A special form of a generalized inverse of an arbitrary complex matrix

Equations for inversion of singular matrix - special form of generalized inverse of arbitrary complex matri

On the variational equations for Householder transformations in feature selection

Results that suggest the possibility of using a sequential monotone process for solving the feature selection problem using Householder transformations are applied to the divergence separability criterion and an expression for the gradient of the divergence with respect to the generator of a single Householder transformation will be developed. This expression for the gradient is used in any number of differential correction schemes (iterators) that attempt to extremize the divergence. Data sets provided by the Earth Observations Division-JSC are used to demonstrate selecting the Householder transformations that generate the kxn matrix defining the best (in the sense of extremizing the divergence) k linear combinations of features. The tests allow initial comparisons to be made with results. In particular, this technique does not appear to require initial guesses for the iterator to be generated without replacement, exhaustive search, or other similar schemes

Feature combinations and the divergence criterion

Classifying large quantities of multidimensional remotely sensed agricultural data requires efficient and effective classification techniques and the construction of certain transformations of a dimension reducing, information preserving nature. The construction of transformations that minimally degrade information (i.e., class separability) is described. Linear dimension reducing transformations for multivariate normal populations are presented. Information content is measured by divergence

Feature combinations and the Bhattacharyya criterion

A procedure for calculating a kxn rank k matrix B for data compression using the Bhattacharyya bound on the probability of error and an iterative construction using Householder transformation was developed. Two sets of remotely sensed agricultural data are used to demonstrate the application of the procedure. The results of the applications gave some indication of the extent to which the Bhattacharyya bound on the probability of error is affected by such transformations for multivariate normal populations

Linear feature selection with applications

There are no author-identified significant results in this report

Image 100 procedures manual development: Applications system library definition and Image 100 software definition

An outline for an Image 100 procedures manual for Earth Resources Program image analysis was developed which sets forth guidelines that provide a basis for the preparation and updating of an Image 100 Procedures Manual. The scope of the outline was limited to definition of general features of a procedures manual together with special features of an interactive system. Computer programs were identified which should be implemented as part of an applications oriented library for the system

Householder transformations and optimal linear combinations

Several theorems related to the Householder transformation and separability criteria are proven. Orthogonal transformations, topology, divergence, mathematical matrices, and group theory are discussed

Characterizations of linear sufficient statistics

A surjective bounded linear operator T from a Banach space X to a Banach space Y must be a sufficient statistic for a dominated family of probability measures defined on the Borel sets of X. These results were applied, so that they characterize linear sufficient statistics for families of the exponential type, including as special cases the Wishart and multivariate normal distributions. The latter result was used to establish precisely which procedures for sampling from a normal population had the property that the sample mean was a sufficient statistic

Linear dimension reduction and Bayes classification

An explicit expression for a compression matrix T of smallest possible left dimension K consistent with preserving the n variate normal Bayes assignment of X to a given one of a finite number of populations and the K variate Bayes assignment of TX to that population was developed. The Bayes population assignment of X and TX were shown to be equivalent for a compression matrix T explicitly calculated as a function of the means and covariances of the given populations

Development of mathematical techniques for the analysis of remote sensing data

There are no author-identified significant results in this report