QDC

Quadratic Bayes Normal Classifier (Bayes-Normal-2)

    [W,R,S,M] = QDC(A,R,S,M)
            W = A*QDC([],R,S)

Input
A	Dataset
R,S	Regularization parameters, 0 <= R,S <= 1 (optional; default: no regularization, i.e. R,S = 0)
M	Dimension of subspace structure in covariance matrix (default: K,  all dimensions)

Output
W	Quadratic Bayes Normal Classifier mapping
R	Value of regularization parameter R as used
S	Value of regularization parameter S as used
M	Value of regularization parameter M as used

Description

Computation of the quadratic classifier between the classes of the dataset  A assuming normal densities. R and S (0 <= R,S <= 1) are regularization  parameters used for finding the covariance matrix by

     G = (1-R-S)*G + R*diag(diag(G)) + S*mean(diag(G))*eye(size(G,1))

This covariance matrix is then decomposed as G = W*W' + sigma^2 * eye(K),  where W is a K x M matrix containing the M leading principal components  and sigma^2 is the mean of the K-M smallest eigenvalues.

The use of soft labels is supported. The classification A*W is computed by  NORMAL_MAP.

If R, S or M is NaN the regularisation parameter is optimised by REGOPTC.  The best result are usually obtained by R = 0, S = NaN, M = [], or by  R = 0, S = 0, M = NaN (which is for problems of moderate or low dimensionality  faster). If no regularisation is supplied a pseudo-inverse of the  covariance matrix is used in case it is close to singular.

Example(s)

Reference(s)

1. R.O. Duda, P.E. Hart, and D.G. Stork, Pattern classification, 2nd edition, John Wiley and Sons, New York, 2001.
2. A. Webb, Statistical Pattern Recognition, John Wiley & Sons, New York, 2002.

See also

mappings, datasets, regoptc, nmc, nmsc, ldc, udc, quadrc, normal_map,