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Thread Subject:
variance of a cluster

Subject: variance of a cluster

From: yafit maymon

Date: 15 Mar, 2011 11:38:07

Message: 1 of 3

hello!

i need some help please....

i have done some clustering to matrics with 20 random variables , each variable has 1000 observations ). i got 4 clusters

and i need to test how good the clustering is by calculating the variance in each cluster.
does anyone knows how can i calculate the variance?

 i can easily calculate the variance of each coulmne in my matrix (e.g the variance of each random variable) but i want to calculate the variance of the whole cluster

does anyone know how it can be done ?
 thanks!!!!

Subject: variance of a cluster

From: Torsten

Date: 15 Mar, 2011 12:34:18

Message: 2 of 3

On 15 Mrz., 12:38, "yafit maymon" <yafit_may...@hotmail.com> wrote:
> hello!
>
> i need some help please....
>
> i have done some clustering to  matrics with 20 random variables , each variable has 1000 observations ). i got 4 clusters
>
> and i need to test how good the clustering is by calculating the variance in each cluster.
> does anyone knows how can i calculate the variance?
>
>  i can easily calculate the variance of each coulmne in my matrix (e.g the variance of each random variable)  but i want to calculate the variance of the  whole cluster
>
> does anyone know how it can be done ?
>  thanks!!!!

If
mu_i = 1/|C_i| * sum_{x in C_i} x
is the mean of cluster i, the variance within cluster i should be
given by
sigma_i^2 = 1/(|C_i|-1) * sum_{x in C_i} (x-mu_i)'*(x-mu_i).

Here |C_i| is the number of elements in cluster i and ' denotes
'transpose'.

Best wishes
Torsten.

Subject: variance of a cluster

From: yafit maymon

Date: 11 Apr, 2011 07:24:05

Message: 3 of 3


hello Torsten,

sorry for the delay i have just seen your replay....
thank you very much ,it helps a lot !
Is this way of calculating varience for vectors wrriten anywhere in the litrature couse when i looked for it i couldnt find it....

anyway ,thank you!
yafit

Torsten <Torsten.Hennig@umsicht.fraunhofer.de> wrote in message <f7b121aa-f5e5-4c55-9a1e-19ec50cb3155@s3g2000vbf.googlegroups.com>...
> On 15 Mrz., 12:38, "yafit maymon" <yafit_may...@hotmail.com> wrote:
> > hello!
> >
> > i need some help please....
> >
> > i have done some clustering to  matrics with 20 random variables , each variable has 1000 observations ). i got 4 clusters
> >
> > and i need to test how good the clustering is by calculating the variance in each cluster.
> > does anyone knows how can i calculate the variance?
> >
> >  i can easily calculate the variance of each coulmne in my matrix (e.g the variance of each random variable)  but i want to calculate the variance of the  whole cluster
> >
> > does anyone know how it can be done ?
> >  thanks!!!!
>
> If
> mu_i = 1/|C_i| * sum_{x in C_i} x
> is the mean of cluster i, the variance within cluster i should be
> given by
> sigma_i^2 = 1/(|C_i|-1) * sum_{x in C_i} (x-mu_i)'*(x-mu_i).
>
> Here |C_i| is the number of elements in cluster i and ' denotes
> 'transpose'.
>
> Best wishes
> Torsten.

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