# 21_init.EM: Initialization and EM Algorithm In EMCluster: EM Algorithm for Model-Based Clustering of Finite Mixture Gaussian Distribution

 Initialization and EM R Documentation

## Initialization and EM Algorithm

### Description

These functions perform initializations (including em.EM and RndEM) followed by the EM iterations for model-based clustering of finite mixture multivariate Gaussian distribution with unstructured dispersion in both of unsupervised and semi-supervised clusterings.

### Usage

```init.EM(x, nclass = 1, lab = NULL, EMC = .EMC,
stable.solution = TRUE, min.n = NULL, min.n.iter = 10,
method = c("em.EM", "Rnd.EM"))
em.EM(x, nclass = 1, lab = NULL, EMC = .EMC,
stable.solution = TRUE, min.n = NULL, min.n.iter = 10)
rand.EM(x, nclass = 1, lab = NULL, EMC = .EMC.Rnd,
stable.solution = TRUE, min.n = NULL, min.n.iter = 10)
exhaust.EM(x, nclass = 1, lab = NULL,
EMC = .EMControl(short.iter = 1, short.eps = Inf),
method = c("em.EM", "Rnd.EM"),
stable.solution = TRUE, min.n = NULL, min.n.iter = 10);
```

### Arguments

 `x` the data matrix, dimension n * p. `nclass` the desired number of clusters, K. `lab` labeled data for semi-supervised clustering, length n. `EMC` the control for the EM iterations. `stable.solution` if returning a stable solution. `min.n` restriction for a stable solution, the minimum number of observations for every final clusters. `min.n.iter` restriction for a stable solution, the minimum number of iterations for trying a stable solution. `method` an initialization method.

### Details

The `init.EM` calls either `em.EM` if `method="em.EM"` or `rand.EM` if `method="Rnd.EM"`.

The `em.EM` has two steps: short-EM has loose convergent tolerance controlled by `.EMC\$short.eps` and try several random initializations controlled by `.EMC\$short.iter`, while long-EM starts from the best short-EM result (in terms of log likelihood) and run to convergence with a tight tolerance controlled by `.EMC\$em.eps`.

The `rand.EM` also has two steps: first randomly pick several random initializations controlled by `.EMC\$short.iter`, and second starts from the best of the random result (in terms of log likelihood) and run to convergence.

The `lab` is only for the semi-supervised clustering, and it contains pre-labeled indices between 1 and K for labeled observations. Observations with index 0 is non-labeled and has to be clustered by the EM algorithm. Indices will be assigned by the results of the EM algorithm. See `demo(allinit_ss,'EMCluster')` for details.

The `exhaust.EM` also calls the `init.EM` with different `EMC` and perform `exhaust.iter` times of EM algorithm with different initials. The best result is returned.

### Value

These functions return an object `emobj` with class `emret` which can be used in post-process or other functions such as `e.step`, `m.step`, `assign.class`, `em.ic`, and `dmixmvn`.

### Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

### References

`emcluster`, `.EMControl`.

### Examples

```## Not run:
library(EMCluster, quietly = TRUE)
set.seed(1234)
x <- da1\$da

ret.em <- init.EM(x, nclass = 10, method = "em.EM")
ret.Rnd <- init.EM(x, nclass = 10, method = "Rnd.EM", EMC = .EMC.Rnd)

emobj <- simple.init(x, nclass = 10)
ret.init <- emcluster(x, emobj, assign.class = TRUE)

par(mfrow = c(2, 2))
plotem(ret.em, x)
plotem(ret.Rnd, x)
plotem(ret.init, x)

## End(Not run)
```

EMCluster documentation built on Aug. 20, 2022, 5:05 p.m.