<s>
Ordering	O
points	O
to	O
identify	O
the	O
clustering	O
structure	O
(	O
OPTICS	B-Algorithm
)	O
is	O
an	O
algorithm	O
for	O
finding	O
density-based	O
clusters	B-Algorithm
in	O
spatial	O
data	O
.	O
</s>
<s>
Its	O
basic	O
idea	O
is	O
similar	O
to	O
DBSCAN	B-Algorithm
,	O
but	O
it	O
addresses	O
one	O
of	O
DBSCAN	B-Algorithm
's	O
major	O
weaknesses	O
:	O
the	O
problem	O
of	O
detecting	O
meaningful	O
clusters	B-Algorithm
in	O
data	O
of	O
varying	O
density	O
.	O
</s>
<s>
This	O
is	O
represented	O
as	O
a	O
dendrogram	B-Application
.	O
</s>
<s>
Like	O
DBSCAN	B-Algorithm
,	O
OPTICS	B-Algorithm
requires	O
two	O
parameters	O
:	O
,	O
which	O
describes	O
the	O
maximum	O
distance	O
(	O
radius	O
)	O
to	O
consider	O
,	O
and	O
,	O
describing	O
the	O
number	O
of	O
points	O
required	O
to	O
form	O
a	O
cluster	O
.	O
</s>
<s>
In	O
contrast	O
to	O
DBSCAN	B-Algorithm
,	O
OPTICS	B-Algorithm
also	O
considers	O
points	O
that	O
are	O
part	O
of	O
a	O
more	O
densely	O
packed	O
cluster	O
,	O
so	O
each	O
point	O
is	O
assigned	O
a	O
core	O
distance	O
that	O
describes	O
the	O
distance	O
to	O
the	O
th	O
closest	O
point	O
:	O
</s>
<s>
Hence	O
,	O
the	O
parameter	O
is	O
required	O
to	O
cut	O
off	O
the	O
density	O
of	O
clusters	B-Algorithm
that	O
are	O
no	O
longer	O
interesting	O
,	O
and	O
to	O
speed	O
up	O
the	O
algorithm	O
.	O
</s>
<s>
OPTICS	B-Algorithm
abstracts	O
from	O
DBSCAN	B-Algorithm
by	O
removing	O
this	O
parameter	O
,	O
at	O
least	O
to	O
the	O
extent	O
of	O
only	O
having	O
to	O
give	O
the	O
maximum	O
value	O
.	O
</s>
<s>
The	O
basic	O
approach	O
of	O
OPTICS	B-Algorithm
is	O
similar	O
to	O
DBSCAN	B-Algorithm
,	O
but	O
instead	O
of	O
maintaining	O
known	O
,	O
but	O
so	O
far	O
unprocessed	O
cluster	O
members	O
in	O
a	O
set	O
,	O
they	O
are	O
maintained	O
in	O
a	O
priority	B-Application
queue	I-Application
(	O
e.g.	O
</s>
<s>
using	O
an	O
indexed	O
heap	B-Application
)	O
.	O
</s>
<s>
In	O
update( )	O
,	O
the	O
priority	B-Application
queue	I-Application
Seeds	O
is	O
updated	O
with	O
the	O
-neighborhood	O
of	O
and	O
,	O
respectively	O
:	O
</s>
<s>
OPTICS	B-Algorithm
hence	O
outputs	O
the	O
points	O
in	O
a	O
particular	O
ordering	O
,	O
annotated	O
with	O
their	O
smallest	O
reachability	O
distance	O
(	O
in	O
the	O
original	O
algorithm	O
,	O
the	O
core	O
distance	O
is	O
also	O
exported	O
,	O
but	O
this	O
is	O
not	O
required	O
for	O
further	O
processing	O
)	O
.	O
</s>
<s>
Using	O
a	O
reachability-plot	O
(	O
a	O
special	O
kind	O
of	O
dendrogram	B-Application
)	O
,	O
the	O
hierarchical	B-Algorithm
structure	O
of	O
the	O
clusters	B-Algorithm
can	O
be	O
obtained	O
easily	O
.	O
</s>
<s>
It	O
is	O
a	O
2D	O
plot	O
,	O
with	O
the	O
ordering	O
of	O
the	O
points	O
as	O
processed	O
by	O
OPTICS	B-Algorithm
on	O
the	O
x-axis	O
and	O
the	O
reachability	O
distance	O
on	O
the	O
y-axis	O
.	O
</s>
<s>
Since	O
points	O
belonging	O
to	O
a	O
cluster	O
have	O
a	O
low	O
reachability	O
distance	O
to	O
their	O
nearest	O
neighbor	O
,	O
the	O
clusters	B-Algorithm
show	O
up	O
as	O
valleys	O
in	O
the	O
reachability	O
plot	O
.	O
</s>
<s>
The	O
upper	O
right	O
part	O
visualizes	O
the	O
spanning	O
tree	O
produced	O
by	O
OPTICS	B-Algorithm
,	O
and	O
the	O
lower	O
part	O
shows	O
the	O
reachability	O
plot	O
as	O
computed	O
by	O
OPTICS	B-Algorithm
.	O
</s>
<s>
Colors	O
in	O
this	O
plot	O
are	O
labels	O
,	O
and	O
not	O
computed	O
by	O
the	O
algorithm	O
;	O
but	O
it	O
is	O
well	O
visible	O
how	O
the	O
valleys	O
in	O
the	O
plot	O
correspond	O
to	O
the	O
clusters	B-Algorithm
in	O
above	O
data	O
set	O
.	O
</s>
<s>
They	O
are	O
usually	O
not	O
assigned	O
to	O
clusters	B-Algorithm
,	O
except	O
the	O
omnipresent	O
"	O
all	O
data	O
"	O
cluster	O
in	O
a	O
hierarchical	B-Algorithm
result	O
.	O
</s>
<s>
Extracting	O
clusters	B-Algorithm
from	O
this	O
plot	O
can	O
be	O
done	O
manually	O
by	O
selecting	O
a	O
range	O
on	O
the	O
x-axis	O
after	O
visual	O
inspection	O
,	O
by	O
selecting	O
a	O
threshold	O
on	O
the	O
y-axis	O
(	O
the	O
result	O
is	O
then	O
similar	O
to	O
a	O
DBSCAN	B-Algorithm
clustering	O
result	O
with	O
the	O
same	O
and	O
parameters	O
;	O
here	O
a	O
value	O
of	O
0.1	O
may	O
yield	O
good	O
results	O
)	O
,	O
or	O
by	O
different	O
algorithms	O
that	O
try	O
to	O
detect	O
the	O
valleys	O
by	O
steepness	O
,	O
knee	O
detection	O
,	O
or	O
local	O
maxima	O
.	O
</s>
<s>
Clusterings	O
obtained	O
this	O
way	O
usually	O
are	O
hierarchical	B-Algorithm
,	O
and	O
cannot	O
be	O
achieved	O
by	O
a	O
single	O
DBSCAN	B-Algorithm
run	O
.	O
</s>
<s>
Like	O
DBSCAN	B-Algorithm
,	O
OPTICS	B-Algorithm
processes	O
each	O
point	O
once	O
,	O
and	O
performs	O
one	O
-neighborhood	O
query	O
during	O
this	O
processing	O
.	O
</s>
<s>
The	O
authors	O
of	O
the	O
original	O
OPTICS	B-Algorithm
paper	O
report	O
an	O
actual	O
constant	O
slowdown	O
factor	O
of	O
1.6	O
compared	O
to	O
DBSCAN	B-Algorithm
.	O
</s>
<s>
Even	O
when	O
no	O
spatial	O
index	O
is	O
available	O
,	O
this	O
comes	O
at	O
additional	O
cost	O
in	O
managing	O
the	O
heap	B-Application
.	O
</s>
<s>
OPTICS-OF	O
is	O
an	O
outlier	B-Algorithm
detection	I-Algorithm
algorithm	O
based	O
on	O
OPTICS	B-Algorithm
.	O
</s>
<s>
The	O
main	O
use	O
is	O
the	O
extraction	O
of	O
outliers	O
from	O
an	O
existing	O
run	O
of	O
OPTICS	B-Algorithm
at	O
low	O
cost	O
compared	O
to	O
using	O
a	O
different	O
outlier	B-Algorithm
detection	I-Algorithm
method	O
.	O
</s>
<s>
The	O
better	O
known	O
version	O
LOF	B-Algorithm
is	O
based	O
on	O
the	O
same	O
concepts	O
.	O
</s>
<s>
DeLi-Clu	O
,	O
Density-Link-Clustering	O
combines	O
ideas	O
from	O
single-linkage	B-Algorithm
clustering	I-Algorithm
and	O
OPTICS	B-Algorithm
,	O
eliminating	O
the	O
parameter	O
and	O
offering	O
performance	O
improvements	O
over	O
OPTICS	B-Algorithm
.	O
</s>
<s>
HiSC	O
is	O
a	O
hierarchical	B-Algorithm
subspace	O
clustering	O
(	O
axis-parallel	O
)	O
method	O
based	O
on	O
OPTICS	B-Algorithm
.	O
</s>
<s>
HiCO	O
is	O
a	O
hierarchical	B-Algorithm
correlation	B-Algorithm
clustering	I-Algorithm
algorithm	O
based	O
on	O
OPTICS	B-Algorithm
.	O
</s>
<s>
HDBSCAN*	O
is	O
based	O
on	O
a	O
refinement	O
of	O
DBSCAN	B-Algorithm
,	O
excluding	O
border-points	O
from	O
the	O
clusters	B-Algorithm
and	O
thus	O
following	O
more	O
strictly	O
the	O
basic	O
definition	O
of	O
density-levels	O
by	O
Hartigan	O
.	O
</s>
<s>
Java	O
implementations	O
of	O
OPTICS	B-Algorithm
,	O
OPTICS-OF	O
,	O
DeLi-Clu	O
,	O
HiSC	O
,	O
HiCO	O
and	O
DiSH	O
are	O
available	O
in	O
the	O
ELKI	B-Language
data	I-Language
mining	I-Language
framework	I-Language
(	O
with	O
index	O
acceleration	O
for	O
several	O
distance	O
functions	O
,	O
and	O
with	O
automatic	O
cluster	O
extraction	O
using	O
the	O
extraction	O
method	O
)	O
.	O
</s>
<s>
Other	O
Java	O
implementations	O
include	O
the	O
Weka	B-Language
extension	O
(	O
no	O
support	O
for	O
cluster	O
extraction	O
)	O
.	O
</s>
<s>
The	O
R	B-Language
package	O
"	O
dbscan	B-Algorithm
"	O
includes	O
a	O
C++	O
implementation	O
of	O
OPTICS	B-Algorithm
(	O
with	O
both	O
traditional	O
dbscan-like	O
and	O
cluster	O
extraction	O
)	O
using	O
a	O
k-d	B-Data_Structure
tree	I-Data_Structure
for	O
index	O
acceleration	O
for	O
Euclidean	O
distance	O
only	O
.	O
</s>
<s>
Python	O
implementations	O
of	O
OPTICS	B-Algorithm
are	O
available	O
in	O
the	O
library	O
and	O
in	O
scikit-learn	B-Application
.	O
</s>
