.
This
file
con ains
245
di e en
GO
e ms
and
he
a e age
numbe
o
GO
e ms
pe
gene
is
equal
o
10.6.
Fo
GDS2914
da a
se ,
658
genes
a e
anno a ed
om
a
o al
numbe
o
975
genes,
he
file
170
c
o
m
p
u
e
m
e
h
o
d
s
a
n
d
p
o
g
a
m
s
i
n
b
i
o
m
e
d
i
c
i
n
e
1
1
9
(
2
0
1
5
)
163–180
Fig.
2
–
The
p oposed
imp o emen
me hod:
a
es
example.
con ains
256
GO
e ms
and
he
a e age
numbe
o
GO
e ms
pe
gene
is
10.1.
3.2.
Resul s
In
his
sec ion
he
esul s
a e
ga he ed
wi h
he
pu pose
o
e alua ing
he
impo ance
o
in eg a ing
biological
knowledge
o
find
high-quali y
biclus e s.
The
esul s
ob ained
om
he
p oposed
algo i hm
o
di e en
configu a ions
o
he
fi -
ness
unc ion
a e
p esen ed
and
compa ed
wi h
espec
o
se e al
ypical
a iables
such
as
he
size
o
biclus e s,
o e -
lapping
among
biclus e s
and
en ichmen
o
biclus e s.
Also,
he
esul s
ob ained
om
di e en
eposi o ies
such
as
GO,
KEGG
pa hways
and
In e P o
a e
p esen ed.
Each
un
o
he
algo i hm
ob ains
100
biclus e s.
This
numbe
has
been
cho-
sen
because
o
ob ain
a
high
numbe
o
biclus e s
is
desi able
due
o
he
compa ison
among
biclus e ing
algo i hms
is
usu-
ally
es ablished
in
e ms
o
pe cen ages
o
en iched
biclus e s.
No e
ha
he
algo i hm
ob ains
each
biclus e
h ough
an
independen
non-de e minis ic
p ocedu e.
Table
1
p esen s
he
pe cen age
o
en iched
biclus e s
ob ained
by
he
p o-
posed
algo i hm
o
di e en
numbe s
o
biclus e s
(namely,
10,
50
and
100).
I
can
be
obse ed
ha
he
pe cen age
does
no
depend
on
he
numbe
o
biclus e s
conside ed
as
inpu
pa ame e .
The
fi ness
unc ion
pa ame e
se ing
is
expe i-
men al
s udied
o
analyze
he
pe o mance
o
he
biological
in eg a ion
measu es.
Table
2
summa izes
he
quali y
o
biclus e s
ob ained
by
he
p oposed
algo i hm
o
GDS1116
and
GDS2914
da ase s
when
di e en
configu a ions
o
he
fi ness
unc ion
ha e
been
conside ed.
Specifically,
he
column
Measu e,
indica es
i
he
fi ness
unc ion
akes
in o
accoun
biological
in o ma-
ion
by
means
o
he
measu es
SimNTO
(Eq.
(7))
o
F acGO
(Eq.
(6))
o
no
( 3=
0
in
Eq.
(1)).
The
column
Pa ame e s
ep esen s
he
weigh
co esponding
o
each
e m
o
he
fi ness
unc ion.
I
is
impo an
o
highligh
ha
all
e ms
i a y
be ween
0
and
1.
Gi en
he
impo ance
o
a oiding
i ial
biclus e s
wi h
a
low
numbe
o
genes
o
condi ions,
o
example
only
wo
genes
o
condi ions,
he
pa ame e
M1associa ed
o
he
ol-
ume
o
he
biclus e
always
has
been
se
o
2
[25].
Namely,
he
ollowing
h ee
configu a ions
ha e
been
analyzed
when
he
biological
knowledge
is
in eg a ed
in
he
fi ness
unc ion:
o
find
biclus e s
wi h
unde lying
co ela ed
pa e ns
and
o
find
biological
high-quali y
biclus e s
a e
equally
impo an
(M2=
1,
M3=
1),
o
find
biclus e s
wi h
co ela ed
pa e ns
is
mo e
impo an
han
o
find
biological
high-quali y
biclus-
e s
(M2=
2,
M3=
1)
o
ice- e sa
(M2=
1,
M3=
2);
when
he
algo i hm
sea ches
o
biclus e s
wi hou
a
p io i
biological
knowledge
(M3=
0),
wo
configu a ions
ha e
been
analyzed
depending
on
he
ele ance
o
finding
biclus e s
wi h
enclosed
pa e ns
(M2=
1
o
M2=
2).
No e
ha
M1canno
be
equal
o
ze o
o
a oid
i ial
biclus e s
[25].
On
he
o he
hand,
i
M2=
0
he
numbe
o
condi ions
is
no
co ec ly
con olled
by
he
fi ness
unc ion,
and
he e o e,
he
algo i hm
is
no
a
biclus-
e ing
algo i hm
because
can
clus e
genes
bu
no
condi ions.
Finally,
M3=
0
is
conside ed
when
biological
in o ma ion
is
no
conside ed.
The
nex
columns
in
Table
2,
size,
en iched
biclus e s
(%),
GO
e ms
pe
biclus e
and
ime,
show
he
a e age
numbe
o
genes
and
condi ions
o
100
biclus e s
ob ained
by
he
p oposed
algo i hm,
he
pe cen age
o
en iched
biclus e s,
he
a e age
numbe
o
en iched
GO
e ms
pe
biclus e
and
he
compu a ion
ime
o
he
algo i hm
o
ob ain
a
biclus e ,
espec i ely.
Al hough
he
en ichmen
o
biological
signifi-
cance
o
GO
e ms
is
usually
s udied
ega ding
he
biological
p ocess
(BP)
domain
o
GO,
in
his
wo k
he
biological
signifi-
cance
has
been
also
s udied
o
molecula
unc ion
(MF)
and
cellula
componen
(CC)
domains.
No e
ha
he
pe cen age
o
en iched
biclus e s
is
he
s anda d
biological
e alua ion
c i-
e ion
commonly
used
in
biclus e ing
[6,44].
I
should
also
c
o
m
p
u
e
m
e
h
o
d
s
a
n
d
p
o
g
a
m
s
i
n
b
i
o
m
e
d
i
c
i
n
e
1
1
9
(
2
0
1
5
)
163–180
171
Table
1
–
Pe cen age
o
en iched
biclus e s
ob ained
by
he
p oposed
algo i hm
o
di e en
numbe s
o
biclus e s.
Fi ness
unc ion
configu a ion
Numbe
o
biclus e s
(M1,
M2,
M3)
En iched
biclus e s
(%)
BP
MF
CC
1-SimNTO
10
(2,1,1)
100
100
100
1-SimNTO
50
(2,1,1)
100
98
100
1-SimNTO
100
(2,1,1)
99
97
97
1-F acGO
10
(2,1,1)
100
70
50
1-F acGO
50
(2,1,1)
100
72
64
1-F acGO
100
(2,1,1)
100
73
67
0
10
(2,1,0)
85
82
88
0
50
(2,1,0)
82
72
84
0
100
(2,1,0)
85
82
88
Table
2
–
Resul s
ob ained
by
di e en
fi ness
unc ion
configu a ions
o
bo h
da ase s.
Each
ow
shows
a
un
ha
ob ains
100
biclus e s.
Da ase
Fi ness
unc ion
Size
En iched
biclus e s
(%)
GO
e ms
pe
biclus.
(BP)
Time
(s)
Measu e
3Pa ame e s
(M1,
M2,
M3)
BP
MF
CC
(2,
1,
1)
(11.6
×
15.6)
99
97
97
5.74
28.65
1-SimNTO
(2,
1,
2)
(8.7
×
15.2)
87
75
84
3.67
15.78
(2,
2,
1)
(10.1
×
5.1)
95
83
89
4.5
24.03
GDS1116
(2,
1,
1)
(181.6
×
19.4)
100
73
67
1
5410.98
1-F acGO
(2,
1,
2)
(193.9
×
19.3)
100
79
79
1
5546.12
(2,
2,
1)
(109.2
×
3)
100
47
52
1
5682.65
(2,
1,
0)
(23.5
×
14.7)
85
82
88
2.16
38.29
0
(2,
2,
0)
(46.8
×
3.2)
25
17
21
0.4
11.51
(2,
1,
1)
(10.9
×
10.9)
87
33
33
5.45
27.76
1-SimNTO
(2,
1,
2)
(8.0
×
10.2)
65
24
33
2.94
15.67
(2,
2,
1)
(9.5
×
3.3)
87
25
30
5.39
22.18
GDS2914
(2,
1,
1)
(180.6
×
15.1)
100
97
94
1.01
5420.84
1-F acGO
(2,
1,
2)
(193.2
×
15.8)
100
98
94
1
5920.09
(2,
2,
1)
(102.8
×
3)
100
72
67
1
6311.43
(2,
1,
0)
(24.1
×
9.0)
2
5
6
0.02
13.14
0
(2,
2,
0)
(37.1
×
3.1)
13
15
17
0.19
7.16
Fig.
3
–
Pe cen age
o
en iched
biclus e s
o
GDS1116
om
Tables
2
and
3.
178
c
o
m
p
u
e
m
e
h
o
d
s
a
n
d
p
o
g
a
m
s
i
n
b
i
o
m
e
d
i
c
i
n
e
1
1
9
(
2
0
1
5
)
163–180
Fig.
11
–
GO
e m
clus e s
epo ed
by
Re igo
om
biclus e
1
o
he
F acGO
measu e
and
211
configu a ion.
Only
wo
gene al
GO
e ms
a e
epo ed:
p o ein-ubiqui ina ion
and
me abolism.
measu e
cap u es
biclus e s
whe e
genes
a e
oge he
in
a
same
GO
e m,
and
as
a
consequence,
hei
genes
a e
anno-
a ed
in
he
uppe
le els
o
he
GO
hie a chy.
No e
ha
he
anno a ion
files
used
as
inpu
pa ame e
a e
gene a ed
cap-
u ing
all
he
associa ed
pa en
e ms
o
each
gene.
Gene
Te m
Linke
[48]
and
Re igo
[49]
ools
ha e
been
used
o
con-
fi m
ha
he
biclus e s
based
on
he
F acGO
measu e
show
e y
gene al
GO
in o ma ion.
Fi s ly,
he
fi s
ool
fil e s
i ele-
an
GO
in o ma ion
by
iden i ying
me ag oups
o
genes
wi h
cohe en
biological
significance.
Secondly,
Re igo
summa izes
a
lis
o
hese
GO
e ms
by
finding
ep esen a i e
subse s
o
e ms
using
a
clus e ing
p ocedu e
ha
emo es
edundan
e ms.
Fig.
11
shows
he
significan
en iched
GO
e m
in
he
fi s
biclus e
ob ained
by
he
F acGO
measu e
and
211
con-
figu a ion.
All
en iched
GO
e ms
ha e
been
clus e ed
in
wo
e y
gene al
e ms
in
GO:
me abolism
and
p o ein
ubiqui-
a ion.
A e
ha ing
applied
his
pipeline
analysis,
Gene
Te m
Linke
and
Re igo,
all
epo ed
en iched
GO
e ms
a e
clus-
e ed
in
gene al
GO
e ms.
The e o e,
he
assump ion
ha
F acGO-based
biclus e s
a e
composed
o
genes
anno a ed
in
he
uppe
le els
o
he
GO
hie a chy
is
confi med.
The
F acGO
measu e
finds
biclus e s
wi h
a
gene al
in o ma ion
in
GO,
and
hence,
hese
biclus e s
a e
composed
o
genes
ha
a e
no
ela ed
as
g oup
wi h
any
pa hway.
The
comple e
in o ma ion
o
all
figu es
can
be
ead
as
Supplemen a y
in o ma ion.
4.
Conclusions
A
sca e
sea ch-based
biclus e ing
algo i hm
ha
in eg a es
biological
in o ma ion
has
been
p oposed
in
his
pape .
The
da a
inpu
o
he
p oposed
algo i hm
a e
he
gene
exp es-
sion
ma ix
and
a
di ec
anno a ion
file
linking
genes
wi h
se s
o
biological
e ms
ex ac ed
om
a
biological
eposi o y
o
da abase.
The
Gene
On ology,
KEGG
pa hways
and
In e P o
da abases
ha e
been
used
as
sou ce
o
gene a ing
hese
files
in
his
wo k.
Two
di e en
biological
measu es,
F acGO
and
SimNTO,
ha e
been
p oposed
o
in eg a e
his
in o ma ion
by
means
o
i s
addi ion
o
he
fi ness
unc ion
o
be
op imized
o
e alua e
he
quali y
o
he
biclus e s
in
he
sca e
sea ch.
The
measu e
F acGO
is
based
on
he
biological
en ichmen
and
SimNTO
is
based
on
he
o e lapping
among
GO
anno a ions
o
pai s
o
genes.
Expe imen al
esul s
om
he
applica ion
o
he
p oposed
algo i hm
o
wo
da ase s
ha e
been
epo ed
and
discussed
showing
a
be e
pe o mance
when
biological
knowledge
is
in eg a ed
and
be e
biclus e s
han
ha
o
he
classical
biclus e ing
algo i hms.
The
main
mo i a ion
has
been
o
use
a
s anda d
biolog-
ical
alida ion
c i e ion
in
biclus e ing
[6,44]
as
mechanism
o
in eg a e
biological
knowledge.
This
c i e ion
is
based
on
he
pe cen age
o
en iched
biclus e s
ha
is
calcula ed
using
di ec
anno a ion
files.
I
hese
files
a e
GO
files
which
ha e
been
gene a ed
by
p opaga ing
anno a ions
o
uppe
le els
in
he
GO
hie a chy,
he
expe imen al
esul s
show
ha
F acGO-
based
biclus e s
only
sha e
gene al
GO
e ms
and
hey
do
no
cap u e
ele an
biological
in o ma ion.
In
his
case,
he
Sim-
NTO
measu e,
which
is
based
on
he
e m
o e lap
defined
in
[32]
and
uses
anno a ion
files
as
inpu ,
is
as e
and
simple
han
o he
GO
seman ic
measu es
and
sol es
his
p oblem.
Se e al
expe imen s
show
ha
SimNTO-based
biclus e s
cap u e
el-
e an
biological
in o ma ion
ha
p esen
pa hways
mapping
in
Reac ome,
o
example.
I
is
impo an
o
no e
ha
SimNTO
cap u es
he
GO
hie a chical
s uc u e
i
he
anno a ion
files
con ain
all
pa en
e ms
o
each
e m.
As
a
summa y,
he
di -
e ences
be ween
he
F acGO
and
SimNTO
measu es
depend
on
he
da a
sou ce
and
how
he
anno a ion
file
has
been
buil
in
he
case
GO
is
used.
Fu u e
wo k
will
be
ocused
on
he
s udy
o
o he
biolog-
ical
measu es
o
handle
mic oRNA/mRNA
da a
and
how
o
in eg a e
in o ma ion
om
di e en
biological
sou ces.
Some
imp o emen s
in
he
sea ch
p ocedu e
o
he
p oposed
algo-
i hm
will
be
also
analyzed
such
as
he
se ing
configu a ion
o
inne
pa ame e s.
Conflic s
o
in e es
We
decla e
ha
we
ha e
no
any
ac ual
o
po en ial
compe ing
financial
in e es s.
Acknowledgmen s
We
would
like
o
hank
Spanish
Minis y
o
Science
and
Inno-
a ion,
Jun a
de
Andalucía
and
Uni e si y
Pablo
de
Ola ide
o
he
financial
suppo
unde
p ojec s
TIN2011-28956-C02-02,
P12-TIC-1728
and
APPB813097,
espec i ely.
Appendix
A.
Supplemen a y
da a
Supplemen a y
da a
associa ed
wi h
his
a icle
can
be
ound,
in
he
online
e sion,
a
h p://dx.doi.o g/10.1016/j.
cmpb.2015.02.010.
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