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In-Depth Information
selected consistent set to determine the NUN distance thresholds for each sample
in the given set.
10. Repeat Step 3 through 8 using all the samples in the given set to identify a
new consistent set. This process of recursive application of step 2 through 8 is
continued till the selected set is no longer getting smaller. It is easy to see that
under this procedure this final subset remains consistent, i.e., is able to classify
all samples in the original set correctly.
•
Modified Selective Algorithm (MSS)
[
9
]—Let
R
i
be the set of all
X
i
in
TR
such
that
X
j
is of the same class of
X
i
and is closer to
X
i
than the nearest neighbor of
X
i
in
TR
of a different class than
X
i
. Then, MSS is defined as that subset of the
TR
containing, for every
X
i
in
TR
, that element of its
R
i
that is the nearest to a
different class than that of
X
i
.
An efficient algorithmic representation of the
MSS
method is depicted as:
TR
Sort the instances
{
X
j
}
Q
=
n
j
=
1
according to increasing values
of enemy distance
(
D
j
)
.
For each instance
X
i
do
add
FALSE
For each instance
X
j
do
If
x
j
←
∈
Q
∧
d
(
X
i
,
X
j
)<
D
j
then
Q
←
Q
−{
X
j
}
add
TRUE
If
add
then
S
←
S
∪{
X
i
}
If
Q
←
=∅
then return
S
8.4.1.3 Batch
•
Patterns by Ordered Projections (POP)
[
135
]—This algorithm consists of elim-
inating the examples that are not within the limits of the regions to which they
belong. For it, each attribute is studied separately, sorting and increasing a value,
called
weakness
, associated to each one of the instances, if it is not within a limit.
The instances with a value of
weakness
equal to the number of attributes are
eliminated.
•
Max Nearest Centroid Neighbor (Max-NCN)
[
112
] This algorithm is based on
the Nearest Centroid Neighborhood (NCN) concept, defined by:
1. The first NCN of
X
i
is also its NN,
Y
1
.
2. The
i
-th NCN,
Y
i
,
i
≥
2, is such that the centroid of this and previously selected
NCN,
Y
1
, ...,
Y
i
is the closest to
X
i
.
