[R] Von Mises mixtures: mu and kappa?

Bert Gunter bgunter.4567 at gmail.com
Wed Mar 1 01:58:47 CET 2017 

If you believe that a fit to simulated data should give you parameter
estimates identical to those used for the simulation, then I suggest
that you stop posting and consult a local statistical expert: you
don't know what you're doing.

If I have misunderstood your post, then just ignore the above and
hopefully someone with greater understanding than I will be able to
help you.

Cheers,
Bert


Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Tue, Feb 28, 2017 at 7:39 AM, Peter Mills <peter.mills at strath.ac.uk> wrote:
> Thank you Bert for the references. I have found mix.vmf as a possible alternative to movMF but am stuck with applying either to my application.
>
> Does anyone know why mix.vmf requires to 2 columns for x?
>
> For example when I use:
> gWD <- c(0.1, 1, 0.9, 0.7,0.3)
>> mix.vmf(gWD, 2)
>
> I get the error:
> ‘Error in matrix(nrow = n, ncol = g) : non-numeric matrix extent’
>
> The following code works but I'm not sure how to adapt this to the application I require. What I need is to calculate the mixture parameters for a vector of directional data not a matrix. Could anyone suggest how I can do this?
>
> k <- c(1, 2)
> prob <- c(0.3, 0.4, 0.3)
> mu <- matrix(rnorm(4), ncol = 2)
> mu <- mu / sqrt( rowSums(mu^2) )
> x <- rmixvmf(10, prob, mu, k)$x
> mix.vmf(x, 3)
>
> With regards to my original post and using movMF I'm stuck with this also. I found the following from [1], I thought this was the answer however it seems to need some adjustment as it is not giving me the theta and kappa values I started with:
> kappa2 <- row_norms(y2$theta)
> mu2<-y2$theta/row_norms(y2$theta)
>
> [1] On lines 94 and 107 of “v58i10.R: R example code from the paper “ available from https://www.jstatsoft.org/article/view/v058i10
>
> Any suggestion would be greatly appreciated as after a further week of researching this and trying code I still don't seem to have working code.
>
>
> Here is some code I am using as a testing example:
> ################################################
> ## Generate and fit a "small-mix" data set a la Banerjee et al.
> mu1 <- rbind(c(-0.251, -0.968),
>             c(0.399, 0.917))
> kappa1 <- c(4, 4)
> theta <- kappa1 * mu1
> alpha <- c(0.48, 0.52)
> ## Generate a sample of size n = 50 from the von Mises-Fisher mixture ## with the above parameters.
> set.seed(123)
> x <- rmovMF(50, theta, alpha)
> ## Fit a von Mises-Fisher mixture with the "right" number of components, ## using 10 EM runs.
> y2 <- movMF(x, 2, nruns = 10)
>
> kappa2 <- row_norms(y2$theta)
> mu2<-y2$theta/row_norms(y2$theta)
>
>
> mu3c <- lapply(y2, function(x) y2$theta / row_norms(y2$theta)) ################################################
>
> I don't understand why this doesn't give me the values of mu and kappa I started with. I have tried to adapted this code to have the same number of mu and kappa values but it doesn't work then as mu is know longer a matrix.
>
> I don't understand why both movMF and mix.vmf give both mu1 and mu2 values per kappa value. In other words for a Von Mises mixture with 3 mixtures (clusters) the code gives 6 mu values and 3 kappa values. I was expecting to get 3 preferred directions (mu).
>
> For example:
> mix.vmf(x, 3) gives
>
> $param
>                 mu1             mu2             kappa     probs
> Cluster 1 0.4985047 -0.8668870 12.281773 0.3571429
> Cluster 2 0.9490725  0.3150578 34.028465 0.2857143
> Cluster 3 0.1017800  0.9948069  4.182367 0.3571429
>
> Many thanks
> Peter
>
> -----Original Message-----
> From: Bert Gunter [mailto:bgunter.4567 at gmail.com]
> Sent: 14 February 2017 17:49
> To: Peter Mills
> Cc: r-help at r-project.org
> Subject: Re: [R] Von Mises mixtures: mu and kappa?
>
> Please search before posting!
>
> Searching "von mises mixture distributions" on rseek.org brought up what appeared to be several relevant hits. If none of these meet your needs, you should probably explain why not in a follow up post.
>
> Cheers,
> Bert
>
>
> Bert Gunter
>
> "The trouble with having an open mind is that people keep coming along and sticking things into it."
> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
>
>
> On Tue, Feb 14, 2017 at 8:55 AM, Peter Mills <peter.mills at strath.ac.uk> wrote:
>> Hello
>>
>> I am trying to calculate the values of the concentration parameters (kappa) and preferred direction (mu) for a Von Mises mixture model. I currently have some R code that gives me optimised values for the product of kappa and mu, but I'm not sure how to calculate them when both are unknown? How could I calculate mu and kappa from y2 if I didn't know either in the 1st place? I what to use movMF to give me values of kappa from some directional data where I don't know either kappa or mu.
>>
>>
>> ## Generate and fit a "small-mix" data set a la Banerjee et al.
>> mu <- rbind(c(-0.251, -0.968),
>>             c(0.399, 0.917))
>> kappa <- c(4, 4)
>>
>> theta <- kappa * mu
>> theta
>> alpha <- c(0.48, 0.52)
>>
>> ## Generate a sample of size n = 50 from the von Mises-Fisher mixture
>> ## with the above parameters.
>> set.seed(123)
>> x <- rmovMF(50, theta, alpha)
>> ## Fit a von Mises-Fisher mixture with the "right" number of
>> components, ## using 10 EM runs.
>> y2 <- movMF(x, 2, nruns = 10)
>>
>> Y2 gives
>>> y2
>> theta:
>>        [,1]      [,2]
>> 1  2.443225  5.259337
>> 2 -1.851384 -4.291278
>> alpha:
>> [1] 0.4823648 0.5176352
>> L:
>> [1] 24.98124
>>
>> How could I calculate kappa and mu if I didn't know either in the 1st place?
>>
>> Thanks
>> Peter
>>
>>
>>         [[alternative HTML version deleted]]
>>
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>> and provide commented, minimal, self-contained, reproducible code.
> ______________________________________________
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> and provide commented, minimal, self-contained, reproducible code.

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