Development of mathematical techniques for the analysis of remote sensing data
There are no author-identified significant results in this report.
Decell, H. P., Jr.↗
Engineering topics
Peters, B. C.
Publications and source records attributed to Peters, B. C..
Small grains separation and optimal pass selection
There are no author-identified significant results in this report.
Decell, H. P., Jr.↗
Results on the two population feature selection problem using probability of correct classification as a criterion
Variational equations are presented for maximizing the probability of correct classification as a function of a 1xn feature selection matrix B for the two-population problem. For the special case of equal covariance matrices the optimal B is unique up to scalar multiples and rank one sufficient. For equal population means, the best 1xn B is an eigenvector corresponding either to the largest or smallest eigenvalue of sigma sub 2 to the minus 1 power sigma sub 1 where sigma sub 1 and sigma sub 2 are the nxn covariance matrices of the two populations. The transformed probability of correct classification depends only on the eigenvalue. Finally, a procedure is proposed for constructing an optimal or nearly optimal kxn matrix of rank k without solving the k-dimensional variational equation.
Peters, B. C.↗
On differentiating the probability of error in the multipopulation feature selection problem, 2
A condition for the Gateaux differentiability of the probability of misclassification as a function of a feature selection matrix B, assuming a maximum likelihood classifier and normally distributed populations, is given. It is also shown that if the probability of error has a local minimum at B then it is differentiable at B.
Peters, B. C.↗
On differentiating the probability of error in multipopular feature selection
A method of linear feature selection for n dimensional observation vectors which belong to one of m populations is presented. Each population has a known apriori probability and is described by a known multivariate normal density function. Specifically we consider the problem of finding a k x n matrix B of rank k (k n) for which the transformed probability of misclassification is minimized. Providing that the transformed a posterior probabilities are distinct theoretical results are obtained which, for the case k = l, give rise to a numerically tractable formula for the derivative of the probability of misclassification. It is shown that for the two population problem this condition is also necessary. The dependence of the minimum probability of error on the a priori probabilities is investigated. The minimum probability of error satisfies a uniform Lipschitz condition with respect to the a priori probabilities.
Peters, B. C.↗