Re: [Java-ML-support] Question about AIC and BIC scores

[Thomas A. <th...@ab...>]

Okay.

If it's a case of "it depends", I'll make it a parameter that users have 
to specify when constructing the metric.

I've committed a patch to that effect to the repository.

cheers,
Thomas
On 11/22/2013 11:45 AM, Sergio Pulido wrote:
> Hi Tomas,
>
> I found this:
> http://books.nips.cc/papers/files/nips16/NIPS2003_AA36.pdf
> http://www.autonlab.org/autonweb/14661/version/3/part/5/data/pelleg-xmeans.pdf?branch=main&language=en
>
> They say that actually k (the number of free parameters) is bigger 
> than the number of clusters - 1 as was my initial thought. It also 
> depends on dimensionality, k should be:
>
> The papers do not agree in what should be the numbers of free 
> parameters (I just looked at them very fast so I am probably wrong or 
> not seeing something obvious)
>
> The first papers says: "p = k(d + 1) is the number of parameters in 
> the model"
> double k = clusters.lenght * (clusters[0].get(0).noAttributes() + 1);
>
> the second says: "the number of free parameters p is simply the sum of 
> k - 1 class probabilities, M.K centroid coordinates, and one variance 
> estimate"
> double k = (clusters.lenght - 1) + 
> clusters.lenght*(clusters[0].get(0).noAttributes() + 1);
>
> I think the second is the best:
> 1. It put additional penalties for the number of clusters but not 
> greatly (just an aditional clusters.lenght - 1). It count as a 
> parameter the existence of each cluster (?)
> 2. It have the -1... in the other one I do not see the bound parameter 
> anywhere.
>
> The problem I see with this is that that is the calculation of free 
> parameters for a KMeans clustering, but not necessary for other types 
> of clustering algorithms with different assumptions, K-means assumes a 
> Gaussian circular distribution.
>
> Anyhow, it should be better than just k = 1 :)
>
> Cheers,
> Sergio.
>
>
>
>
>
>
> On Fri, Nov 22, 2013 at 3:18 PM, Thomas Abeel <th...@ab... 
> <mailto:th...@ab...>> wrote:
>
>     Hi Sergio,
>
>     This has been a while. This may be a bug. Can you point me to any
>     literature reference that says the number of free parameters =
>     clusters.length-1?
>
>     cheers,
>     Thomas
>
>     On 11/12/2013 9:08 AM, Sergio Pulido wrote:
>>     Hello all,
>>
>>     I see that the implementation of AICScore and BICScore uses a k=1
>>     as the number of free parameters
>>
>>     // number of free parameters K
>>     double k = 1;
>>
>>     Can you explain me why the number of free parameters is not the
>>     number of clusters -1?
>>
>>     // number of free parameters K
>>     double k = clusters.length - 1;
>>
>>     Thank you a lot,
>>     Sergio.
>>
>>
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