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A criterion for linear feature selection is proposed which is based on mean square apporximation of class density functions. It is shown that for the widest possible class of approximants, the criterion reduces to Devijver's Bayesian distance. For linear approximants the criterion is equivalent to well known generalized Fisher criteria.
Feature selection and the information content of Thematic Mapper Simulator (TMS) data are investigated for a forested region in northern Idaho. The optimal TMS channels for forest structural characteristics are determined, and the capability of TMS data to describe the structural variability within a forest stand is evaluated. The comparative performance of TMS and MSS data to discriminate forest structural factors using per-pixel maximum likelihood classification is examined, and four optimal TMS channels are classified in order to ascertain if the full complement of TM channels provide higher accuracies than the four optimal ones.
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.
The computational procedure and associated computer program for a linear feature selection technique are presented. The technique assumes that: a finite number, m, of classes exists; each class is described by an n-dimensional multivariate normal density function of its measurement vectors; the mean vector and covariance matrix for each density function are known (or can be estimated); and the a priori probability for each class is known. The technique produces a single linear combination of the original measurements which minimizes the one-dimensional probability of misclassification defined by the transformed densities.
A new clustering algorithm is presented that is based on dimensional information. The algorithm includes an inherent feature selection criterion, which is discussed. Further, a heuristic method for choosing the proper number of intervals for a frequency distribution histogram, a feature necessary for the algorithm, is presented. The algorithm, although usable as a stand-alone clustering technique, is then utilized as a global approximator. Local clustering techniques and configuration of a global-local scheme are discussed, and finally the complete global-local and feature selector configuration is shown in application to a real-time adaptive classification scheme for the analysis of remote sensed multispectral scanner data.
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.
The B-average divergence for m-distinct classes, resulting from the linear transformation y = Bx, is proposed as a feature selection criterion, where B is a k by n matrix of rank k not greater than n. It is shown that if the B-average divergence resulting from B is large enough, then the probability of misclassification, considered as a function f the class of all k by n matrices, is essentially minimized by B. A computer program, utilizing a gradient procedure, is developed to numerically maximize the B-average divergence and results are presented for the Cl flight line. For this example, corresponding to 9-distinct classes, most of the discriminatory information is found to lie in a 3-dimensional subspace, defined by an appropriately chosen 3 by 12 matrix B.
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.
The paper shows that it is possible to construct two k x n matrices, both of which maximize divergence in the transformed space of the linear feature selection problem in multiclass pattern recognition, and which are not row equivalent. Thus, even under extremely strong conditions, it is not possible to assume that all matrix solutions which maximize transformed divergence are row equivalent.
A Technology Benefit Estimator (T/BEST) system has been developed to provide a formal method to assess advanced aerospace technologies and quantify the benefit contributions for prioritization. An open-ended, modular approach is used to allow for upgrade and insertion of advanced technology modules. T/BEST's software framework, beginner-to-expert operation, interface architecture, and key analysis modules are discussed. In this paper, selected features and applications of T/BEST are demonstrated. Sample cases pertaining to structural analysis of titanium and composite blades are presented. The performance of hot and cold composite fan blades is also discussed. The cost required to manufacture titanium and composite fan blades is estimated.
The use of a Monte Carlo model for generating sample directional reflectance data for two simplified target canopies at two different solar positions is reported. Successive iterations through the model permit the calculation of a mean vector and covariance matrix for canopy reflectance for varied sensor view angles. These data may then be used to calculate the divergence between the target distributions for various wavelength combinations and for these view angles. Results of a feature selection analysis indicate that different sets of wavelengths are optimum for target discrimination depending on sensor view angle and that the targets may be more easily discriminated for some scan angles than others. The time-varying behavior of these results is also pointed out.
An assessment is made of the information content of Thematic Mapper Simulator (TMS) data for the case of a forested region, in order to determine the sensitivity of such data to forest crown closure and tree size class. Principal components analysis and Monte Carlo simulation indicated that channels 4, 7, 5 and 3 were optimal for four-channel forest structure analysis. As the number of channels supplied to the Monte Carlo feature selection routine increased, classification accuracy increased. The greatest sensitivity to the forest structural parameters, which included succession within clearcuts as well as crown closure and size class, was obtained from the 7-channel TMS data.
Selected lunar topographic features by photometry with computer data reduction at 23 phase angles
An algorithm is proposed for dimensionality reduction in the context of clustering techniques based on histogram analysis. The approach is based on an evaluation of the hills and valleys in the unidimensional histograms along the different features and provides an economical means of assessing the significance of the features in a nonparametric unsupervised data environment. The method has relevance to remote sensing applications.
The use of satellite-acquired (LANDSAT) multispectral scanner (MSS) data to conduct an inventory of some crop of economic interest such as wheat over a large geographical area is considered in relation to the development of accurate and efficient algorithms for data classification. The dimension of the measurement space and the computational load for a classification algorithm is increased by the use of multitemporal measurements. Feature selection/combination techniques used to reduce the dimensionality of the problem are described.
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Fabry-Perot interferometry of Comet Kohoutek (1973f) at 1.1 microns with a resolution of 1.2 A showed emission features identified as OH and CN lines in addition to a strong Fraunhofer continuum. Central intensities have been derived for three cases (uniform, Gaussian, and Gaussian plus inverse-rho law) of brightness profiles in the comet coma. Limits for CH4, H2O, HeI, SiI and CrI are also derived.
A maximum likelihood estimation technique is used for the analysis of agricultural remote sensor data. The m-class probability of misclassification is estimated using unlabeled test samples and labeled training samples. A bound on the variance of a proposed unbiased estimator of the m-class probability of error is derived. The particular case in which each class density is assumed to be a mixture of multivariate normal densities is considered. The extension of spectral signatures in space and time is discussed.