<s>
Fuzzy	B-Algorithm
clustering	I-Algorithm
by	O
Local	O
Approximation	O
of	O
MEmberships	O
(	O
FLAME	O
)	O
is	O
a	O
data	B-Algorithm
clustering	I-Algorithm
algorithm	O
that	O
defines	O
clusters	O
in	O
the	O
dense	O
parts	O
of	O
a	O
dataset	O
and	O
performs	O
cluster	O
assignment	O
solely	O
based	O
on	O
the	O
neighborhood	O
relationships	O
among	O
objects	O
.	O
</s>
<s>
The	O
key	O
feature	O
of	O
this	O
algorithm	O
is	O
that	O
the	O
neighborhood	O
relationships	O
among	O
neighboring	O
objects	O
in	O
the	O
feature	O
space	O
are	O
used	O
to	O
constrain	O
the	O
memberships	O
of	O
neighboring	O
objects	O
in	O
the	O
fuzzy	B-General_Concept
membership	I-General_Concept
space	O
.	O
</s>
<s>
Local/Neighborhood	O
approximation	O
of	O
fuzzy	B-General_Concept
memberships	I-General_Concept
:	O
</s>
<s>
Initialization	O
of	O
fuzzy	B-General_Concept
membership	I-General_Concept
:	O
</s>
<s>
Then	O
the	O
fuzzy	B-General_Concept
memberships	I-General_Concept
of	O
all	O
type	O
3	O
objects	O
are	O
updated	O
by	O
a	O
converging	O
iterative	O
procedure	O
called	O
Local/Neighborhood	O
Approximation	O
of	O
Fuzzy	B-General_Concept
Memberships	I-General_Concept
,	O
in	O
which	O
the	O
fuzzy	B-General_Concept
membership	I-General_Concept
of	O
each	O
object	O
is	O
updated	O
by	O
a	O
linear	O
combination	O
of	O
the	O
fuzzy	B-General_Concept
memberships	I-General_Concept
of	O
its	O
nearest	O
neighbors	O
.	O
</s>
<s>
Cluster	O
construction	O
from	O
fuzzy	B-General_Concept
memberships	I-General_Concept
in	O
two	O
possible	O
ways	O
:	O
</s>
<s>
The	O
Local/Neighborhood	O
Approximation	O
of	O
Fuzzy	B-General_Concept
Memberships	I-General_Concept
is	O
a	O
procedure	O
to	O
minimize	O
the	O
Local/Neighborhood	O
Approximation	O
Error	O
(	O
LAE/NAE	O
)	O
defined	O
as	O
the	O
following	O
:	O
</s>
<s>
where	O
is	O
the	O
set	O
of	O
all	O
type	O
3	O
objects	O
,	O
is	O
the	O
fuzzy	B-General_Concept
membership	I-General_Concept
vector	O
of	O
object	O
,	O
is	O
the	O
set	O
of	O
nearest	O
neighbors	O
of	O
,	O
and	O
with	O
are	O
the	O
coefficients	O
reflecting	O
the	O
relative	O
proximities	O
of	O
the	O
nearest	O
neighbors	O
.	O
</s>
