<s>
In	O
machine	O
learning	O
and	O
statistical	B-General_Concept
classification	I-General_Concept
,	O
multiclass	B-General_Concept
classification	I-General_Concept
or	O
multinomial	O
classification	O
is	O
the	O
problem	O
of	O
classifying	O
instances	O
into	O
one	O
of	O
three	O
or	O
more	O
classes	O
(	O
classifying	O
instances	O
into	O
one	O
of	O
two	O
classes	O
is	O
called	O
binary	B-General_Concept
classification	I-General_Concept
)	O
.	O
</s>
<s>
While	O
many	O
classification	O
algorithms	O
(	O
notably	O
multinomial	O
logistic	O
regression	O
)	O
naturally	O
permit	O
the	O
use	O
of	O
more	O
than	O
two	O
classes	O
,	O
some	O
are	O
by	O
nature	O
binary	B-General_Concept
algorithms	O
;	O
these	O
can	O
,	O
however	O
,	O
be	O
turned	O
into	O
multinomial	O
classifiers	B-General_Concept
by	O
a	O
variety	O
of	O
strategies	O
.	O
</s>
<s>
Multiclass	B-General_Concept
classification	I-General_Concept
should	O
not	O
be	O
confused	O
with	O
multi-label	B-Algorithm
classification	I-Algorithm
,	O
where	O
multiple	O
labels	O
are	O
to	O
be	O
predicted	O
for	O
each	O
instance	O
.	O
</s>
<s>
hierarchical	B-Algorithm
classification	I-Algorithm
.	O
</s>
<s>
This	O
section	O
discusses	O
strategies	O
for	O
reducing	O
the	O
problem	O
of	O
multiclass	B-General_Concept
classification	I-General_Concept
to	O
multiple	O
binary	B-General_Concept
classification	I-General_Concept
problems	O
.	O
</s>
<s>
The	O
techniques	O
developed	O
based	O
on	O
reducing	O
the	O
multi-class	O
problem	O
into	O
multiple	O
binary	B-General_Concept
problems	O
can	O
also	O
be	O
called	O
problem	O
transformation	O
techniques	O
.	O
</s>
<s>
One-vs.-rest	O
(	O
OvR	O
or	O
one-vs.-all	O
,	O
OvA	O
or	O
one-against-all	O
,	O
OAA	O
)	O
strategy	O
involves	O
training	O
a	O
single	O
classifier	B-General_Concept
per	O
class	O
,	O
with	O
the	O
samples	O
of	O
that	O
class	O
as	O
positive	O
samples	O
and	O
all	O
other	O
samples	O
as	O
negatives	O
.	O
</s>
<s>
This	O
strategy	O
requires	O
the	O
base	O
classifiers	B-General_Concept
to	O
produce	O
a	O
real-valued	O
confidence	O
score	O
for	O
its	O
decision	O
,	O
rather	O
than	O
just	O
a	O
class	O
label	O
;	O
discrete	O
class	O
labels	O
alone	O
can	O
lead	O
to	O
ambiguities	O
,	O
where	O
multiple	O
classes	O
are	O
predicted	O
for	O
a	O
single	O
sample	O
.	O
</s>
<s>
In	O
pseudocode	O
,	O
the	O
training	O
algorithm	O
for	O
an	O
OvR	O
learner	O
constructed	O
from	O
a	O
binary	B-General_Concept
classification	I-General_Concept
learner	O
is	O
as	O
follows	O
:	O
</s>
<s>
Making	O
decisions	O
means	O
applying	O
all	O
classifiers	B-General_Concept
to	O
an	O
unseen	O
sample	O
and	O
predicting	O
the	O
label	O
for	O
which	O
the	O
corresponding	O
classifier	B-General_Concept
reports	O
the	O
highest	O
confidence	O
score	O
:	O
</s>
<s>
Although	O
this	O
strategy	O
is	O
popular	O
,	O
it	O
is	O
a	O
heuristic	B-Algorithm
that	O
suffers	O
from	O
several	O
problems	O
.	O
</s>
<s>
Firstly	O
,	O
the	O
scale	O
of	O
the	O
confidence	O
values	O
may	O
differ	O
between	O
the	O
binary	B-General_Concept
classifiers	I-General_Concept
.	O
</s>
<s>
Second	O
,	O
even	O
if	O
the	O
class	O
distribution	O
is	O
balanced	O
in	O
the	O
training	O
set	O
,	O
the	O
binary	B-General_Concept
classification	I-General_Concept
learners	O
see	O
unbalanced	O
distributions	O
because	O
typically	O
the	O
set	O
of	O
negatives	O
they	O
see	O
is	O
much	O
larger	O
than	O
the	O
set	O
of	O
positives	O
.	O
</s>
<s>
In	O
the	O
one-vs.-one	O
(	O
OvO	O
)	O
reduction	O
,	O
one	O
trains	O
binary	B-General_Concept
classifiers	I-General_Concept
for	O
a	O
-way	O
multiclass	B-General_Concept
problem	I-General_Concept
;	O
each	O
receives	O
the	O
samples	O
of	O
a	O
pair	O
of	O
classes	O
from	O
the	O
original	O
training	O
set	O
,	O
and	O
must	O
learn	O
to	O
distinguish	O
these	O
two	O
classes	O
.	O
</s>
<s>
At	O
prediction	O
time	O
,	O
a	O
voting	O
scheme	O
is	O
applied	O
:	O
all	O
classifiers	B-General_Concept
are	O
applied	O
to	O
an	O
unseen	O
sample	O
and	O
the	O
class	O
that	O
got	O
the	O
highest	O
number	O
of	O
"	O
+1	O
"	O
predictions	O
gets	O
predicted	O
by	O
the	O
combined	O
classifier	B-General_Concept
.	O
</s>
<s>
This	O
section	O
discusses	O
strategies	O
of	O
extending	O
the	O
existing	O
binary	B-General_Concept
classifiers	I-General_Concept
to	O
solve	O
multi-class	B-General_Concept
classification	I-General_Concept
problems	O
.	O
</s>
<s>
Several	O
algorithms	O
have	O
been	O
developed	O
based	O
on	O
neural	B-Architecture
networks	I-Architecture
,	O
decision	B-Algorithm
trees	I-Algorithm
,	O
k-nearest	B-General_Concept
neighbors	I-General_Concept
,	O
naive	B-General_Concept
Bayes	I-General_Concept
,	O
support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
and	O
extreme	B-Algorithm
learning	I-Algorithm
machines	I-Algorithm
to	O
address	O
multi-class	B-General_Concept
classification	I-General_Concept
problems	O
.	O
</s>
<s>
Instead	O
of	O
just	O
having	O
one	O
neuron	O
in	O
the	O
output	O
layer	O
,	O
with	O
binary	B-General_Concept
output	O
,	O
one	O
could	O
have	O
N	O
binary	B-General_Concept
neurons	O
leading	O
to	O
multi-class	B-General_Concept
classification	I-General_Concept
.	O
</s>
<s>
In	O
practice	O
,	O
the	O
last	O
layer	O
of	O
a	O
neural	B-Architecture
network	I-Architecture
is	O
usually	O
a	O
softmax	B-Algorithm
function	I-Algorithm
layer	O
,	O
which	O
is	O
the	O
algebraic	O
simplification	O
of	O
N	O
logistic	O
classifiers	B-General_Concept
,	O
normalized	O
per	O
class	O
by	O
the	O
sum	O
of	O
the	O
N-1	O
other	O
logistic	O
classifiers	B-General_Concept
.	O
</s>
<s>
Extreme	B-Algorithm
learning	I-Algorithm
machines	I-Algorithm
(	O
ELM	O
)	O
is	O
a	O
special	O
case	O
of	O
single	O
hidden	O
layer	O
feed-forward	O
neural	B-Architecture
networks	I-Architecture
(	O
SLFNs	O
)	O
wherein	O
the	O
input	O
weights	O
and	O
the	O
hidden	O
node	O
biases	O
can	O
be	O
chosen	O
at	O
random	O
.	O
</s>
<s>
Many	O
variants	O
and	O
developments	O
are	O
made	O
to	O
the	O
ELM	O
for	O
multiclass	B-General_Concept
classification	I-General_Concept
.	O
</s>
<s>
k-nearest	B-General_Concept
neighbors	I-General_Concept
kNN	O
is	O
considered	O
among	O
the	O
oldest	O
non-parametric	O
classification	O
algorithms	O
.	O
</s>
<s>
Naive	B-General_Concept
Bayes	I-General_Concept
is	O
a	O
successful	O
classifier	B-General_Concept
based	O
upon	O
the	O
principle	O
of	O
maximum	O
a	O
posteriori	O
(	O
MAP	O
)	O
.	O
</s>
<s>
Decision	B-Algorithm
tree	I-Algorithm
learning	I-Algorithm
is	O
a	O
powerful	O
classification	O
technique	O
.	O
</s>
<s>
The	O
tree	B-Application
tries	O
to	O
infer	O
a	O
split	O
of	O
the	O
training	O
data	O
based	O
on	O
the	O
values	O
of	O
the	O
available	O
features	O
to	O
produce	O
a	O
good	O
generalization	O
.	O
</s>
<s>
The	O
algorithm	O
can	O
naturally	O
handle	O
binary	B-General_Concept
or	O
multiclass	B-General_Concept
classification	I-General_Concept
problems	O
.	O
</s>
<s>
The	O
leaf	B-Application
nodes	I-Application
can	O
refer	O
to	O
any	O
of	O
the	O
K	O
classes	O
concerned	O
.	O
</s>
<s>
Support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
are	O
based	O
upon	O
the	O
idea	O
of	O
maximizing	O
the	O
margin	O
i.e.	O
</s>
<s>
The	O
basic	O
SVM	B-Algorithm
supports	O
only	O
binary	B-General_Concept
classification	I-General_Concept
,	O
but	O
extensions	O
have	O
been	O
proposed	O
to	O
handle	O
the	O
multiclass	B-General_Concept
classification	I-General_Concept
case	O
as	O
well	O
.	O
</s>
<s>
Multi	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
(	O
MEP	O
)	O
is	O
an	O
evolutionary	O
algorithm	O
for	O
generating	O
computer	O
programs	O
(	O
that	O
can	O
be	O
used	O
for	O
classification	O
tasks	O
too	O
)	O
.	O
</s>
<s>
Each	O
of	O
these	O
programs	O
can	O
be	O
used	O
to	O
generate	O
the	O
output	O
for	O
a	O
class	O
,	O
thus	O
making	O
MEP	O
naturally	O
suitable	O
for	O
solving	O
multi-class	B-General_Concept
classification	I-General_Concept
problems	O
.	O
</s>
<s>
Hierarchical	B-Algorithm
classification	I-Algorithm
tackles	O
the	O
multi-class	B-General_Concept
classification	I-General_Concept
problem	O
by	O
dividing	O
the	O
output	O
space	O
i.e.	O
</s>
<s>
into	O
a	O
tree	B-Application
.	O
</s>
<s>
Each	O
parent	B-Application
node	I-Application
is	O
divided	O
into	O
multiple	O
child	O
nodes	O
and	O
the	O
process	O
is	O
continued	O
until	O
each	O
child	O
node	O
represents	O
only	O
one	O
class	O
.	O
</s>
<s>
Several	O
methods	O
have	O
been	O
proposed	O
based	O
on	O
hierarchical	B-Algorithm
classification	I-Algorithm
.	O
</s>
<s>
Based	O
on	O
learning	O
paradigms	O
,	O
the	O
existing	O
multi-class	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
learning	I-Algorithm
.	O
</s>
<s>
The	O
online	B-Algorithm
learning	I-Algorithm
algorithms	O
,	O
on	O
the	O
other	O
hand	O
,	O
incrementally	O
build	O
their	O
models	O
in	O
sequential	O
iterations	O
.	O
</s>
