Density Estimations and the Characterization of Binary Infrared Spectra

A truncated orthogonal expansion has been used to represent binary data taken from a multidimensional file of infrared data. The expansion represents an approximation for the true class conditional probability density functions (pdf's). As a first approximation, statistical independence is assumed and the only terms necessary are the estimated class conditional probabilities for each peak. A more accurate estimation of the pdf is attained when a second term, a correlation term, is included in the expansion. The data set consists of 2600 spectra in thirteen mutually exclusive classes with each spectrum represented by 139 dimemqions. Results are obtained for a maximum discriminant function case, as well as for pairwise discrimination among the classes. For the thirteen class problem, correct classification occurs 67.2% of the time by the class conditional probabilities and 87.3% of the time when the correlation terms are inclrlded. For pairwise discrimination, the results are 92.9% and 98.1% respectively.