Information Technology Reference
In-Depth Information
Q
P
R
Fig. 6.21 A simple example with
M
-nearest neighbors of point
Q
,
M
=9
;the
9
-neighborhood of
Q
corresponds to points inside the dotted region.
Fig. 6.22
The
9
-neighborhood vector field of point
Q
.
An
M
-neighborhood vector field can be interpreted as a probability density
function and represented, in this example, by a two-dimensional empirical
PDF
μ
M
(
x
1
,
x
2
) shown in Fig. 6.23, where each (
x
1
,
x
2
) pair corresponds to
d
ij
vector ends. The vertical bars represent
μ
M
(
x
1
,
x
2
), i.e., ocorrence rates
of
d
ij
vector ends. Note that for any selected data point (
Q
on the present
example) every point belonging to some
R
d
subset is a candidate vector-end
of the
M
-neighborhood vector field.
Fig. 6.23 The histogram of the 9-neighborhood vector field of point Q with a mesh
showing the respective PDF estimate.
As shown in Fig. 6.23, the probability density function associated with
point
Q
, reflects an horizontal
M
-neighborhood structure and, therefore,
the "ideal connection" for
Q
should follow this horizontal direction. Besides
choosing the ideal connection LEGClust also ranks all possible connections