LDC Linear Bayes Normal Classifier (BayesNormal_1)
[W,R,S,M] = LDC(A,R,S,M)
Description Computation of the linear classifier between the classes of the dataset A by assuming normal densities with equal covariance matrices. The joint covariance matrix is the weighted (by a priori probabilities) average of the class covariance matrices. R and S (0 <= R,S <= 1) are regularisation parameters used for finding the covariance matrix G by G = (1RS)*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 KM 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 pseudoinverse of the covariance matrix is used in case it is close to singular. Note that A*(KLMS([],N)*NMC) performs a similar operation by first prewhitening the data in an Ndimensional space, followed by the nearest mean classifier. The regularisation controlled by N is different from the above in LDC as it entirely removes small variance directions. To some extend LDC is also similar to FISHERC. Example(s)prex_plotc, a = gendatd; % generate Gaussian distributed data in two classes
Reference(s)1. R.O. Duda, P.E. Hart, and D.G. Stork, Pattern classification, 2nd edition, John Wiley and Sons, New York, 2001. See alsomappings, datasets, regoptc, nmc, nmsc, ldc, udc, quadrc, normal_map, fisherc,
