Discriminant analysis algorithms for classification mass spectra of exhaled gases

In this paper the algorithms of discriminant analysis for the classification of mass spectra of exhaled gases are considered. It is shown that three algorithms can be used to calculate the coefficients of discriminant functions: 1) an algorithm based on the QR decomposition; 2) an algorithm based on the calculation of the generalized correlation function; and 3) an algorithm based on the solution of an overdetermined system of linear equations by the method of least squares. Tables are given for calculating the probabilities of deciding whether a processed mass spectrum belongs to one of two groups: mass spectra belonging to healthy and unhealthy people. It is shown in the paper that the amplitudes of the mass-spectral peaks of the masses of the exhaled gas as well as the variables resulting from the reduction in the dimension of the data processed by the principal component method can be used as variables for carrying out the classification. It is shown that for an estimation of belonging to one of these groups, it is sufficient to use variables corresponding to the first two principal components. Examples of approbation of the proposed methods are given.