1,277 research outputs found
Feature selection for best mean square approximation of class densities
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
Analytical design of multispectral sensors
An optimal design based on the criterion of minimum mean square representation error using the Karhunen-Loeve expansion was developed to represent the spectral response functions from a stratum based upon a stochastic process scene model. From the overall pattern recognition system perspective, the effect of the representation accuracy on a typical performance criterion (the probability of correct classification) is investigated. The optimum sensor design provides a standard against which practical (suboptimum) operational sensors can be compared. An example design is provided and its performance is illustrated. Although developed primarily for the purpose of sensor design, the procedure has potential for making important contributions to scene understanding. Spectral channels which have narrow bandwidths relative to current sensor systems may be necessary to provide adequate spectral representation and improved classification performance
Modeling the behavior of elastic materials with stochastic microstructure
Even in the simple linear elastic range, the material behavior is not deterministic, but fluctuates randomly around some expectation values. The knowledge about this characteristic is obviously trivial from an experimentalist’s point of view. However, it is not considered in the vast majority of material models in which “only” deterministic behavior is taken into account. One very promising approach to the inclusion of stochastic effects in modeling of materials is provided by the Karhunen-Lo`eve expansion. It has been used, for example, in the stochastic finite element method, where it yields results of the desired kind, but unfortunately at drastically increased numerical costs. This contribution aims to propose a new ansatz that is based on a stochastic series expansion, but at the Gauß point level. Appropriate energy relaxation allows to derive the distribution of a synthesized stress measure, together with explicit formulas for the expectation and variance. The total procedure only needs negligibly more computation effort than a simple elastic calculation. We also present an outlook on how the original approach in [7] can be applied to inelastic material
An efficient polynomial chaos-based proxy model for history matching and uncertainty quantification of complex geological structures
A novel polynomial chaos proxy-based history matching and uncertainty quantification
method is presented that can be employed for complex geological structures in inverse
problems. For complex geological structures, when there are many unknown geological
parameters with highly nonlinear correlations, typically more than 106 full reservoir
simulation runs might be required to accurately probe the posterior probability space
given the production history of reservoir. This is not practical for high-resolution geological
models. One solution is to use a "proxy model" that replicates the simulation
model for selected input parameters. The main advantage of the polynomial chaos
proxy compared to other proxy models and response surfaces is that it is generally
applicable and converges systematically as the order of the expansion increases. The
Cameron and Martin theorem 2.24 states that the convergence rate of the standard
polynomial chaos expansions is exponential for Gaussian random variables. To improve
the convergence rate for non-Gaussian random variables, the generalized polynomial
chaos is implemented that uses an Askey-scheme to choose the optimal basis for polynomial
chaos expansions [199]. Additionally, for the non-Gaussian distributions that
can be effectively approximated by a mixture of Gaussian distributions, we use the
mixture-modeling based clustering approach where under each cluster the polynomial
chaos proxy converges exponentially fast and the overall posterior distribution can be
estimated more efficiently using different polynomial chaos proxies.
The main disadvantage of the polynomial chaos proxy is that for high-dimensional problems,
the number of the polynomial chaos terms increases drastically as the order of the
polynomial chaos expansions increases. Although different non-intrusive methods have
been developed in the literature to address this issue, still a large number of simulation
runs is required to compute high-order terms of the polynomial chaos expansions. This
work resolves this issue by proposing the reduced-terms polynomial chaos expansion
which preserves only the relevant terms in the polynomial chaos representation. We
demonstrated that the sparsity pattern in the polynomial chaos expansion, when used
with the Karhunen-Loéve decomposition method or kernel PCA, can be systematically
captured.
A probabilistic framework based on the polynomial chaos proxy is also suggested in the
context of the Bayesian model selection to study the plausibility of different geological
interpretations of the sedimentary environments. The proposed surrogate-accelerated
Bayesian inverse analysis can be coherently used in practical reservoir optimization
workflows and uncertainty assessments
The analytical design of spectral measurements for multispectral remote sensor systems
The author has identified the following significant results. In order to choose a design which will be optimal for the largest class of remote sensing problems, a method was developed which attempted to represent the spectral response function from a scene as accurately as possible. The performance of the overall recognition system was studied relative to the accuracy of the spectral representation. The spectral representation was only one of a set of five interrelated parameter categories which also included the spatial representation parameter, the signal to noise ratio, ancillary data, and information classes. The spectral response functions observed from a stratum were modeled as a stochastic process with a Gaussian probability measure. The criterion for spectral representation was defined by the minimum expected mean-square error
Multistage classification of multispectral Earth observational data: The design approach
An algorithm is proposed which predicts the optimal features at every node in a binary tree procedure. The algorithm estimates the probability of error by approximating the area under the likelihood ratio function for two classes and taking into account the number of training samples used in estimating each of these two classes. Some results on feature selection techniques, particularly in the presence of a very limited set of training samples, are presented. Results comparing probabilities of error predicted by the proposed algorithm as a function of dimensionality as compared to experimental observations are shown for aircraft and LANDSAT data. Results are obtained for both real and simulated data. Finally, two binary tree examples which use the algorithm are presented to illustrate the usefulness of the procedure
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