MachineLearningem Method

public static RetArray<double> em(
	InArray<double> Samples,
	int k,
	OutArray<double> Sigma = null,
	EMInitializationMethod method = EMInitializationMethod.KMeans_random,
	InArray<double> UserCenters = null,
	int maxiterexit = 10000,
	double centerconverg_exit = 0,001
)

Public Shared Function em ( 
	Samples As InArray(Of Double),
	k As Integer,
	Optional Sigma As OutArray(Of Double) = Nothing,
	Optional method As EMInitializationMethod = EMInitializationMethod.KMeans_random,
	Optional UserCenters As InArray(Of Double) = Nothing,
	Optional maxiterexit As Integer = 10000,
	Optional centerconverg_exit As Double = 0,001
) As RetArray(Of Double)

Dim Samples As InArray(Of Double)
Dim k As Integer
Dim Sigma As OutArray(Of Double)
Dim method As EMInitializationMethod
Dim UserCenters As InArray(Of Double)
Dim maxiterexit As Integer
Dim centerconverg_exit As Double
Dim returnValue As RetArray(Of Double)

returnValue = MachineLearning.em(Samples, k, 
	Sigma, method, UserCenters, maxiterexit, 
	centerconverg_exit)

Parameters

Samples

Type: ILNumericsInArrayDouble
Input data, data points in columns.

k

Type: SystemInt32
Number of clusters.

Sigma (Optional)

Type: ILNumericsOutArrayDouble
[Output] Covariance estimation for all clusters, size d x d x k, d = samples.D[0].

method (Optional)

Type: ILNumerics.ToolboxesEMInitializationMethod
[Optional] Method used for initializing the cluster centers, default: kmeans_random.

UserCenters (Optional)

Type: ILNumericsInArrayDouble
[Optional] For method 'user': initial cluster centers, size samples.D[0] x k, for other methods ignored.

maxiterexit (Optional)

Type: SystemInt32
[Optional] Break after that number of iterations, if no convergence was reached.

centerconverg_exit (Optional)

Type: SystemDouble
[Optional] Exit iteration if norm(L) falls below that value, default: 0.001.

Return Value

The EM algorithm expects the data samples to be drawn from k multivariate normal distributions. It estimates the parameters 'center' and 'sigma (covariance)' of every distribution. Therefore, the position and 'shape' of each distribution is calculated in such a way, that the likelyhood of generating the given sample points is maximized.

The parameter k must be determined by the user. This reflects the a priori knowledge of the number of distributions or clusters in the data.

The algorithm exits, if one of the exit criteria is reached:

• norm(L) < 'centerconverg_exit' - where L is the difference between the centers from the last step and the centers just computed in the current step
• the number of iteration steps exceeds the limit of 'maxiterexit' iterations.

[ILNumerics Machine Learning Toolbox]

Reference