<s>
In	O
may	O
be	O
applied	O
in	O
fields	O
as	O
diverse	O
as	O
astronomy	O
,	O
with	O
its	O
studies	O
of	O
the	O
placement	O
of	O
galaxies	O
in	O
the	O
cosmos	B-Operating_System
,	O
or	O
to	O
chip	O
fabrication	O
engineering	O
,	O
with	O
its	O
use	O
of	O
"	O
place	O
and	O
route	O
"	O
algorithms	O
to	O
build	O
complex	O
wiring	O
structures	O
.	O
</s>
<s>
In	O
a	O
more	O
restricted	O
sense	O
,	O
spatial	O
analysis	O
is	O
geospatial	B-General_Concept
analysis	I-General_Concept
,	O
the	O
technique	O
applied	O
to	O
structures	O
at	O
the	O
human	O
scale	O
,	O
most	O
notably	O
in	O
the	O
analysis	O
of	O
geographic	B-General_Concept
data	I-General_Concept
.	O
</s>
<s>
Geographic	B-Application
information	I-Application
system	I-Application
is	O
currently	O
a	O
major	O
contributor	O
due	O
to	O
the	O
importance	O
of	O
geographic	O
software	O
in	O
the	O
modern	O
analytic	O
toolbox	O
.	O
</s>
<s>
Remote	B-Application
sensing	I-Application
has	O
contributed	O
extensively	O
in	O
morphometric	O
and	O
clustering	O
analysis	O
.	O
</s>
<s>
Computer	B-General_Concept
science	I-General_Concept
has	O
contributed	O
extensively	O
through	O
the	O
study	O
of	O
algorithms	O
,	O
notably	O
in	O
computational	O
geometry	O
.	O
</s>
<s>
Mathematics	O
continues	O
to	O
provide	O
the	O
fundamental	O
tools	O
for	O
analysis	O
and	O
to	O
reveal	O
the	O
complexity	O
of	O
the	O
spatial	O
realm	O
,	O
for	O
example	O
,	O
with	O
recent	O
work	O
on	O
fractals	B-Application
and	O
scale	O
invariance	O
.	O
</s>
<s>
The	O
fractal	B-Application
nature	O
of	O
coastline	O
makes	O
precise	O
measurements	O
of	O
its	O
length	O
difficult	O
if	O
not	O
impossible	O
.	O
</s>
<s>
When	O
results	O
are	O
presented	O
as	O
maps	O
,	O
the	O
presentation	O
combines	O
spatial	B-General_Concept
data	I-General_Concept
which	O
are	O
generally	O
accurate	O
with	O
analytic	O
results	O
which	O
may	O
be	O
inaccurate	O
,	O
leading	O
to	O
an	O
impression	O
that	O
analytic	O
results	O
are	O
more	O
accurate	O
than	O
the	O
data	O
would	O
indicate	O
.	O
</s>
<s>
Computer	O
tools	O
favor	O
the	O
spatial	O
definition	O
of	O
objects	O
as	O
homogeneous	B-General_Concept
and	O
separate	O
elements	O
because	O
of	O
the	O
limited	O
number	O
of	O
database	O
elements	O
and	O
computational	O
structures	O
available	O
,	O
and	O
the	O
ease	O
with	O
which	O
these	O
primitive	O
structures	O
can	O
be	O
created	O
.	O
</s>
<s>
Locational	O
effects	O
also	O
manifest	O
as	O
spatial	O
heterogeneity	B-General_Concept
,	O
or	O
the	O
apparent	O
variation	O
in	O
a	O
process	O
with	O
respect	O
to	O
location	O
in	O
geographic	O
space	O
.	O
</s>
<s>
Spatial	O
heterogeneity	B-General_Concept
means	O
that	O
overall	O
parameters	O
estimated	O
for	O
the	O
entire	O
system	O
may	O
not	O
adequately	O
describe	O
the	O
process	O
at	O
any	O
given	O
location	O
.	O
</s>
<s>
In	O
a	O
Geographic	B-Application
Information	I-Application
System	I-Application
,	O
the	O
analysis	O
can	O
be	O
done	O
quantitatively	O
.	O
</s>
<s>
The	O
second	O
dimension	O
of	O
spatial	O
association	O
(	O
SDA	O
)	O
reveals	O
the	O
association	O
between	O
spatial	O
variables	O
through	O
extracting	O
geographical	B-General_Concept
information	I-General_Concept
at	O
locations	O
outside	O
samples	O
.	O
</s>
<s>
SDA	O
effectively	O
uses	O
the	O
missing	O
geographical	B-General_Concept
information	I-General_Concept
outside	O
sample	O
locations	O
in	O
methods	O
of	O
the	O
first	O
dimension	O
of	O
spatial	O
association	O
(	O
FDA	O
)	O
,	O
which	O
explore	O
spatial	O
association	O
using	O
observations	O
at	O
sample	O
locations	O
.	O
</s>
<s>
Landscape	O
ecologists	O
developed	O
a	O
series	O
of	O
scale	O
invariant	O
metrics	O
for	O
aspects	O
of	O
ecology	O
that	O
are	O
fractal	B-Application
in	O
nature	O
.	O
</s>
<s>
Spatial	O
sampling	O
involves	O
determining	O
a	O
limited	O
number	O
of	O
locations	O
in	O
geographic	O
space	O
for	O
faithfully	O
measuring	O
phenomena	O
that	O
are	O
subject	O
to	O
dependency	O
and	O
heterogeneity	B-General_Concept
.	O
</s>
<s>
But	O
heterogeneity	B-General_Concept
suggests	O
that	O
this	O
relation	O
can	O
change	O
across	O
space	O
,	O
and	O
therefore	O
we	O
cannot	O
trust	O
an	O
observed	O
degree	O
of	O
dependency	O
beyond	O
a	O
region	O
that	O
may	O
be	O
small	O
.	O
</s>
<s>
For	O
example	O
,	O
a	O
pixel	B-Algorithm
represents	O
the	O
average	O
surface	O
temperatures	O
within	O
an	O
area	O
.	O
</s>
<s>
--	O
G	O
.	O
Upton	O
&	O
B	O
.	O
FingeltonGraham	O
J	O
.	O
Upton	O
&	O
Bernard	O
Fingelton	O
:	O
Spatial	B-General_Concept
Data	I-General_Concept
Analysis	O
by	O
Example	O
Volume	O
1	O
:	O
Point	O
Pattern	O
and	O
Quantitative	O
Data	O
John	O
Wiley	O
&	O
Sons	O
,	O
New	O
York	O
.	O
</s>
<s>
Urban	O
and	O
Regional	O
Studies	O
deal	O
with	O
large	O
tables	O
of	O
spatial	B-General_Concept
data	I-General_Concept
obtained	O
from	O
censuses	O
and	O
surveys	O
.	O
</s>
<s>
The	O
possibility	O
of	O
spatial	O
heterogeneity	B-General_Concept
suggests	O
that	O
the	O
estimated	O
degree	O
of	O
autocorrelation	O
may	O
vary	O
significantly	O
across	O
geographic	O
space	O
.	O
</s>
<s>
This	O
allows	O
assessment	O
of	O
the	O
spatial	O
heterogeneity	B-General_Concept
in	O
the	O
estimated	O
relationships	O
between	O
the	O
independent	O
and	O
dependent	O
variables	O
.	O
</s>
<s>
The	O
use	O
of	O
Bayesian	O
hierarchical	O
modeling	O
in	O
conjunction	O
with	O
Markov	B-General_Concept
chain	I-General_Concept
Monte	I-General_Concept
Carlo	I-General_Concept
(	O
MCMC	O
)	O
methods	O
have	O
recently	O
shown	O
to	O
be	O
effective	O
in	O
modeling	O
complex	O
relationships	O
using	O
Poisson-Gamma-CAR	O
,	O
Poisson-lognormal-SAR	O
,	O
or	O
Overdispersed	O
logit	O
models	O
.	O
</s>
<s>
Statistical	O
packages	O
for	O
implementing	O
such	O
Bayesian	O
models	O
using	O
MCMC	O
include	O
WinBugs	B-Algorithm
,	O
CrimeStat	O
and	O
many	O
packages	O
available	O
via	O
R	B-Language
programming	I-Language
language	I-Language
.	O
</s>
<s>
Spatial	O
stochastic	O
processes	O
,	O
such	O
as	O
Gaussian	B-General_Concept
processes	I-General_Concept
are	O
also	O
increasingly	O
being	O
deployed	O
in	O
spatial	O
regression	O
analysis	O
.	O
</s>
<s>
Spatial	O
stochastic	O
process	O
can	O
become	O
computationally	O
effective	O
and	O
scalable	O
Gaussian	B-General_Concept
process	I-General_Concept
models	O
,	O
such	O
as	O
Gaussian	O
Predictive	O
Processes	O
and	O
Nearest	O
Neighbor	O
Gaussian	B-General_Concept
Processes	I-General_Concept
(	O
NNGP	O
)	O
.	O
</s>
<s>
Geospatial	B-General_Concept
and	O
hydrospatial	O
analysis	O
,	O
or	O
just	O
spatial	O
analysis	O
,	O
is	O
an	O
approach	O
to	O
applying	O
statistical	O
analysis	O
and	O
other	O
analytic	O
techniques	O
to	O
data	O
which	O
has	O
a	O
geographical	O
or	O
spatial	O
aspect	O
.	O
</s>
<s>
Such	O
analysis	O
would	O
typically	O
employ	O
software	O
capable	O
of	O
rendering	O
maps	O
processing	O
spatial	B-General_Concept
data	I-General_Concept
,	O
and	O
applying	O
analytical	O
methods	O
to	O
terrestrial	O
or	O
geographic	O
datasets	O
,	O
including	O
the	O
use	O
of	O
geographic	B-Application
information	I-Application
systems	I-Application
and	O
geomatics	O
.	O
</s>
<s>
Geographic	B-Application
information	I-Application
systems	I-Application
(	O
GIS	B-Application
)	O
—	O
a	O
large	O
domain	O
that	O
provides	O
a	O
variety	O
of	O
capabilities	O
designed	O
to	O
capture	O
,	O
store	O
,	O
manipulate	O
,	O
analyze	O
,	O
manage	O
,	O
and	O
present	O
all	O
types	O
of	O
geographical	B-General_Concept
data	I-General_Concept
—	O
utilizes	O
geospatial	B-General_Concept
and	O
hydrospatial	O
analysis	O
in	O
a	O
variety	O
of	O
contexts	O
,	O
operations	O
and	O
applications	O
.	O
</s>
<s>
Geospatial	B-General_Concept
and	O
Hydrospatial	O
analysis	O
,	O
using	O
GIS	B-Application
,	O
was	O
developed	O
for	O
problems	O
in	O
the	O
environmental	O
and	O
life	O
sciences	O
,	O
in	O
particular	O
ecology	O
,	O
geology	O
and	O
epidemiology	O
.	O
</s>
<s>
Vector-based	O
GIS	B-Application
is	O
typically	O
related	O
to	O
operations	O
such	O
as	O
map	O
overlay	O
(	O
combining	O
two	O
or	O
more	O
maps	O
or	O
map	O
layers	O
according	O
to	O
predefined	O
rules	O
)	O
,	O
simple	O
buffering	O
(	O
identifying	O
regions	O
of	O
a	O
map	O
within	O
a	O
specified	O
distance	O
of	O
one	O
or	O
more	O
features	O
,	O
such	O
as	O
towns	O
,	O
roads	O
or	O
rivers	O
)	O
and	O
similar	O
basic	O
operations	O
.	O
</s>
<s>
This	O
reflects	O
(	O
and	O
is	O
reflected	O
in	O
)	O
the	O
use	O
of	O
the	O
term	O
spatial	O
analysis	O
within	O
the	O
Open	O
Geospatial	B-General_Concept
Consortium	O
(	O
OGC	O
)	O
“	O
simple	O
feature	O
specifications	O
”	O
.	O
</s>
<s>
For	O
raster-based	O
GIS	B-Application
,	O
widely	O
used	O
in	O
the	O
environmental	O
sciences	O
and	O
remote	B-Application
sensing	I-Application
,	O
this	O
typically	O
means	O
a	O
range	O
of	O
actions	O
applied	O
to	O
the	O
grid	O
cells	O
of	O
one	O
or	O
more	O
maps	O
(	O
or	O
images	O
)	O
often	O
involving	O
filtering	O
and/or	O
algebraic	O
operations	O
(	O
map	O
algebra	O
)	O
.	O
</s>
<s>
Spatial	O
analysis	O
includes	O
a	O
large	O
variety	O
of	O
statistical	O
techniques	O
(	O
descriptive	O
,	O
exploratory	B-General_Concept
,	O
and	O
explanatory	O
statistics	O
)	O
that	O
apply	O
to	O
data	O
that	O
vary	O
spatially	O
and	O
which	O
can	O
vary	O
over	O
time	O
.	O
</s>
<s>
Geospatial	B-General_Concept
and	O
Hydrospatial	O
analysis	O
goes	O
beyond	O
2D	O
and	O
3D	O
mapping	O
operations	O
and	O
spatial	O
statistics	O
.	O
</s>
<s>
Surface	O
analysis	O
—	O
in	O
particular	O
analysing	O
the	O
properties	O
of	O
physical	O
surfaces	O
,	O
such	O
as	O
gradient	O
,	O
aspect	O
and	O
visibility	B-Application
,	O
and	O
analysing	O
surface-like	O
data	O
“	O
fields	O
”	O
;	O
</s>
<s>
GIS-based	O
network	O
analysis	O
may	O
be	O
used	O
to	O
address	O
a	O
wide	O
range	O
of	O
practical	O
problems	O
such	O
as	O
route	O
selection	O
and	O
facility	O
location	O
(	O
core	O
topics	O
in	O
the	O
field	O
of	O
operations	O
research	O
)	O
,	O
and	O
problems	O
involving	O
flows	O
such	O
as	O
those	O
found	O
in	O
Hydrospatial	O
and	O
hydrology	O
and	O
transportation	O
research	O
.	O
</s>
<s>
GIS	B-Application
packages	O
increasingly	O
provide	O
a	O
range	O
of	O
such	O
tools	O
,	O
providing	O
static	O
or	O
rotating	O
views	O
,	O
draping	O
images	O
over	O
2.5D	O
surface	O
representations	O
,	O
providing	O
animations	O
and	O
fly-throughs	O
,	O
dynamic	O
linking	O
and	O
brushing	O
and	O
spatio-temporal	O
visualisations	O
.	O
</s>
<s>
Traditionally	O
geospatial	B-General_Concept
and	O
hydrospatial	O
computing	O
has	O
been	O
performed	O
primarily	O
on	O
personal	O
computers	O
(	O
PCs	O
)	O
or	O
servers	O
.	O
</s>
<s>
Due	O
to	O
the	O
increasing	O
capabilities	O
of	O
mobile	O
devices	O
,	O
however	O
,	O
geospatial	B-General_Concept
computing	O
in	O
mobile	O
devices	O
is	O
a	O
fast-growing	O
trend	O
.	O
</s>
<s>
The	O
portable	O
nature	O
of	O
these	O
devices	O
,	O
as	O
well	O
as	O
the	O
presence	O
of	O
useful	O
sensors	O
,	O
such	O
as	O
Global	O
Navigation	O
Satellite	O
System	O
(	O
GNSS	O
)	O
receivers	O
and	O
barometric	O
pressure	O
sensors	O
,	O
make	O
them	O
useful	O
for	O
capturing	O
and	O
processing	O
geospatial	B-General_Concept
and	O
hydrospatial	O
information	O
in	O
the	O
field	O
.	O
</s>
<s>
In	O
addition	O
to	O
the	O
local	O
processing	O
of	O
geospatial	B-General_Concept
information	I-General_Concept
on	O
mobile	O
devices	O
,	O
another	O
growing	O
trend	O
is	O
cloud-based	O
geospatial	B-General_Concept
computing	O
.	O
</s>
<s>
In	O
a	O
similar	O
manner	O
,	O
geospatial	B-General_Concept
and	O
hydrospatial	O
information	O
can	O
be	O
made	O
available	O
to	O
connected	O
mobile	O
devices	O
via	O
the	O
cloud	O
,	O
allowing	O
access	O
to	O
vast	O
databases	O
of	O
geospatial	B-General_Concept
and	O
hydrospatial	O
information	O
anywhere	O
where	O
a	O
wireless	O
data	O
connection	O
is	O
available	O
.	O
</s>
<s>
Geographic	B-Application
information	I-Application
systems	I-Application
(	O
GIS	B-Application
)	O
and	O
the	O
underlying	O
geographic	B-General_Concept
information	I-General_Concept
science	O
that	O
advances	O
these	O
technologies	O
have	O
a	O
strong	O
influence	O
on	O
spatial	O
analysis	O
.	O
</s>
<s>
The	O
increasing	O
ability	O
to	O
capture	O
and	O
handle	O
geographic	B-General_Concept
data	I-General_Concept
means	O
that	O
spatial	O
analysis	O
is	O
occurring	O
within	O
increasingly	O
data-rich	O
environments	O
.	O
</s>
<s>
Geographic	B-General_Concept
data	I-General_Concept
capture	O
systems	O
include	O
remotely	O
sensed	O
imagery	O
,	O
environmental	O
monitoring	O
systems	O
such	O
as	O
intelligent	O
transportation	O
systems	O
,	O
and	O
location-aware	O
technologies	O
such	O
as	O
mobile	O
devices	O
that	O
can	O
report	O
location	O
in	O
near-real	O
time	O
.	O
</s>
<s>
GIS	B-Application
provide	O
platforms	O
for	O
managing	O
these	O
data	O
,	O
computing	O
spatial	O
relationships	O
such	O
as	O
distance	O
,	O
connectivity	O
and	O
directional	O
relationships	O
between	O
spatial	O
units	O
,	O
and	O
visualizing	O
both	O
the	O
raw	O
data	O
and	O
spatial	O
analytic	O
results	O
within	O
a	O
cartographic	O
context	O
.	O
</s>
<s>
Geovisualization	O
(	O
GVis	O
)	O
combines	O
scientific	O
visualization	O
with	O
digital	O
cartography	O
to	O
support	O
the	O
exploration	O
and	O
analysis	O
of	O
geographic	B-General_Concept
data	I-General_Concept
and	I-General_Concept
information	I-General_Concept
,	O
including	O
the	O
results	O
of	O
spatial	O
analysis	O
or	O
simulation	O
.	O
</s>
<s>
GVis	O
leverages	O
the	O
human	O
orientation	O
towards	O
visual	O
information	O
processing	O
in	O
the	O
exploration	O
,	O
analysis	O
and	O
communication	O
of	O
geographic	B-General_Concept
data	I-General_Concept
and	I-General_Concept
information	I-General_Concept
.	O
</s>
<s>
Geographic	O
knowledge	O
discovery	O
(	O
GKD	O
)	O
is	O
the	O
human-centered	O
process	O
of	O
applying	O
efficient	O
computational	O
tools	O
for	O
exploring	O
massive	O
spatial	B-Algorithm
databases	I-Algorithm
.	O
</s>
<s>
GKD	O
includes	O
geographic	B-General_Concept
data	I-General_Concept
mining	O
,	O
but	O
also	O
encompasses	O
related	O
activities	O
such	O
as	O
data	O
selection	O
,	O
data	O
cleaning	O
and	O
pre-processing	O
,	O
and	O
interpretation	O
of	O
results	O
.	O
</s>
<s>
Spatial	B-Application
decision	I-Application
support	I-Application
systems	I-Application
(	O
SDSS	O
)	O
take	O
existing	O
spatial	B-General_Concept
data	I-General_Concept
and	O
use	O
a	O
variety	O
of	O
mathematical	O
models	O
to	O
make	O
projections	O
into	O
the	O
future	O
.	O
</s>
