<s>
Category	B-General_Concept
utility	I-General_Concept
is	O
a	O
measure	O
of	O
"	O
category	B-General_Concept
goodness	I-General_Concept
"	O
defined	O
in	O
and	O
.	O
</s>
<s>
It	O
was	O
intended	O
to	O
supersede	O
more	O
limited	O
measures	O
of	O
category	B-General_Concept
goodness	I-General_Concept
such	O
as	O
"	O
cue	O
validity	O
"	O
(	O
;	O
)	O
and	O
"	O
collocation	O
index	O
"	O
.	O
</s>
<s>
In	O
this	O
sense	O
the	O
motivation	O
for	O
the	O
category	B-General_Concept
utility	I-General_Concept
measure	O
is	O
similar	O
to	O
the	O
information	B-Algorithm
gain	I-Algorithm
metric	O
used	O
in	O
decision	B-Algorithm
tree	I-Algorithm
learning	O
.	O
</s>
<s>
A	O
review	O
of	O
category	B-General_Concept
utility	I-General_Concept
in	O
its	O
probabilistic	O
incarnation	O
,	O
with	O
applications	O
to	O
machine	O
learning	O
,	O
is	O
provided	O
in	O
.	O
</s>
<s>
The	O
probability-theoretic	O
definition	O
of	O
category	B-General_Concept
utility	I-General_Concept
given	O
in	O
and	O
is	O
as	O
follows	O
:	O
</s>
<s>
The	O
motivation	O
and	O
development	O
of	O
this	O
expression	O
for	O
category	B-General_Concept
utility	I-General_Concept
,	O
and	O
the	O
role	O
of	O
the	O
multiplicand	O
as	O
a	O
crude	O
overfitting	O
control	O
,	O
is	O
given	O
in	O
the	O
above	O
sources	O
.	O
</s>
<s>
Loosely	O
,	O
the	O
term	O
is	O
the	O
expected	O
number	O
of	O
attribute	O
values	O
that	O
can	O
be	O
correctly	O
guessed	O
by	O
an	O
observer	O
using	O
a	O
probability-matching	B-General_Concept
strategy	O
together	O
with	O
knowledge	O
of	O
the	O
category	O
labels	O
,	O
while	O
is	O
the	O
expected	O
number	O
of	O
attribute	O
values	O
that	O
can	O
be	O
correctly	O
guessed	O
by	O
an	O
observer	O
the	O
same	O
strategy	O
but	O
without	O
any	O
knowledge	O
of	O
the	O
category	O
labels	O
.	O
</s>
<s>
The	O
information-theoretic	O
definition	O
of	O
category	B-General_Concept
utility	I-General_Concept
for	O
a	O
set	O
of	O
entities	O
with	O
size	O
-	O
binary	O
feature	O
set	O
,	O
and	O
a	O
binary	O
category	O
is	O
given	O
in	O
as	O
follows	O
:	O
</s>
<s>
The	O
value	O
of	O
the	O
category	B-General_Concept
utility	I-General_Concept
will	O
,	O
in	O
the	O
above	O
formulation	O
,	O
be	O
negative	O
(	O
???	O
</s>
<s>
and	O
mention	O
that	O
the	O
category	B-General_Concept
utility	I-General_Concept
is	O
equivalent	O
to	O
the	O
mutual	O
information	O
.	O
</s>
<s>
If	O
the	O
original	O
definition	O
of	O
the	O
category	B-General_Concept
utility	I-General_Concept
from	O
above	O
is	O
rewritten	O
with	O
,	O
</s>
<s>
This	O
equation	O
clearly	O
has	O
the	O
same	O
form	O
as	O
the	O
(	O
blue	O
)	O
equation	O
expressing	O
the	O
mutual	O
information	O
between	O
the	O
feature	O
set	O
and	O
the	O
category	O
variable	O
;	O
the	O
difference	O
is	O
that	O
the	O
sum	O
in	O
the	O
category	B-General_Concept
utility	I-General_Concept
equation	O
runs	O
over	O
independent	O
binary	O
variables	O
,	O
whereas	O
the	O
sum	O
in	O
the	O
mutual	O
information	O
runs	O
over	O
values	O
of	O
the	O
single	O
-ary	O
variable	O
.	O
</s>
<s>
Like	O
the	O
mutual	O
information	O
,	O
the	O
category	B-General_Concept
utility	I-General_Concept
is	O
not	O
sensitive	O
to	O
any	O
ordering	O
in	O
the	O
feature	O
or	O
category	O
variable	O
values	O
.	O
</s>
<s>
That	O
is	O
,	O
as	O
far	O
as	O
the	O
category	B-General_Concept
utility	I-General_Concept
is	O
concerned	O
,	O
the	O
category	O
set	O
 { small , medium , large , jumbo } 	O
is	O
not	O
qualitatively	O
different	O
from	O
the	O
category	O
set	O
 { desk , fish , tree , mop } 	O
since	O
the	O
formulation	O
of	O
the	O
category	B-General_Concept
utility	I-General_Concept
does	O
not	O
account	O
for	O
any	O
ordering	O
of	O
the	O
class	O
variable	O
.	O
</s>
<s>
As	O
far	O
as	O
the	O
category	B-General_Concept
utility	I-General_Concept
or	O
mutual	O
information	O
are	O
concerned	O
,	O
all	O
category	O
and	O
feature	O
variables	O
are	O
nominal	O
variables	O
.	O
</s>
<s>
For	O
this	O
reason	O
,	O
category	B-General_Concept
utility	I-General_Concept
does	O
not	O
reflect	O
any	O
gestalt	O
aspects	O
of	O
"	O
category	B-General_Concept
goodness	I-General_Concept
"	O
that	O
might	O
be	O
based	O
on	O
such	O
ordering	O
effects	O
.	O
</s>
<s>
This	O
section	O
provides	O
some	O
background	O
on	O
the	O
origins	O
of	O
,	O
and	O
need	O
for	O
,	O
formal	O
measures	O
of	O
"	O
category	B-General_Concept
goodness	I-General_Concept
"	O
such	O
as	O
the	O
category	B-General_Concept
utility	I-General_Concept
,	O
and	O
some	O
of	O
the	O
history	O
that	O
lead	O
to	O
the	O
development	O
of	O
this	O
particular	O
metric	O
.	O
</s>
<s>
Such	O
abstractions	B-Application
do	O
not	O
designate	O
any	O
particular	O
individual	O
in	O
the	O
world	O
,	O
and	O
yet	O
we	O
can	O
scarcely	O
imagine	O
being	O
able	O
to	O
comprehend	O
the	O
world	O
without	O
their	O
use	O
.	O
</s>
<s>
The	O
question	O
of	O
locus	O
was	O
an	O
important	O
issue	O
on	O
which	O
the	O
classical	O
schools	O
of	O
Plato	B-Operating_System
and	O
Aristotle	O
famously	O
differed	O
.	O
</s>
<s>
From	O
this	O
base	O
,	O
Mill	O
reaches	O
the	O
following	O
conclusion	O
,	O
which	O
foreshadows	O
much	O
subsequent	O
thinking	O
about	O
category	B-General_Concept
goodness	I-General_Concept
,	O
including	O
the	O
notion	O
of	O
category	B-General_Concept
utility	I-General_Concept
:	O
</s>
<s>
One	O
may	O
compare	O
this	O
to	O
the	O
"	O
category	B-General_Concept
utility	I-General_Concept
hypothesis	O
"	O
proposed	O
by	O
:	O
"	O
A	O
category	O
is	O
useful	O
to	O
the	O
extent	O
that	O
it	O
can	O
be	O
expected	O
to	O
improve	O
the	O
ability	O
of	O
a	O
person	O
to	O
accurately	O
predict	O
the	O
features	O
of	O
instances	O
of	O
that	O
category.	O
"	O
</s>
<s>
One	O
may	O
also	O
compare	O
this	O
idea	O
to	O
Aristotle	O
's	O
criterion	O
of	O
counter-predication	O
for	O
definitional	O
predicates	O
,	O
as	O
well	O
as	O
to	O
the	O
notion	O
of	O
concepts	O
described	O
in	O
formal	B-Algorithm
concept	I-Algorithm
analysis	I-Algorithm
.	O
</s>
<s>
A	O
variety	O
of	O
different	O
measures	O
have	O
been	O
suggested	O
with	O
an	O
aim	O
of	O
formally	O
capturing	O
this	O
notion	O
of	O
"	O
category	B-General_Concept
goodness	I-General_Concept
,	O
"	O
the	O
best	O
known	O
of	O
which	O
is	O
probably	O
the	O
"	O
cue	O
validity	O
"	O
.	O
</s>
<s>
The	O
category	B-General_Concept
utility	I-General_Concept
was	O
introduced	O
as	O
a	O
more	O
sophisticated	O
refinement	O
of	O
the	O
cue	O
validity	O
,	O
which	O
attempts	O
to	O
more	O
rigorously	O
quantify	O
the	O
full	O
inferential	O
power	O
of	O
a	O
class	O
structure	O
.	O
</s>
<s>
As	O
shown	O
above	O
,	O
on	O
a	O
certain	O
view	O
the	O
category	B-General_Concept
utility	I-General_Concept
is	O
equivalent	O
to	O
the	O
mutual	O
information	O
between	O
the	O
feature	O
variable	O
and	O
the	O
category	O
variable	O
.	O
</s>
<s>
It	O
has	O
been	O
suggested	O
that	O
categories	O
having	O
the	O
greatest	O
overall	O
category	B-General_Concept
utility	I-General_Concept
are	O
those	O
that	O
are	O
not	O
only	O
those	O
"	O
best	O
"	O
in	O
a	O
normative	O
sense	O
,	O
but	O
also	O
those	O
human	O
learners	O
prefer	O
to	O
use	O
,	O
e.g.	O
,	O
"	O
basic	O
"	O
categories	O
.	O
</s>
<s>
Other	O
related	O
measures	O
of	O
category	B-General_Concept
goodness	I-General_Concept
are	O
"	O
cohesion	O
"	O
(	O
;	O
)	O
and	O
"	O
salience	O
"	O
.	O
</s>
<s>
Category	O
utilility	O
is	O
used	O
as	O
the	O
category	O
evaluation	O
measure	O
in	O
the	O
popular	O
conceptual	B-Algorithm
clustering	I-Algorithm
algorithm	O
called	O
COBWEB	O
.	O
</s>
