GAUSS

Generation of a multivariate Gaussian dataset

    A = GAUSS(N,U,G,LABTYPE)

INPUT (in case of generation a 1-class dataset in K dimensions)    N Number of objects to be generated (default 50).
    U Desired mean (vector of length K).
    G K x K covariance matrix. Default eye(K).
    LABTYPE Label type (default 'crisp')

INPUT (in case of generation a C-class dataset in K dimensions)    N Vector of length C with numbers of objects per class.
    U C x K matrix with class means, or
            Dataset with means, labels and priors of classes
            (default: zeros(C,K))
    G K x K x C covariance matrix of right size.
            Default eye(K);
    LABTYPE Label type (default 'crisp')

Output
A	Dataset containing multivariate Gaussian data

Description

Generation of N K-dimensional Gaussian distributed samples for C classes.  The covariance matrices should be specified in G (size K*K*C) and the  means, labels and prior probabilities can be defined by the dataset U with  size (C*K). If U is not a dataset, it should be a C*K matrix and A will  be a dataset with C classes.

If N is a vector, exactly N(I) objects are generated for class I, I = 1..C.

Example(s)

 1. Generation of 100 points in 2D with mean [1 1] and default covariance
    matrix: 

         GAUSS(100,[1 1])

2. Generation of 50 points for each of two 1-dimensional distributions with     mean -1 and 1 and with variances 1 and 2:

        GAUSS([50 50],[-1;1],CAT(3,1,2))

    Note that the two 1-dimensional class means should be given as a column
    vector [1;-1], as [1 -1] defines a single 2-dimensional mean. Note that
    the 1-dimensional covariance matrices degenerate to scalar variances,
    but have still to be combined into a collection of square matrices using
    the CAT(3,....) function.

3. Generation of 300 points for 3 classes with means [0 0], [0 1] and     [1 1] and covariance matrices [2 1; 1 4], EYE(2) and EYE(2):

       GAUSS(300,[0 0; 0 1; 1 1]*3,CAT(3,[2 1; 1 4],EYE(2),EYE(2)))

See also

datasets, prdatasets,