EMsinvMmix {ClusTorus} R Documentation

## Fitting mixtures of bivariate von Mises distribution

### Description

`EMsinvMmix` returns fitted parameters of J-mixture of bivariate sine von Mises.

### Usage

```EMsinvMmix(
data,
J = 4,
parammat = EMsinvMmix.init(data, J),
THRESHOLD = 1e-10,
maxiter = 200,
type = c("circular", "axis-aligned", "general"),
kmax = 500,
verbose = TRUE
)
```

### Arguments

 `data` n x 2 matrix of toroidal data on [0, 2π)^2 `J` number of components of mixture density `parammat` 6 x J parameter data with the following components: `parammat[1, ]` : the weights for each von Mises sine density `parammat[n + 1, ]` : κ_n for each von Mises sine density for n = 1, 2, 3 `parammat[m + 4, ]` : μ_m for each von Mises sine density for m = 1, 2 `THRESHOLD` number of threshold for difference between updating and updated parameters. `maxiter` the maximal number of iteration. `type` a string one of "circular", "axis-aligned", "general", and "Bayesian" which determines the fitting method. `kmax` the maximal number of kappa. If estimated kappa is larger than `kmax`, then put kappa as `kmax`. `verbose` boolean index, which indicates whether display additional details as to what the algorithm is doing or how many loops are done.

### Details

This algorithm is based on ECME algorithm. That is, constructed with E - step and M - step and M - step maximizes the parameters with given `type`.

If `type == "circular"`, then the mixture density is just a product of two independent von Mises.

If `type == "axis-aligned"`, then the mixture density is the special case of `type == "circular"`: only need to take care of the common concentration parameter.

If`type == "general"`, then the fitting the mixture density is more complicated than before, check the detail of the reference article.

### Value

returns approximated parameters for bivariate normal distribution with `list`:

`list\$Sigmainv[j]` : approximated covariance matrix for j-th bivariate normal distribution, approximation of the j-th von Mises.

`list\$c[j]` : approximated |2πΣ|^{-1} for j-th bivariate normal distribution, approximation of the j-th von Mises.

### References

'S. Jung, K. Park, and B. Kim (2021), "Clustering on the torus by conformal prediction"

### Examples

```
data <- ILE[1:200, 1:2]

EMsinvMmix(data, J = 3,
THRESHOLD = 1e-10, maxiter = 200,
type = "general", kmax = 500, verbose = FALSE)

```

[Package ClusTorus version 0.1.3 Index]