[3dem] clustering algorithms

[Penczek, Pawel A]

Hi,

I may say I am somewhat familiar with the technique and I even published on the subject in a distant past:
Leszczynski, K., Penczek, P. and Grochulski, W.: Sugeno's fuzzy measure and fuzzy clustering. Fuzzy Sets and Systems 15:147-158, 1985.
There are also some comments in the supplement of:
Cheng, Y., Grigorieff, N., Penczek, P.A., Walz, T.: A Primer to Single-Particle Cryo-Electron Microscopy. Cell, 161:438-449, 2015.

Regrettably, it is not a subject that easily yields itself to a discussion on a mailing list.  More like 30 minutes lecture.

Very briefly, fuzzy clustering does not merge anything with maximum likelihood (ML) approach.  To the contrary, fuzzy sets theory was
developed in 1962 by Zadeh as a substitute for probability-based descriptions.  The idea was that having
arbitrary “membership functions” designed by the researcher instead of probability distributions
derived from the data would give more “freedom" and improve “accuracy”, particularly for small samples.

There was a surge of fuzzy sets-based clustering algorithm developed in the 80s (see above).

I will not get into detailed comparative analysis of ML-based versus fuzzy clustering methods here.
Very briefly, ML is not really applicable to clustering unless some heuristics are added.  Fuzzy methods are all heuristics.

Greetings from Houston.
We are slowly getting back to normal and the fact I could write the above note means my senses are coming back,
but it is an arduous process.
Pawel.

> On Aug 31, 2017, at 9:24 AM, Morgan, David Gene <dagmorga at indiana.edu> wrote:
> 
> Hi,
> 
>    The recent flurry of e-mail about k-means clustering has made me wonder whether anyone in our field has tried to use c-means clustering instead.  As I understand it, c-means clustering is an application of "fuzzy logic" to the clustering problem, and another way of describing it (one that might spark a bit more interest) would be to say it merges a clustering algorithm with maximum likelihood:  at the end of the process, every particle has a weighted membership in every class.  I have no idea whether this would actually be useful for our problems, but I can see some ways that it might be.
> 
>    So, has anyone tried it, and if so, what are the conclusions?  If no-one has tried it, maybe someone will!
> 
>    Finally, best wishes to our friends in the Houston area.
> 
> --
>            David Gene Morgan
>        Electron Microscopy Center
>             047D Simon Hall
>             IU Bloomington
>          812 856 1457 (office)
>          812 856 3221 (3200)
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