<s>
In	O
representation	B-General_Concept
learning	I-General_Concept
,	O
knowledge	B-Algorithm
graph	I-Algorithm
embedding	I-Algorithm
(	O
KGE	O
)	O
,	O
also	O
referred	O
to	O
as	O
knowledge	O
representation	B-General_Concept
learning	I-General_Concept
(	O
KRL	O
)	O
,	O
or	O
multi-relation	O
learning	O
,	O
is	O
a	O
machine	O
learning	O
task	O
of	O
learning	O
a	O
low-dimensional	O
representation	O
of	O
a	O
knowledge	B-Application
graph	I-Application
's	O
entities	O
and	O
relations	O
while	O
preserving	O
their	O
semantic	B-Application
meaning	O
.	O
</s>
<s>
Leveraging	O
their	O
embedded	O
representation	O
,	O
knowledge	B-Application
graphs	I-Application
(	O
KGs	O
)	O
can	O
be	O
used	O
for	O
various	O
applications	O
such	O
as	O
link	B-Application
prediction	I-Application
,	O
triple	O
classification	O
,	O
entity	O
recognition	O
,	O
clustering	B-Algorithm
,	O
and	O
relation	O
extraction	O
.	O
</s>
<s>
A	O
knowledge	B-Application
graph	I-Application
is	O
a	O
collection	O
of	O
entities	O
,	O
relations	O
,	O
and	O
facts	O
.	O
</s>
<s>
A	O
knowledge	B-Application
graph	I-Application
represents	O
the	O
knowledge	O
related	O
to	O
a	O
specific	O
domain	O
;	O
leveraging	O
this	O
structured	O
representation	O
,	O
it	O
is	O
possible	O
to	O
infer	O
a	O
piece	O
of	O
new	O
knowledge	O
from	O
it	O
after	O
some	O
refinement	O
steps	O
.	O
</s>
<s>
The	O
embedding	O
of	O
a	O
knowledge	B-Application
graph	I-Application
translates	O
each	O
entity	O
and	O
relation	O
of	O
a	O
knowledge	B-Application
graph	I-Application
,	O
into	O
a	O
vector	O
of	O
a	O
given	O
dimension	O
,	O
called	O
embedding	O
dimension	O
.	O
</s>
<s>
The	O
collection	O
of	O
embedding	O
vectors	O
for	O
all	O
the	O
entities	O
and	O
relations	O
in	O
the	O
knowledge	B-Application
graph	I-Application
are	O
a	O
more	O
dense	O
and	O
efficient	O
representation	O
of	O
the	O
domain	O
that	O
can	O
more	O
easily	O
be	O
used	O
for	O
many	O
different	O
tasks	O
.	O
</s>
<s>
A	O
knowledge	B-Algorithm
graph	I-Algorithm
embedding	I-Algorithm
is	O
characterized	O
by	O
four	O
different	O
aspects	O
:	O
</s>
<s>
Additional	O
information	O
:	O
Any	O
additional	O
information	O
coming	O
from	O
the	O
knowledge	B-Application
graph	I-Application
that	O
can	O
enrich	O
the	O
embedded	O
representation	O
.	O
</s>
<s>
All	O
the	O
different	O
knowledge	B-Algorithm
graph	I-Algorithm
embedding	I-Algorithm
models	O
follow	O
roughly	O
the	O
same	O
procedure	O
to	O
learn	O
the	O
semantic	B-Application
meaning	O
of	O
the	O
facts	O
.	O
</s>
<s>
First	O
of	O
all	O
,	O
to	O
learn	O
an	O
embedded	O
representation	O
of	O
a	O
knowledge	B-Application
graph	I-Application
,	O
the	O
embedding	O
vectors	O
of	O
the	O
entities	O
and	O
relations	O
are	O
initialized	O
to	O
random	O
values	O
.	O
</s>
<s>
Usually	O
,	O
the	O
stop	O
condition	O
is	O
given	O
by	O
the	O
overfitting	B-Error_Name
over	O
the	O
training	O
set	O
.	O
</s>
<s>
For	O
each	O
iteration	O
,	O
is	O
sampled	O
a	O
batch	O
of	O
size	O
from	O
the	O
training	O
set	O
,	O
and	O
for	O
each	O
triple	O
of	O
the	O
batch	O
is	O
sampled	O
a	O
random	O
corrupted	O
facti.e.	O
,	O
a	O
triple	O
that	O
does	O
not	O
represent	O
a	O
true	O
fact	O
in	O
the	O
knowledge	B-Application
graph	I-Application
.	O
</s>
<s>
At	O
the	O
end	O
of	O
the	O
algorithm	O
,	O
the	O
learned	O
embeddings	O
should	O
have	O
extracted	O
the	O
semantic	B-Application
meaning	O
from	O
the	O
triples	O
and	O
should	O
correctly	O
unseen	O
true	O
facts	O
in	O
the	O
knowledge	B-Application
graph	I-Application
.	O
</s>
<s>
Knowledge	B-Application
graph	I-Application
completion	O
(	O
KGC	O
)	O
is	O
a	O
collection	O
of	O
techniques	O
to	O
infer	O
knowledge	O
from	O
an	O
embedded	O
knowledge	B-Application
graph	I-Application
representation	O
.	O
</s>
<s>
Clustering	B-Algorithm
is	O
another	O
application	O
that	O
leverages	O
the	O
embedded	O
representation	O
of	O
a	O
sparse	O
knowledge	B-Application
graph	I-Application
to	O
condense	O
the	O
representation	O
of	O
similar	O
semantic	B-Application
entities	O
close	O
in	O
a	O
2D	O
space	O
.	O
</s>
<s>
The	O
use	O
of	O
knowledge	B-Algorithm
graph	I-Algorithm
embedding	I-Algorithm
is	O
increasingly	O
pervasive	O
in	O
many	O
applications	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
recommender	B-Application
systems	I-Application
,	O
the	O
use	O
of	O
knowledge	B-Algorithm
graph	I-Algorithm
embedding	I-Algorithm
can	O
overcome	O
the	O
limitations	O
of	O
the	O
usual	O
reinforcement	O
learning	O
.	O
</s>
<s>
Training	O
this	O
kind	O
of	O
recommender	B-Application
system	I-Application
requires	O
a	O
huge	O
amount	O
of	O
information	O
from	O
the	O
users	O
;	O
however	O
,	O
knowledge	B-Application
graph	I-Application
techniques	O
can	O
address	O
this	O
issue	O
by	O
using	O
a	O
graph	O
already	O
constructed	O
over	O
a	O
prior	O
knowledge	O
of	O
the	O
item	O
correlation	O
and	O
using	O
the	O
embedding	O
to	O
infer	O
from	O
it	O
the	O
recommendation	O
.	O
</s>
<s>
It	O
is	O
possible	O
to	O
use	O
the	O
task	O
of	O
link	B-Application
prediction	I-Application
to	O
infer	O
a	O
new	O
connection	O
between	O
an	O
already	O
existing	O
drug	O
and	O
a	O
disease	O
by	O
using	O
a	O
biomedical	O
knowledge	B-Application
graph	I-Application
built	O
leveraging	O
the	O
availability	O
of	O
massive	O
literature	O
and	O
biomedical	O
databases	O
.	O
</s>
<s>
Knowledge	B-Algorithm
graph	I-Algorithm
embedding	I-Algorithm
can	O
also	O
be	O
used	O
in	O
the	O
domain	O
of	O
social	O
politics	O
.	O
</s>
<s>
Given	O
a	O
collection	O
of	O
triples	O
(	O
or	O
facts	O
)	O
,	O
the	O
knowledge	B-Algorithm
graph	I-Algorithm
embedding	I-Algorithm
model	O
produces	O
,	O
for	O
each	O
entity	O
and	O
relation	O
present	O
in	O
the	O
knowledge	B-Application
graph	I-Application
a	O
continuous	O
vector	O
representation	O
.	O
</s>
<s>
propose	O
a	O
taxonomy	O
of	O
the	O
embedding	O
models	O
and	O
identifies	O
three	O
main	O
families	O
of	O
models	O
:	O
tensor	B-Device
decomposition	O
models	O
,	O
geometric	O
models	O
,	O
and	O
deep	O
learning	O
models	O
.	O
</s>
<s>
The	O
tensor	B-Device
decomposition	O
is	O
a	O
family	O
of	O
knowledge	B-Algorithm
graph	I-Algorithm
embedding	I-Algorithm
models	O
that	O
use	O
a	O
multi-dimensional	O
matrix	O
to	O
represent	O
a	O
knowledge	B-Application
graph	I-Application
,	O
that	O
is	O
partially	O
knowable	O
due	O
to	O
the	O
gaps	O
of	O
the	O
knowledge	B-Application
graph	I-Application
describing	O
a	O
particular	O
domain	O
thoroughly	O
.	O
</s>
<s>
In	O
particular	O
,	O
these	O
models	O
use	O
a	O
three-way	O
(	O
3D	O
)	O
tensor	B-Device
,	O
which	O
is	O
then	O
factorized	O
into	O
low-dimensional	O
vectors	O
that	O
are	O
the	O
entities	O
and	O
relations	O
embeddings	O
.	O
</s>
<s>
The	O
third-order	O
tensor	B-Device
is	O
a	O
suitable	O
methodology	O
to	O
represent	O
a	O
knowledge	B-Application
graph	I-Application
because	O
it	O
records	O
only	O
the	O
existence	O
or	O
the	O
absence	O
of	O
a	O
relation	O
between	O
entities	O
,	O
and	O
for	O
this	O
reason	O
is	O
simple	O
,	O
and	O
there	O
is	O
no	O
need	O
to	O
know	O
a	O
priori	O
the	O
network	O
structure	O
,	O
making	O
this	O
class	O
of	O
embedding	O
models	O
light	O
,	O
and	O
easy	O
to	O
train	O
even	O
if	O
they	O
suffer	O
from	O
high-dimensional	O
and	O
sparsity	O
of	O
data	O
.	O
</s>
<s>
This	O
approach	O
is	O
scalable	O
to	O
a	O
large	O
knowledge	B-Application
graph	I-Application
in	O
terms	O
of	O
time	O
and	O
space	O
cost	O
.	O
</s>
<s>
ANALOGY	O
:	O
This	O
model	O
encodes	O
in	O
the	O
embedding	O
the	O
analogical	O
structure	O
of	O
the	O
knowledge	B-Application
graph	I-Application
to	O
simulate	O
inductive	O
reasoning	O
.	O
</s>
<s>
SimplE	O
:	O
This	O
model	O
is	O
the	O
improvement	O
of	O
canonical	O
polyadic	O
decomposition	O
(	O
CP	O
)	O
,	O
in	O
which	O
an	O
embedding	O
vector	O
for	O
the	O
relation	O
and	O
two	O
independent	O
embedding	O
vectors	O
for	O
each	O
entity	O
are	O
learned	O
,	O
depending	O
on	O
whether	O
it	O
is	O
a	O
head	O
or	O
a	O
tail	O
in	O
the	O
knowledge	B-Application
graph	I-Application
fact	O
.	O
</s>
<s>
HolE	O
:	O
HolE	O
uses	O
circular	O
correlation	O
to	O
create	O
an	O
embedded	O
representation	O
of	O
the	O
knowledge	B-Application
graph	I-Application
,	O
which	O
can	O
be	O
seen	O
as	O
a	O
compression	O
of	O
the	O
matrix	O
product	O
,	O
but	O
is	O
more	O
computationally	O
efficient	O
and	O
scalable	O
while	O
keeping	O
the	O
capabilities	O
to	O
express	O
asymmetric	O
relation	O
since	O
the	O
circular	O
correlation	O
is	O
not	O
commutative	O
.	O
</s>
<s>
HolE	O
links	O
holographic	O
and	O
complex	O
embeddings	O
since	O
,	O
if	O
used	O
together	O
with	O
Fourier	B-Algorithm
,	O
can	O
be	O
seen	O
as	O
a	O
special	O
case	O
of	O
ComplEx	O
.	O
</s>
<s>
TuckER	O
:	O
TuckER	O
sees	O
the	O
knowledge	B-Application
graph	I-Application
as	O
a	O
tensor	B-Device
that	O
could	O
be	O
decomposed	O
using	O
the	O
Tucker	B-Algorithm
decomposition	I-Algorithm
in	O
a	O
collection	O
of	O
vectorsi.e.	O
,	O
the	O
embeddings	O
of	O
entities	O
and	O
relationswith	O
a	O
shared	O
core	O
.	O
</s>
<s>
The	O
weights	O
of	O
the	O
core	O
tensor	B-Device
are	O
learned	O
together	O
with	O
the	O
embeddings	O
and	O
represent	O
the	O
level	O
of	O
interaction	O
of	O
the	O
entries	O
.	O
</s>
<s>
Each	O
entity	O
and	O
relation	O
has	O
its	O
own	O
embedding	O
dimension	O
,	O
and	O
the	O
size	O
of	O
the	O
core	O
tensor	B-Device
is	O
determined	O
by	O
the	O
shape	O
of	O
the	O
entities	O
and	O
relations	O
that	O
interact	O
.	O
</s>
<s>
MEI	O
:	O
MEI	O
introduces	O
the	O
multi-partition	O
embedding	O
interaction	O
technique	O
with	O
the	O
block	O
term	O
tensor	B-Device
format	O
,	O
which	O
is	O
a	O
generalization	O
of	O
CP	O
decomposition	O
and	O
Tucker	B-Algorithm
decomposition	I-Algorithm
.	O
</s>
<s>
MEIM	O
:	O
MEIM	O
goes	O
beyond	O
the	O
block	O
term	O
tensor	B-Device
format	O
to	O
introduce	O
the	O
independent	O
core	O
tensor	B-Device
for	O
ensemble	O
boosting	O
effects	O
and	O
the	O
soft	O
orthogonality	O
for	O
max-rank	O
relational	O
mapping	O
,	O
in	O
addition	O
to	O
multi-partition	O
embedding	O
interaction	O
.	O
</s>
<s>
Geometric	O
models	O
are	O
similar	O
to	O
the	O
tensor	B-Device
decomposition	O
model	O
,	O
but	O
the	O
main	O
difference	O
between	O
the	O
two	O
is	O
that	O
they	O
have	O
to	O
preserve	O
the	O
applicability	O
of	O
the	O
transformation	O
in	O
the	O
geometric	O
space	O
in	O
which	O
it	O
is	O
defined	O
.	O
</s>
<s>
This	O
class	O
of	O
models	O
is	O
inspired	O
by	O
the	O
idea	O
of	O
translation	O
invariance	O
introduced	O
in	O
word2vec	B-Algorithm
.	O
</s>
<s>
The	O
embedding	O
will	O
be	O
exact	O
if	O
each	O
entity	O
and	O
relation	O
appears	O
in	O
only	O
one	O
fact	O
,	O
and	O
,	O
for	O
this	O
reason	O
,	O
in	O
practice	O
does	O
not	O
well	O
represent	O
one-to-many	B-Application
,	O
many-to-one	B-Application
,	O
and	O
asymmetric	O
relations	O
.	O
</s>
<s>
TransR	O
:	O
TransR	O
is	O
an	O
evolution	O
of	O
TransH	O
because	O
it	O
uses	O
two	O
different	O
spaces	O
to	O
represent	O
the	O
embedded	O
representation	O
of	O
the	O
entities	O
and	O
the	O
relations	O
,	O
and	O
separate	O
completely	O
the	O
semantic	B-Application
space	O
of	O
entities	O
and	O
relations	O
.	O
</s>
<s>
The	O
first	O
vector	O
is	O
used	O
to	O
represent	O
the	O
semantic	B-Application
meaning	O
of	O
the	O
entities	O
and	O
relations	O
,	O
the	O
second	O
one	O
to	O
compute	O
the	O
mapping	O
matrix	O
.	O
</s>
<s>
Since	O
the	O
vector	O
representation	O
of	O
the	O
entities	O
and	O
relations	O
is	O
not	O
perfect	O
,	O
a	O
pure	O
translation	O
of	O
could	O
be	O
distant	O
from	O
,	O
and	O
a	O
spherical	B-Application
equipotential	O
Euclidean	O
distance	O
makes	O
it	O
hard	O
to	O
distinguish	O
which	O
is	O
the	O
closest	O
entity	O
.	O
</s>
<s>
It	O
is	O
possible	O
to	O
associate	O
additional	O
information	O
to	O
each	O
element	O
in	O
the	O
knowledge	B-Application
graph	I-Application
and	O
their	O
common	O
representation	O
facts	O
.	O
</s>
<s>
Each	O
entity	O
and	O
relation	O
can	O
be	O
enriched	O
with	O
text	O
descriptions	O
,	O
weights	O
,	O
constraints	O
,	O
and	O
others	O
in	O
order	O
to	O
improve	O
the	O
overall	O
description	O
of	O
the	O
domain	O
with	O
a	O
knowledge	B-Application
graph	I-Application
.	O
</s>
<s>
During	O
the	O
embedding	O
of	O
the	O
knowledge	B-Application
graph	I-Application
,	O
this	O
information	O
can	O
be	O
used	O
to	O
learn	O
specialized	O
embeddings	O
for	O
these	O
characteristics	O
together	O
with	O
the	O
usual	O
embedded	O
representation	O
of	O
entities	O
and	O
relations	O
,	O
with	O
the	O
cost	O
of	O
learning	O
a	O
more	O
significant	O
number	O
of	O
vectors	O
.	O
</s>
<s>
STransE	O
:	O
This	O
model	O
is	O
the	O
result	O
of	O
the	O
combination	O
of	O
TransE	O
and	O
of	O
the	O
structure	O
embedding	O
in	O
such	O
a	O
way	O
it	O
is	O
able	O
to	O
better	O
represent	O
the	O
one-to-many	B-Application
,	O
many-to-one	B-Application
,	O
and	O
many-to-many	B-Architecture
relations	O
.	O
</s>
<s>
It	O
is	O
shown	O
that	O
the	O
model	O
is	O
capable	O
of	O
embedding	O
symmetric	O
,	O
asymmetric	O
,	O
inversion	O
,	O
and	O
composition	O
relations	O
from	O
the	O
knowledge	B-Application
graph	I-Application
.	O
</s>
<s>
This	O
group	O
of	O
embedding	O
models	O
uses	O
deep	O
neural	O
network	O
to	O
learn	O
patterns	O
from	O
the	O
knowledge	B-Application
graph	I-Application
that	O
are	O
the	O
input	O
data	O
.	O
</s>
<s>
These	O
models	O
have	O
the	O
generality	O
to	O
distinguish	O
the	O
type	O
of	O
entity	O
and	O
relation	O
,	O
temporal	O
information	O
,	O
path	O
information	O
,	O
underlay	O
structured	O
information	O
,	O
and	O
resolve	O
the	O
limitations	O
of	O
distance-based	O
and	O
semantic-matching-based	O
models	O
in	O
representing	O
all	O
the	O
features	O
of	O
a	O
knowledge	B-Application
graph	I-Application
.	O
</s>
<s>
The	O
use	O
of	O
deep	O
learning	O
for	O
knowledge	B-Algorithm
graph	I-Algorithm
embedding	I-Algorithm
has	O
shown	O
good	O
predictive	O
performance	O
even	O
if	O
they	O
are	O
more	O
expensive	O
in	O
the	O
training	O
phase	O
,	O
angry	O
of	O
data	O
,	O
and	O
often	O
required	O
a	O
pre-trained	O
embedding	O
representation	O
of	O
knowledge	B-Application
graph	I-Application
coming	O
from	O
a	O
different	O
embedding	O
model	O
.	O
</s>
<s>
ConvE	O
uses	O
a	O
one-dimensional	O
-sized	O
embedding	O
to	O
represent	O
the	O
entities	O
and	O
relations	O
of	O
a	O
knowledge	B-Application
graph	I-Application
.	O
</s>
<s>
This	O
family	O
of	O
models	O
uses	O
capsule	B-Algorithm
neural	I-Algorithm
networks	I-Algorithm
to	O
create	O
a	O
more	O
stable	O
representation	O
that	O
is	O
able	O
to	O
recognize	O
a	O
feature	O
in	O
the	O
input	O
without	O
losing	O
spatial	O
information	O
.	O
</s>
<s>
This	O
class	O
of	O
models	O
leverages	O
the	O
use	O
of	O
recurrent	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
.	O
</s>
<s>
Recurrent	O
skipping	O
networks	O
(	O
RSN	O
)	O
uses	O
a	O
recurrent	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
to	O
learn	O
relational	O
path	O
using	O
a	O
random	O
walk	O
sampling	O
.	O
</s>
<s>
The	O
machine	O
learning	O
task	O
for	O
knowledge	B-Algorithm
graph	I-Algorithm
embedding	I-Algorithm
that	O
is	O
more	O
often	O
used	O
to	O
evaluate	O
the	O
embedding	O
accuracy	O
of	O
the	O
models	O
is	O
the	O
link	B-Application
prediction	I-Application
.	O
</s>
<s>
+Table	O
summary	O
of	O
the	O
memory	O
complexity	O
and	O
the	O
link	B-Application
prediction	I-Application
accuracy	O
of	O
the	O
knowledge	B-Algorithm
graph	I-Algorithm
embedding	I-Algorithm
models	O
according	O
to	O
Rossi	O
et	O
al	O
.	O
</s>
