Analysis of Generalized Pattern Searches

Audet, Charles; Dennis, John E.

doi:10.1137/s1052623400378742

Cited by 846 publications

(669 citation statements)

References 28 publications

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“…-Trust-region reflective algorithm 33 Non-derivative based: -Simplex algorithm 34 -Pattern search optimization 35 The Levenberg-Marquardt as well as the Trust-region reflective algorithm are based on the method of steepest descent and the line search approach. They differ in the solution of the quadratic subproblems 36 .…”

Section: Sequential and Simultaneous Parameter Estimation And Verificmentioning

confidence: 99%

A Comprehensive Methodology for Development, Parameter Estimation, and Uncertainty Analysis of Group Contribution Based Property Models—An Application to the Heat of Combustion

et al. 2015

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ABSTRACT:A rigorous methodology is developed that addresses numerical and statistical issues when developing group contribution (GC) based property models such as regression methods, optimization algorithms, performance statistics, outlier treatment, parameter identifiability and uncertainty of the prediction. The methodology is evaluated through development of a GC method for prediction of the heat of combustion ( ) for pure components. The results showed that robust regression lead to best performance statistics for parameter estimation. Bootstrap method is found a valid alternative to calculate parameter estimation errors when underlying distribution of residuals is unknown. Many parameters (first, second, third order groups contributions) are found unidentifiable from the typically available data, with large estimation error bounds and significant correlation. Due to this poor parameter 2 identifiability issues, reporting of the 95%-confidence intervals of the predicted property values should be mandatory as opposed to reporting only single value prediction, currently the norm in literature. Moreover, inclusion of higher order groups (additional parameters) does not always lead to improved prediction accuracy for the GC-models, in some cases it may even increase the prediction error (hence worse prediction accuracy). However, additional parameters do not affect calculated 95%-confidence interval. Last but not least, the newly developed GC model of the heat of combustion ( ) shows predictions of great accuracy and quality (the most data falling within the 95% confidence intervals) and provides additional information on the uncertainty of each prediction compared to other models reported in literature.

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Section: Sequential and Simultaneous Parameter Estimation And Verificmentioning

confidence: 99%

A Comprehensive Methodology for Development, Parameter Estimation, and Uncertainty Analysis of Group Contribution Based Property Models—An Application to the Heat of Combustion

et al. 2015

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“…For the optimization task we used a function available in the MATLAB Optimization Toolbox that implements the Pattern Search (Audet et al, 2003) algorithm. This function permits to impose constraints to the search procedure.…”

Section: Experimental Protocolmentioning

confidence: 99%

A Method to Estimate Temporal Interaction in a Conditional Random Field Based Approach for Crop Recognition

Diaz¹,

Feitosa²,

Sanches³

et al. 2016

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:This paper presents a method to estimate the temporal interaction in a Conditional Random Field (CRF) based approach for crop recognition from multitemporal remote sensing image sequences. This approach models the phenology of different crop types as a CRF. Interaction potentials are assumed to depend only on the class labels of an image site at two consecutive epochs. In the proposed method, the estimation of temporal interaction parameters is considered as an optimization problem, whose goal is to find the transition matrix that maximizes the CRF performance, upon a set of labelled data. The objective functions underlying the optimization procedure can be formulated in terms of different accuracy metrics, such as overall and average class accuracy per crop or phenological stages. To validate the proposed approach, experiments were carried out upon a dataset consisting of 12 co-registered LANDSAT images of a region in southeast of Brazil. Pattern Search was used as the optimization algorithm. The experimental results demonstrated that the proposed method was able to substantially outperform estimates related to joint or conditional class transition probabilities, which rely on training samples.

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“…The strategy for picking such points is left entirely to the user. Common choices are discussed in [4] or [5], for example.…”

Section: Mesh Adaptive Direct Search (Mads)mentioning

confidence: 99%

Characteristic Shape Sequences for Measures on Images

Pinge¹,

Abramson²,

Asaki³

et al. 2006

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Researchers in many fields often need to quantify the similarity between images using metrics that measure qualities of interest in a robust quantitative manner. We present here the concept of image dimension reduction through characteristic shape sequences. We formulate the problem as a nonlinear optimization program and demonstrate the solution on a test problem of extracting maximal area ellipses from twodimensional image data. To solve the problem numerically, we augment the class of mesh adaptive direct search (MADS) algorithms with a filter, so as to allow infeasible starting points and to achieve better local solutions. Results here show that the MADS filter algorithm is successful in the test problem of finding good characteristic ellipse solutions from simple but noisy images.

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Analysis of Generalized Pattern Searches

Cited by 846 publications

References 28 publications

A Comprehensive Methodology for Development, Parameter Estimation, and Uncertainty Analysis of Group Contribution Based Property Models—An Application to the Heat of Combustion

A Comprehensive Methodology for Development, Parameter Estimation, and Uncertainty Analysis of Group Contribution Based Property Models—An Application to the Heat of Combustion

A Method to Estimate Temporal Interaction in a Conditional Random Field Based Approach for Crop Recognition

Characteristic Shape Sequences for Measures on Images

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