# [R] fuzzy clustering in e1071

Fri Nov 30 13:54:04 CET 2001

>
> Could anybody indicate me a more general reference(s)
> for e1071 functions on fuzzy classification that the articles
> that are mentioned in the help?
the references in the help pages *are* general, but if you need something
like a book then try

@InBook{clvalidity:Bezdek:1981b,
author =       {James C. Bezdek},
title =        {Pattern Recognition with Fuzzy Objective Function
Algorithms},  chapter =      {Cluster Validity},
publisher =    {Plenum Press},
year =         1981,
}

> Or, perhaps, may be someone could explain
>
> 1. How the fuzzy membership is calculated. I understand that
> if m=1, the classification proceeds as a crisp classification
> with the Euclidean distance and that m>1 modifies this
> distance to make it fuzzy, but how?

here is a very short description:

The $c$-means algorithm (or fuzzy $k$-means) is one of the classic
fuzzy clustering methods. As opposed to its competitive learning
variants, this is an off-line method, i.e., the center updates are
based on the whole training sample:
\begin{itemize}
\item Fix the number of clusters $k$, $2\leq k<N$ where $N$ is the
number of data points. Fix $q$, $1<q<\infty$, where $q$ is the
defuzzification parameter.
\item Set iteration counter $t=0$ and initialize the cluster centers
$v_i$.
\item Calculate the fuzzy $k$-partition $U$ from
\begin{equation}

U_{t+1}=u_{ij,~t+1}={\left[\sum_{l=1}^{k}{\left(\frac{||x_i-v_{j,t}||}{||x_i-v_{l,t}||}\right)}^{\frac{2}{q-1}}\right]}^{-1}
\end{equation}
and update the cluster centers according to
\begin{equation}
V_{t+1}=v_{t+1}=\frac{\sum_{i=1}^N{(u_{ij,~t+1})}^q
x_i}{\sum_{i=1}^N{(u_{ij,~t+1})}^q}
\end{equation}
where  $1\leq i\leq N$ and $1\leq j\leq k$.
\item If $||U_t-U_{t-1}||\leq \epsilon$ then stop or else $t=t+1$.
\end{itemize}

> 2. What are the main differences among cmeanscl, cshell and
> scaclust?
you should update your e1071 package. you are obviously
using an older version.
check the descriptions in the functions help pages to get the
differences among the algortihms. everything you need is already described
there.

-v
> Thanks
>
> Agus
>
>
> Dr. Agustin Lobo
> Instituto de Ciencias de la Tierra (CSIC)
> Lluis Sole Sabaris s/n
> 08028 Barcelona SPAIN
> tel 34 93409 5410
> fax 34 93411 0012
> alobo at ija.csic.es
>
>
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