<s>
Data	B-General_Concept
reduction	I-General_Concept
is	O
the	O
transformation	O
of	O
numerical	O
or	O
alphabetical	O
digital	B-General_Concept
information	I-General_Concept
derived	O
empirically	O
or	O
experimentally	B-General_Concept
into	O
a	O
corrected	O
,	O
ordered	O
,	O
and	O
simplified	O
form	O
.	O
</s>
<s>
The	O
purpose	O
of	O
data	B-General_Concept
reduction	I-General_Concept
can	O
be	O
two-fold	O
:	O
reduce	O
the	O
number	O
of	O
data	O
records	O
by	O
eliminating	O
invalid	O
data	O
or	O
produce	O
summary	O
data	O
and	O
statistics	O
at	O
different	O
aggregation	O
levels	O
for	O
various	O
applications	O
.	O
</s>
<s>
When	O
the	O
data	O
are	O
already	O
in	O
digital	O
form	O
the	O
'	O
reduction	O
 '	O
of	O
the	O
data	O
typically	O
involves	O
some	O
editing	O
,	O
scaling	B-Algorithm
,	O
encoding	B-Algorithm
,	O
sorting	B-Algorithm
,	O
collating	O
,	O
and	O
producing	O
tabular	O
summaries	O
.	O
</s>
<s>
When	O
the	O
observations	O
are	O
discrete	O
but	O
the	O
underlying	O
phenomenon	O
is	O
continuous	O
then	O
smoothing	B-Application
and	O
interpolation	B-Algorithm
are	O
often	O
needed	O
.	O
</s>
<s>
The	O
data	B-General_Concept
reduction	I-General_Concept
is	O
often	O
undertaken	O
in	O
the	O
presence	O
of	O
reading	O
or	O
measurement	O
errors	O
.	O
</s>
<s>
An	O
example	O
in	O
astronomy	O
is	O
the	O
data	B-General_Concept
reduction	I-General_Concept
in	O
the	O
Kepler	O
satellite	O
.	O
</s>
<s>
The	O
on-board	O
data	B-General_Concept
reduction	I-General_Concept
encompasses	O
co-adding	O
the	O
raw	O
frames	O
for	O
thirty	O
minutes	O
,	O
reducing	O
the	O
bandwidth	O
by	O
a	O
factor	O
of	O
300	O
.	O
</s>
<s>
Research	O
has	O
also	O
been	O
carried	O
out	O
on	O
the	O
use	O
of	O
data	B-General_Concept
reduction	I-General_Concept
in	O
wearable	O
(	O
wireless	O
)	O
devices	O
for	O
health	O
monitoring	O
and	O
diagnosis	O
applications	O
.	O
</s>
<s>
For	O
example	O
,	O
in	O
the	O
context	O
of	O
epilepsy	O
diagnosis	O
,	O
data	B-General_Concept
reduction	I-General_Concept
has	O
been	O
used	O
to	O
increase	O
the	O
battery	O
lifetime	O
of	O
a	O
wearable	O
EEG	O
device	O
by	O
selecting	O
and	O
only	O
transmitting	O
,	O
EEG	O
data	O
that	O
is	O
relevant	O
for	O
diagnosis	O
and	O
discarding	O
background	O
activity	O
.	O
</s>
<s>
Dimensionality	B-Algorithm
reduction	I-Algorithm
helps	O
reduce	O
noise	O
in	O
the	O
data	O
and	O
allows	O
for	O
easier	O
visualization	O
,	O
such	O
as	O
the	O
example	O
below	O
where	O
3-dimensional	O
data	O
is	O
transformed	O
into	O
2	O
dimensions	O
to	O
show	O
hidden	O
parts	O
.	O
</s>
<s>
One	O
method	O
of	O
dimensionality	B-Algorithm
reduction	I-Algorithm
is	O
wavelet	B-Algorithm
transform	I-Algorithm
,	O
in	O
which	O
data	O
is	O
transformed	O
to	O
preserver	O
relative	O
distance	O
between	O
objects	O
at	O
different	O
levels	O
of	O
resolution	O
,	O
and	O
is	O
often	O
used	O
for	O
image	B-General_Concept
compression	I-General_Concept
.	O
</s>
<s>
This	O
method	O
of	O
data	B-General_Concept
reduction	I-General_Concept
reduces	O
the	O
data	O
volume	O
by	O
choosing	O
alternate	O
,	O
smaller	O
forms	O
of	O
data	O
representation	O
.	O
</s>
<s>
Data	B-General_Concept
reduction	I-General_Concept
can	O
be	O
obtained	O
by	O
assuming	O
a	O
statistical	O
model	O
for	O
the	O
data	O
.	O
</s>
<s>
Classical	O
principles	O
of	O
data	B-General_Concept
reduction	I-General_Concept
include	O
sufficiency	O
,	O
likelihood	O
,	O
conditionality	O
and	O
equivariance	O
.	O
</s>
