<s>
Matrix	B-Application
factorization	I-Application
is	O
a	O
class	O
of	O
collaborative	B-Algorithm
filtering	I-Algorithm
algorithms	O
used	O
in	O
recommender	B-Application
systems	I-Application
.	O
</s>
<s>
Matrix	B-Application
factorization	I-Application
algorithms	O
work	O
by	O
decomposing	O
the	O
user-item	O
interaction	O
matrix	B-Architecture
into	O
the	O
product	O
of	O
two	O
lower	O
dimensionality	O
rectangular	O
matrices	O
.	O
</s>
<s>
The	O
idea	O
behind	O
matrix	B-Application
factorization	I-Application
is	O
to	O
represent	O
users	O
and	O
items	O
in	O
a	O
lower	O
dimensional	O
latent	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
Since	O
the	O
initial	O
work	O
by	O
Funk	O
in	O
2006	O
a	O
multitude	O
of	O
matrix	B-Application
factorization	I-Application
approaches	O
have	O
been	O
proposed	O
for	O
recommender	B-Application
systems	I-Application
.	O
</s>
<s>
The	O
original	O
algorithm	O
proposed	O
by	O
Simon	O
Funk	O
in	O
his	O
blog	O
post	O
factorized	O
the	O
user-item	O
rating	O
matrix	B-Architecture
as	O
the	O
product	O
of	O
two	O
lower	O
dimensional	O
matrices	O
,	O
the	O
first	O
one	O
has	O
a	O
row	O
for	O
each	O
user	O
,	O
while	O
the	O
second	O
has	O
a	O
column	O
for	O
each	O
item	O
.	O
</s>
<s>
The	O
predicted	O
ratings	O
can	O
be	O
computed	O
as	O
,	O
where	O
is	O
the	O
user-item	O
rating	O
matrix	B-Architecture
,	O
contains	O
the	O
user	O
's	O
latent	O
factors	O
and	O
the	O
item	O
's	O
latent	O
factors	O
.	O
</s>
<s>
It	O
has	O
been	O
demonstrated	O
that	O
a	O
matrix	B-Application
factorization	I-Application
with	O
one	O
latent	O
factor	O
is	O
equivalent	O
to	O
a	O
most	O
popular	O
or	O
top	O
popular	O
recommender	B-Application
(	O
e.g.	O
</s>
<s>
Increasing	O
the	O
number	O
of	O
latent	O
factors	O
will	O
improve	O
personalization	O
,	O
therefore	O
recommendation	O
quality	O
,	O
until	O
the	O
number	O
of	O
factors	O
becomes	O
too	O
high	O
,	O
at	O
which	O
point	O
the	O
model	O
starts	O
to	O
overfit	B-Error_Name
and	O
the	O
recommendation	O
quality	O
will	O
decrease	O
.	O
</s>
<s>
A	O
common	O
strategy	O
to	O
avoid	O
overfitting	B-Error_Name
is	O
to	O
add	O
regularization	O
terms	O
to	O
the	O
objective	O
function	O
.	O
</s>
<s>
Modern	O
day	O
recommender	B-Application
systems	I-Application
should	O
exploit	O
all	O
available	O
interactions	O
both	O
explicit	O
(	O
e.g.	O
</s>
<s>
This	O
is	O
an	O
example	O
of	O
a	O
cold-start	B-General_Concept
problem	O
,	O
that	O
is	O
the	O
recommender	B-Application
cannot	O
deal	O
efficiently	O
with	O
new	O
users	O
or	O
items	O
and	O
specific	O
strategies	O
should	O
be	O
put	O
in	O
place	O
to	O
handle	O
this	O
disadvantage	O
.	O
</s>
<s>
A	O
possible	O
way	O
to	O
address	O
this	O
cold	B-General_Concept
start	I-General_Concept
problem	O
is	O
to	O
modify	O
SVD++	O
in	O
order	O
for	O
it	O
to	O
become	O
a	O
model-based	O
algorithm	O
,	O
therefore	O
allowing	O
to	O
easily	O
manage	O
new	O
items	O
and	O
new	O
users	O
.	O
</s>
<s>
Note	O
that	O
this	O
does	O
not	O
entirely	O
solve	O
the	O
cold-start	B-General_Concept
problem	O
,	O
since	O
the	O
recommender	B-Application
still	O
requires	O
some	O
reliable	O
interactions	O
for	O
new	O
users	O
,	O
but	O
at	O
least	O
there	O
is	O
no	O
need	O
to	O
recompute	O
the	O
whole	O
model	O
every	O
time	O
.	O
</s>
<s>
It	O
has	O
been	O
demonstrated	O
that	O
this	O
formulation	O
is	O
almost	O
equivalent	O
to	O
a	O
SLIM	O
model	O
,	O
which	O
is	O
an	O
item-item	O
model	O
based	O
recommender	B-Application
.	O
</s>
<s>
With	O
this	O
formulation	O
,	O
the	O
equivalent	O
item-item	O
recommender	B-Application
would	O
be	O
.	O
</s>
<s>
Therefore	O
the	O
similarity	O
matrix	B-Architecture
is	O
symmetric	O
.	O
</s>
<s>
As	O
opposed	O
to	O
the	O
model-based	O
SVD	O
here	O
the	O
user	O
latent	O
factor	O
matrix	B-Architecture
H	O
is	O
replaced	O
by	O
Q	O
,	O
which	O
learns	O
the	O
user	O
's	O
preferences	O
as	O
function	O
of	O
their	O
ratings	O
.	O
</s>
<s>
With	O
this	O
formulation	O
,	O
the	O
equivalent	O
item-item	O
recommender	B-Application
would	O
be	O
.	O
</s>
<s>
Since	O
matrices	O
Q	O
and	O
W	O
are	O
different	O
the	O
similarity	O
matrix	B-Architecture
is	O
asymmetric	O
,	O
hence	O
the	O
name	O
of	O
the	O
model	O
.	O
</s>
<s>
A	O
group-specific	O
SVD	O
can	O
be	O
an	O
effective	O
approach	O
for	O
the	O
cold-start	B-General_Concept
problem	O
in	O
many	O
scenarios	O
.	O
</s>
<s>
In	O
recent	O
years	O
many	O
other	O
matrix	B-Application
factorization	I-Application
models	O
have	O
been	O
developed	O
to	O
exploit	O
the	O
ever	O
increasing	O
amount	O
and	O
variety	O
of	O
available	O
interaction	O
data	O
and	O
use	O
cases	O
.	O
</s>
<s>
In	O
recent	O
years	O
a	O
number	O
of	O
neural	O
and	O
deep-learning	O
techniques	O
have	O
been	O
proposed	O
,	O
some	O
of	O
which	O
generalize	O
traditional	O
Matrix	B-Application
factorization	I-Application
algorithms	O
via	O
a	O
non-linear	O
neural	O
architecture	O
.	O
</s>
<s>
its	O
real	O
effectiveness	O
when	O
used	O
in	O
a	O
simple	O
Collaborative	B-Algorithm
filtering	I-Algorithm
scenario	O
has	O
been	O
put	O
into	O
question	O
.	O
</s>
<s>
Similar	O
issues	O
have	O
been	O
spotted	O
also	O
in	O
sequence-aware	O
recommender	B-Application
systems	I-Application
.	O
</s>
