Re: fuzzy clusters

Thomas Runkler (runkler@mchp.siemens.de)
Sat, 31 Jan 1998 16:25:21 +0100 (MET)

In comp.ai.fuzzy Dave Lorenz <lorenz@usgs.gov> wrote:

: |
: |
: | .02
: | + X
: | .08
: |
: |____________________________________

: In this diagram, there are two cluster centers, marked by a + and an X,
: and the points in question are represented by .02 and .08. My expectation
: is that the point marked by .02 membership in X should actually have a
: larger membership score that it now has because it is much closer to X
: than is the point that has a .08 score.

Dave,

the effect you encountered stems from the normalization condition of the
fuzzy c-means model which requires the sum of memberships for each data
point to be equal to one. The .02 point has a membership of .98 in +,
and the .08 point has a membership of .92 in X. I assume that this is
the result that you expected, since the .02 point is closer to + than
the .08 point.

If you expect the memberships of the .02 point to be higher than those of
the .08 point in *both* clusters, you have to abandon the normalization
condition. The solution are alternating cluster extimation (ACE) methods.
One instance of ACE models is the possibilistic c-means alternating
optimization (PCM-AO) which may help. If you are focussed mainly on the
distances between the points you might prefer another instance of the ACE
model called the dancing cones (DC) algorithm.

Hope this helps

Thomas