Statistics: fitgmdist

### Function Reference: `fitgmdist`

statistics: GMdist = fitgmdist (data, k, param1, value1, …)

Fit a Gaussian mixture model with k components to data. Each row of data is a data sample. Each column is a variable.

Optional parameters are:

- `"start"`: Initialization conditions. Possible values are:
  - `"randSample"` (default) Takes means uniformly from rows of data.
  - `"plus"` Use k-means++ to initialize means.
  - `"cluster"` Performs an initial clustering with 10% of the data.
  - vector A vector whose length is the number of rows in data, and whose values are 1 to k specify the components each row is initially allocated to. The mean, variance, and weight of each component is calculated from that.
  - structure A structure with fields `mu`, `Sigma` and `ComponentProportion`.

  For `"randSample"`, `"plus"`, and `"cluster"`, the initial variance of each component is the variance of the entire data sample.

- `"Replicates"`: Number of random restarts to perform.
- `"RegularizationValue"` or `"Regularize"`: A small number added to the diagonal entries of the covariance to prevent singular covariances.
- `"SharedCovariance"` or `"SharedCov"` (logical). True if all components must share the same variance, to reduce the number of free parameters
- `"CovarianceType"` or `"CovType"` (string). Possible values are:
  - `"full"` (default) Allow arbitrary covariance matrices.
  - `"diagonal"` Force covariances to be diagonal, to reduce the number of free parameters.
- `"Options"`: A structure with all of the following fields:
  - `MaxIter` Maximum number of EM iterations (default 100).
  - `TolFun` Threshold increase in likelihood to terminate EM (default 1e-6).
  - `Display` Possible values are:
    - `"off"` (default): Display nothing.
    - `"final"`: Display the total number of iterations and likelihood once the execution completes.
    - `"iter"`: Display the number of iteration and likelihood after each iteration.
- `"Weight"`: A column vector or N×2 matrix. The first column consists of non-negative weights given to the samples. If these are all integers, this is equivalent to specifying `weight(i)` copies of row `i` of data, but potentially faster. If a row of data is used to represent samples that are similar but not identical, then the second column of weight indicates the variance of those original samples. Specifically, in the EM algorithm, the contribution of row `i` towards the variance is set to at least `weight(i,2)`, to prevent spurious components with zero variance.

See also: gmdistribution, kmeans

Source Code: fitgmdist

### Example: 1

     ## Generate a two-cluster problem
     C1 = randn (100, 2) + 2;
     C2 = randn (100, 2) - 2;
     data = [C1; C2];

     ## Perform clustering
     GMModel = fitgmdist (data, 2);

     ## Plot the result
     figure
     [heights, bins] = hist3([C1; C2]);
     [xx, yy] = meshgrid(bins{1}, bins{2});
     bbins = [xx(:), yy(:)];
     contour (reshape (GMModel.pdf (bbins), size (heights)));

### Example: 2

     Angle_Theta = [ 30 + 10 * randn(1, 10),  60 + 10 * randn(1, 10) ]';
     nbOrientations = 2;
     initial_orientations = [38.0; 18.0];
     initial_weights = ones (1, nbOrientations) / nbOrientations;
     initial_Sigma = 10 * ones (1, 1, nbOrientations);
     start = struct ("mu", initial_orientations, "Sigma", initial_Sigma, ...
                     "ComponentProportion", initial_weights);
     GMModel_Theta = fitgmdist (Angle_Theta, nbOrientations, "Start", start , ...
                                "RegularizationValue", 0.0001)

    Gaussian mixture distribution with 2 components in 1 dimension(s)
    Clust 1: weight 0.70508
    	Mean: 52.5568
    	Variance:156.17
    Clust 2: weight 0.29492
    	Mean: 20.0915
    	Variance:1.8459
    AIC=164.862 BIC=169.841 NLogL=77.431 Iter=5 Cged=1 Reg=0.0001