EFFECT OF ESTIMATION AND DIMENSIONALITY ON THE PERFORMANCE OF TWO-CLASS GAUSSIAN CLASSIFIERS
| dc.contributor.advisor | Wacker, A. G. | |
| dc.creator | El-Sheikh, Talaat Salem | |
| dc.date.accessioned | 2024-05-16T22:18:14Z | |
| dc.date.available | 2024-05-16T22:18:14Z | |
| dc.date.issued | 1980-04 | |
| dc.date.submitted | April 1980 | |
| dc.description.abstract | In this thesis the phenomenon observed in "real life", where the probability of correct classification P cr (for classifiers based on estimated distributions) peaks with the dimensionality N, is extensively investigated for two-class multivariate Gaussian classifiers. The case of equal prior class probabilities is the only case considered. Regarding the parameters of the class distributions, two main situations are considered. For the first situation it is assumed that the two class distributions have a common covariance matrix and that this information is known a priori. For the other and more general case, the parameters of the two class distributions are assumed to be different (i.e. the two covariance matrices are unequal and the two mean vectors are unequal). On the other hand, three interesting cases with different degrees of knowledge of the parameters are considered. In the first case all the parameters of the class distributions are assumed known. For the second case the covariance matrices are assumed known, while all the parameters are assumed unknown in the last and most general case. For the two latter cases, it is assumed that a number of design vectors K are available from each class to be used for estimating the unknown parameters. The classification rule considered is a suboptimal Bayes (minimum error for known distributions) rule in which the unbiased sample mean vectors and unbiased sample covariance matrices are used in place of the true parameters, generally resulting in hyperquadratic decision boundaries. For the known common covariance matrix case, a basic question investigated is the variation (with N) in the Mahalanobis distance (between the true distributions) required tb keep P cr constant. Numeri-cal results are plotted for several cases. Analytical results are also obtained which relate the rate of variation of the Mahalanobis distance with N and the corresponding asymptotic behaviour of P cr. Results for more highly structured problems, involving specific covariance matrices, show that in some cases increasing correlation between the measurements yields higher values of P cr. | |
| dc.identifier.uri | https://hdl.handle.net/10388/15685 | |
| dc.title | EFFECT OF ESTIMATION AND DIMENSIONALITY ON THE PERFORMANCE OF TWO-CLASS GAUSSIAN CLASSIFIERS | |
| dc.type.genre | Thesis | |
| thesis.degree.department | Electrical Engineering | |
| thesis.degree.grantor | University of Saskatchewan | en_US |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Doctor of Philosophy (Ph.D.) |