<div dir="ltr">Hi,<div>Just FYI, the classifications in cryoSPARC <i>do</i> report membership probabilities for every class. They take the maximum probability class (apply a threshold, default 0.9) during particle selection, but all the values are present in the metadata file.</div><div><br></div><div>Best,</div><div>-da</div></div><div class="gmail_extra"><br><div class="gmail_quote">On Thu, Aug 31, 2017 at 7:59 AM, Penczek, Pawel A <span dir="ltr"><<a href="mailto:Pawel.A.Penczek@uth.tmc.edu" target="_blank">Pawel.A.Penczek@uth.tmc.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Hi,<br>
<br>
I may say I am somewhat familiar with the technique and I even published on the subject in a distant past:<br>
Leszczynski, K., Penczek, P. and Grochulski, W.: Sugeno's fuzzy measure and fuzzy clustering. Fuzzy Sets and Systems 15:147-158, 1985.<br>
There are also some comments in the supplement of:<br>
Cheng, Y., Grigorieff, N., Penczek, P.A., Walz, T.: A Primer to Single-Particle Cryo-Electron Microscopy. Cell, 161:438-449, 2015.<br>
<br>
Regrettably, it is not a subject that easily yields itself to a discussion on a mailing list. More like 30 minutes lecture.<br>
<br>
Very briefly, fuzzy clustering does not merge anything with maximum likelihood (ML) approach. To the contrary, fuzzy sets theory was<br>
developed in 1962 by Zadeh as a substitute for probability-based descriptions. The idea was that having<br>
arbitrary “membership functions” designed by the researcher instead of probability distributions<br>
derived from the data would give more “freedom" and improve “accuracy”, particularly for small samples.<br>
<br>
There was a surge of fuzzy sets-based clustering algorithm developed in the 80s (see above).<br>
<br>
I will not get into detailed comparative analysis of ML-based versus fuzzy clustering methods here.<br>
Very briefly, ML is not really applicable to clustering unless some heuristics are added. Fuzzy methods are all heuristics.<br>
<br>
Greetings from Houston.<br>
We are slowly getting back to normal and the fact I could write the above note means my senses are coming back,<br>
but it is an arduous process.<br>
Pawel.<br>
<span class=""><br>
> On Aug 31, 2017, at 9:24 AM, Morgan, David Gene <<a href="mailto:dagmorga@indiana.edu">dagmorga@indiana.edu</a>> wrote:<br>
><br>
> Hi,<br>
><br>
> 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.<br>
><br>
> So, has anyone tried it, and if so, what are the conclusions? If no-one has tried it, maybe someone will!<br>
><br>
> Finally, best wishes to our friends in the Houston area.<br>
><br>
> --<br>
> David Gene Morgan<br>
> Electron Microscopy Center<br>
> 047D Simon Hall<br>
> IU Bloomington<br>
> <a href="tel:812%20856%201457" value="+18128561457">812 856 1457</a> (office)<br>
> <a href="tel:812%20856%203221" value="+18128563221">812 856 3221</a> (3200)<br>
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