<s>
In	O
machine	O
learning	O
,	O
multi-label	B-General_Concept
classification	I-General_Concept
or	O
multi-output	O
classification	B-General_Concept
is	O
a	O
variant	O
of	O
the	O
classification	B-General_Concept
problem	O
where	O
multiple	O
nonexclusive	O
labels	O
may	O
be	O
assigned	O
to	O
each	O
instance	O
.	O
</s>
<s>
Multi-label	B-General_Concept
classification	I-General_Concept
is	O
a	O
generalization	O
of	O
multiclass	B-General_Concept
classification	I-General_Concept
,	O
which	O
is	O
the	O
single-label	O
problem	O
of	O
categorizing	O
instances	O
into	O
precisely	O
one	O
of	O
several	O
(	O
more	O
than	O
two	O
)	O
classes	O
.	O
</s>
<s>
In	O
the	O
multi-label	B-Algorithm
problem	O
the	O
labels	O
are	O
nonexclusive	O
and	O
there	O
is	O
no	O
constraint	O
on	O
how	O
many	O
of	O
the	O
classes	O
the	O
instance	O
can	O
be	O
assigned	O
to	O
.	O
</s>
<s>
Formally	O
,	O
multi-label	B-General_Concept
classification	I-General_Concept
is	O
the	O
problem	O
of	O
finding	O
a	O
model	O
that	O
maps	O
inputs	O
x	O
to	O
binary	O
vectors	O
y	O
;	O
that	O
is	O
,	O
it	O
assigns	O
a	O
value	O
of	O
0	O
or	O
1	O
for	O
each	O
element	O
(	O
label	O
)	O
in	O
y	O
.	O
</s>
<s>
Several	O
problem	O
transformation	O
methods	O
exist	O
for	O
multi-label	B-General_Concept
classification	I-General_Concept
,	O
and	O
can	O
be	O
roughly	O
broken	O
down	O
into	O
:	O
</s>
<s>
Transformation	O
into	O
binary	B-General_Concept
classification	I-General_Concept
problems	O
:	O
the	O
baseline	O
approach	O
,	O
called	O
the	O
binary	O
relevance	O
method	O
,	O
amounts	O
to	O
independently	O
training	O
one	O
binary	B-General_Concept
classifier	I-General_Concept
for	O
each	O
label	O
.	O
</s>
<s>
Given	O
an	O
unseen	O
sample	O
,	O
the	O
combined	O
model	O
then	O
predicts	O
all	O
labels	O
for	O
this	O
sample	O
for	O
which	O
the	O
respective	O
classifiers	B-General_Concept
predict	O
a	O
positive	O
result	O
.	O
</s>
<s>
Although	O
this	O
method	O
of	O
dividing	O
the	O
task	O
into	O
multiple	O
binary	O
tasks	O
may	O
resemble	O
superficially	O
the	O
one-vs.-all	O
(	O
OvA	O
)	O
and	O
one-vs.-rest	O
(	O
OvR	O
)	O
methods	O
for	O
multiclass	B-General_Concept
classification	I-General_Concept
,	O
it	O
is	O
essentially	O
different	O
from	O
both	O
,	O
because	O
a	O
single	O
classifier	B-General_Concept
under	O
binary	O
relevance	O
deals	O
with	O
a	O
single	O
label	O
,	O
without	O
any	O
regard	O
to	O
other	O
labels	O
whatsoever	O
.	O
</s>
<s>
A	O
classifier	B-Algorithm
chain	I-Algorithm
is	O
an	O
alternative	O
method	O
for	O
transforming	O
a	O
multi-label	B-General_Concept
classification	I-General_Concept
problem	O
into	O
several	O
binary	B-General_Concept
classification	I-General_Concept
problems	O
.	O
</s>
<s>
It	O
differs	O
from	O
binary	O
relevance	O
in	O
that	O
labels	O
are	O
predicted	O
sequentially	O
,	O
and	O
the	O
output	O
of	O
all	O
previous	O
classifiers	B-General_Concept
(	O
i.e.	O
</s>
<s>
positive	O
or	O
negative	O
for	O
a	O
particular	O
label	O
)	O
are	O
input	O
as	O
features	O
to	O
subsequent	O
classifiers	B-General_Concept
.	O
</s>
<s>
Classifier	B-Algorithm
chains	I-Algorithm
have	O
been	O
applied	O
,	O
for	O
instance	O
,	O
in	O
HIV	O
drug	O
resistance	O
prediction	O
.	O
</s>
<s>
Bayesian	O
network	O
has	O
also	O
been	O
applied	O
to	O
optimally	O
order	O
classifiers	B-General_Concept
in	O
Classifier	B-Algorithm
chains	I-Algorithm
.	O
</s>
<s>
Transformation	O
into	O
multi-class	B-General_Concept
classification	I-General_Concept
problem	O
:	O
The	O
label	O
powerset	O
(	O
LP	O
)	O
transformation	O
creates	O
one	O
binary	B-General_Concept
classifier	I-General_Concept
for	O
every	O
label	O
combination	O
present	O
in	O
the	O
training	O
set	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
possible	O
labels	O
for	O
an	O
example	O
were	O
A	O
,	O
B	O
,	O
and	O
C	O
,	O
the	O
label	O
powerset	O
representation	O
of	O
this	O
problem	O
is	O
a	O
multi-class	B-General_Concept
classification	I-General_Concept
problem	O
with	O
the	O
classes	O
[	O
0	O
0	O
0 ]	O
,	O
[	O
1	O
0	O
0 ]	O
,	O
[	O
0	O
1	O
0 ]	O
,	O
[	O
0	O
0	O
1 ]	O
,	O
[	O
1	O
1	O
0 ]	O
,	O
[	O
1	O
0	O
1 ]	O
,	O
[	O
0	O
1	O
1 ]	O
.	O
</s>
<s>
Ensemble	B-Algorithm
methods	I-Algorithm
:	O
A	O
set	O
of	O
multi-class	O
classifiers	B-General_Concept
can	O
be	O
used	O
to	O
create	O
a	O
multi-label	B-Algorithm
ensemble	B-Algorithm
classifier	I-Algorithm
.	O
</s>
<s>
For	O
a	O
given	O
example	O
,	O
each	O
classifier	B-General_Concept
outputs	O
a	O
single	O
class	O
(	O
corresponding	O
to	O
a	O
single	O
label	O
in	O
the	O
multi-label	B-Algorithm
problem	O
)	O
.	O
</s>
<s>
These	O
predictions	O
are	O
then	O
combined	O
by	O
an	O
ensemble	O
method	O
,	O
usually	O
a	O
voting	O
scheme	O
where	O
every	O
class	O
that	O
receives	O
a	O
requisite	O
percentage	O
of	O
votes	O
from	O
individual	O
classifiers	B-General_Concept
(	O
often	O
referred	O
to	O
as	O
the	O
discrimination	O
threshold	O
)	O
is	O
predicted	O
as	O
a	O
present	O
label	O
in	O
the	O
multi-label	B-Algorithm
output	O
.	O
</s>
<s>
However	O
,	O
more	O
complex	O
ensemble	B-Algorithm
methods	I-Algorithm
exist	O
,	O
such	O
as	O
committee	B-Algorithm
machines	I-Algorithm
.	O
</s>
<s>
Another	O
variation	O
is	O
the	O
random	O
-labelsets	O
(	O
RAKEL	O
)	O
algorithm	O
,	O
which	O
uses	O
multiple	O
LP	O
classifiers	B-General_Concept
,	O
each	O
trained	O
on	O
a	O
random	O
subset	O
of	O
the	O
actual	O
labels	O
;	O
label	O
prediction	O
is	O
then	O
carried	O
out	O
by	O
a	O
voting	O
scheme	O
.	O
</s>
<s>
A	O
set	O
of	O
multi-label	B-Algorithm
classifiers	B-General_Concept
can	O
be	O
used	O
in	O
a	O
similar	O
way	O
to	O
create	O
a	O
multi-label	B-Algorithm
ensemble	B-Algorithm
classifier	I-Algorithm
.	O
</s>
<s>
In	O
this	O
case	O
,	O
each	O
classifier	B-General_Concept
votes	O
once	O
for	O
each	O
label	O
it	O
predicts	O
rather	O
than	O
for	O
a	O
single	O
label	O
.	O
</s>
<s>
Some	O
classification	B-General_Concept
algorithms/models	O
have	O
been	O
adapted	O
to	O
the	O
multi-label	B-Algorithm
task	O
,	O
without	O
requiring	O
problem	O
transformations	O
.	O
</s>
<s>
k-nearest	B-General_Concept
neighbors	I-General_Concept
:	O
the	O
ML-kNN	O
algorithm	O
extends	O
the	O
k-NN	B-General_Concept
classifier	B-General_Concept
to	O
multi-label	B-Algorithm
data	O
.	O
</s>
<s>
decision	B-Algorithm
trees	I-Algorithm
:	O
"	O
Clare	O
"	O
is	O
an	O
adapted	O
C4.5	O
algorithm	O
for	O
multi-label	B-General_Concept
classification	I-General_Concept
;	O
the	O
modification	O
involves	O
the	O
entropy	O
calculations	O
.	O
</s>
<s>
They	O
are	O
also	O
named	O
multi-valued	O
and	O
multi-labeled	O
decision	B-Algorithm
tree	I-Algorithm
classification	B-General_Concept
methods	O
.	O
</s>
<s>
neural	B-Architecture
networks	I-Architecture
:	O
BP-MLL	O
is	O
an	O
adaptation	O
of	O
the	O
popular	O
back-propagation	O
algorithm	O
for	O
multi-label	B-Algorithm
learning	O
.	O
</s>
<s>
Based	O
on	O
learning	O
paradigms	O
,	O
the	O
existing	O
multi-label	B-General_Concept
classification	I-General_Concept
techniques	O
can	O
be	O
classified	O
into	O
batch	O
learning	O
and	O
online	B-Algorithm
machine	I-Algorithm
learning	I-Algorithm
.	O
</s>
<s>
Data	B-General_Concept
streams	I-General_Concept
are	O
possibly	O
infinite	O
sequences	O
of	O
data	O
that	O
continuously	O
and	O
rapidly	O
grow	O
over	O
time	O
.	O
</s>
<s>
Multi-label	B-Algorithm
stream	O
classification	B-General_Concept
(	O
MLSC	O
)	O
is	O
the	O
version	O
of	O
multi-label	B-General_Concept
classification	I-General_Concept
task	O
that	O
takes	O
place	O
in	O
data	B-General_Concept
streams	I-General_Concept
.	O
</s>
<s>
It	O
is	O
sometimes	O
also	O
called	O
online	O
multi-label	B-General_Concept
classification	I-General_Concept
.	O
</s>
<s>
The	O
difficulties	O
of	O
multi-label	B-General_Concept
classification	I-General_Concept
(	O
exponential	O
number	O
of	O
possible	O
label	O
sets	O
,	O
capturing	O
dependencies	O
between	O
labels	O
)	O
are	O
combined	O
with	O
difficulties	O
of	O
data	B-General_Concept
streams	I-General_Concept
(	O
time	O
and	O
memory	O
constraints	O
,	O
addressing	O
infinite	O
stream	O
with	O
finite	O
means	O
,	O
concept	B-Algorithm
drifts	I-Algorithm
)	O
.	O
</s>
<s>
Many	O
MLSC	O
methods	O
resort	O
to	O
ensemble	B-Algorithm
methods	I-Algorithm
in	O
order	O
to	O
increase	O
their	O
predictive	O
performance	O
and	O
deal	O
with	O
concept	B-Algorithm
drifts	I-Algorithm
.	O
</s>
<s>
Below	O
are	O
the	O
most	O
widely	O
used	O
ensemble	B-Algorithm
methods	I-Algorithm
in	O
the	O
literature	O
:	O
</s>
<s>
Online	O
Bagging	O
(	O
OzaBagging	O
)	O
-based	O
methods	O
:	O
Observing	O
the	O
probability	O
of	O
having	O
K	O
many	O
of	O
a	O
certain	O
data	O
point	O
in	O
a	O
bootstrap	O
sample	O
is	O
approximately	O
Poisson(1 )	O
for	O
big	O
datasets	O
,	O
each	O
incoming	O
data	O
instance	O
in	O
a	O
data	B-General_Concept
stream	I-General_Concept
can	O
be	O
weighted	O
proportional	O
to	O
Poisson(1 )	O
distribution	O
to	O
mimic	O
bootstrapping	O
in	O
an	O
online	O
setting	O
.	O
</s>
<s>
Many	O
multi-label	B-Algorithm
methods	O
that	O
use	O
Online	O
Bagging	O
are	O
proposed	O
in	O
the	O
literature	O
,	O
each	O
of	O
which	O
utilizes	O
different	O
problem	O
transformation	O
methods	O
.	O
</s>
<s>
ADWIN	O
Bagging-based	O
methods	O
:	O
Online	O
Bagging	O
methods	O
for	O
MLSC	O
are	O
sometimes	O
combined	O
with	O
explicit	O
concept	B-Algorithm
drift	I-Algorithm
detection	O
mechanisms	O
such	O
as	O
ADWIN	O
(	O
Adaptive	O
Window	O
)	O
.	O
</s>
<s>
EaBR	O
,	O
EaCC	O
,	O
EaHTPS	O
are	O
examples	O
of	O
such	O
multi-label	B-Algorithm
ensembles	O
.	O
</s>
<s>
GOOWE-ML-based	O
methods	O
:	O
Interpreting	O
the	O
relevance	O
scores	O
of	O
each	O
component	O
of	O
the	O
ensemble	O
as	O
vectors	O
in	O
the	O
label	O
space	O
and	O
solving	O
a	O
least	O
squares	O
problem	O
at	O
the	O
end	O
of	O
each	O
batch	O
,	O
Geometrically-Optimum	O
Online-Weighted	O
Ensemble	O
for	O
Multi-label	B-General_Concept
Classification	I-General_Concept
(	O
GOOWE-ML	O
)	O
is	O
proposed	O
.	O
</s>
<s>
GOBR	O
,	O
GOCC	O
,	O
GOPS	O
,	O
GORT	O
are	O
the	O
proposed	O
GOOWE-ML-based	O
multi-label	B-Algorithm
ensembles	O
.	O
</s>
<s>
This	O
allows	O
concept	B-Algorithm
drifts	I-Algorithm
that	O
are	O
independent	O
for	O
each	O
label	O
to	O
be	O
detected	O
,	O
and	O
class-imbalance	O
(	O
skewness	O
in	O
the	O
relevant	O
and	O
non-relevant	O
examples	O
)	O
to	O
be	O
handled	O
.	O
</s>
<s>
Considering	O
to	O
be	O
a	O
set	O
of	O
labels	O
for	O
data	O
sample	O
(	O
do	O
not	O
confuse	O
it	O
with	O
a	O
one-hot	O
vector	O
;	O
it	O
is	O
simply	O
a	O
collection	O
of	O
all	O
of	O
the	O
labels	O
that	O
belong	O
to	O
this	O
sample	O
)	O
,	O
the	O
extent	O
to	O
which	O
a	O
dataset	O
is	O
multi-label	B-Algorithm
can	O
be	O
captured	O
in	O
two	O
statistics	O
:	O
</s>
<s>
Evaluation	O
metrics	O
for	O
multi-label	B-General_Concept
classification	I-General_Concept
performance	O
are	O
inherently	O
different	O
from	O
those	O
used	O
in	O
multi-class	O
(	O
or	O
binary	O
)	O
classification	B-General_Concept
,	O
due	O
to	O
the	O
inherent	O
differences	O
of	O
the	O
classification	B-General_Concept
problem	O
.	O
</s>
<s>
The	O
closely	O
related	O
Jaccard	O
index	O
,	O
also	O
called	O
Intersection	O
over	O
Union	O
in	O
the	O
multi-label	B-Algorithm
setting	O
,	O
is	O
defined	O
as	O
the	O
number	O
of	O
correctly	O
predicted	O
labels	O
divided	O
by	O
the	O
union	O
of	O
predicted	O
and	O
true	O
labels	O
,	O
,	O
where	O
and	O
are	O
sets	O
of	O
predicted	O
labels	O
and	O
true	O
labels	O
respectively	O
.	O
</s>
<s>
Cross-validation	O
in	O
multi-label	B-Algorithm
settings	O
is	O
complicated	O
by	O
the	O
fact	O
that	O
the	O
ordinary	O
(	O
binary/multiclass	O
)	O
way	O
of	O
stratified	O
sampling	O
will	O
not	O
work	O
;	O
alternative	O
ways	O
of	O
approximate	O
stratified	O
sampling	O
have	O
been	O
suggested	O
.	O
</s>
<s>
Java	O
implementations	O
of	O
multi-label	B-Algorithm
algorithms	O
are	O
available	O
in	O
the	O
and	O
software	O
packages	O
,	O
both	O
based	O
on	O
Weka	B-Language
.	O
</s>
<s>
The	O
scikit-learn	B-Application
Python	O
package	O
implements	O
some	O
.	O
</s>
<s>
The	O
Python	O
package	O
specifically	O
caters	O
to	O
the	O
multi-label	B-General_Concept
classification	I-General_Concept
.	O
</s>
<s>
It	O
provides	O
multi-label	B-Algorithm
implementation	O
of	O
several	O
well-known	O
techniques	O
including	O
SVM	O
,	O
kNN	O
and	O
.	O
</s>
<s>
The	O
package	O
is	O
built	O
on	O
top	O
of	O
scikit-learn	B-Application
ecosystem	O
.	O
</s>
<s>
A	O
list	O
of	O
commonly	O
used	O
multi-label	B-Algorithm
data-sets	O
is	O
available	O
at	O
the	O
.	O
</s>
