scholarly journals The convenient setting for ultradifferentiable mappings of Beurling- and Roumieu-type defined by a weight matrix

2015 ◽  
Vol 22 (3) ◽  
pp. 471-510
Author(s):  
Gerhard Schindl
Keyword(s):  
Weight Matrix ◽  
Convenient Setting

scholarly journals Cluster-Wise Weighted NMF for Hyperspectral Images Unmixing with Imbalanced Data

2021 ◽  
Vol 13 (2) ◽  
pp. 268
Author(s):  
Xiaochen Lv ◽  
Wenhong Wang ◽  
Hongfu Liu
Keyword(s):  
Spatial Information ◽  
Hyperspectral Image ◽  
Imbalanced Data ◽  
Reconstruction Error ◽  
Hyperspectral Data ◽  
Weight Matrix ◽  
Hyperspectral Images ◽  
Mixed Data ◽  
Sparsity Constraints ◽  
Additional Constraints

Hyperspectral unmixing is an important technique for analyzing remote sensing images which aims to obtain a collection of endmembers and their corresponding abundances. In recent years, non-negative matrix factorization (NMF) has received extensive attention due to its good adaptability for mixed data with different degrees. The majority of existing NMF-based unmixing methods are developed by incorporating additional constraints into the standard NMF based on the spectral and spatial information of hyperspectral images. However, they neglect to exploit the nature of imbalanced pixels included in the data, which may cause the pixels mixed with imbalanced endmembers to be ignored, and thus the imbalanced endmembers generally cannot be accurately estimated due to the statistical property of NMF. To exploit the information of imbalanced samples in hyperspectral data during the unmixing procedure, in this paper, a cluster-wise weighted NMF (CW-NMF) method for the unmixing of hyperspectral images with imbalanced data is proposed. Specifically, based on the result of clustering conducted on the hyperspectral image, we construct a weight matrix and introduce it into the model of standard NMF. The proposed weight matrix can provide an appropriate weight value to the reconstruction error between each original pixel and the reconstructed pixel in the unmixing procedure. In this way, the adverse effect of imbalanced samples on the statistical accuracy of NMF is expected to be reduced by assigning larger weight values to the pixels concerning imbalanced endmembers and giving smaller weight values to the pixels mixed by majority endmembers. Besides, we extend the proposed CW-NMF by introducing the sparsity constraints of abundance and graph-based regularization, respectively. The experimental results on both synthetic and real hyperspectral data have been reported, and the effectiveness of our proposed methods has been demonstrated by comparing them with several state-of-the-art methods.

scholarly journals A weight matrix for binding recognition by the redox-response regulator ArcA-P of Escherichia coli

1999 ◽  
Vol 32 (1) ◽  
pp. 219-221 ◽  
Author(s):  
Abigail M. McGuire ◽  
Peter De Wulf ◽  
George M. Church ◽  
E. C. C. Lin
Keyword(s):  
Escherichia Coli ◽  
Response Regulator ◽  
Weight Matrix

Air Suspension Optimal Control Based on the Genetic Algorithm

2011 ◽  
Vol 467-469 ◽  
pp. 1066-1071
Author(s):  
Zhong Xin Li ◽  
Ji Wei Guo ◽  
Ming Hong Gao ◽  
Hong Jiang
Keyword(s):  
Genetic Algorithm ◽  
Optimal Control ◽  
Dynamic Model ◽  
Control Method ◽  
Control Model ◽  
Weight Matrix ◽  
Object A ◽  
Full Vehicle ◽  
Air Suspension ◽  
Optimal Control Method

Taking the full-vehicle eight-freedom dynamic model of a type of bus as the simulation object , a new optimal control method is introduced. This method is based on the genetic algorithm, and the full-vehicle optimal control model is built in the MatLab. The weight matrix of the optimal control is optimized through the genetic algorithm; then the outcome is compared with the artificially-set optimal control simulation, which shows that the genetic-algorithm based optimal control presents better performance, thereby creating a smoother ride and improving the steering stability of the vehicle.

scholarly journals Bayesian Spatial Autoregressive for Reducing Blurring Effect in Image

2007 ◽  
Vol 11 (3) ◽  
pp. 308-311
Author(s):  
Siana Halim ◽  
Keyword(s):  
Error Estimate ◽  
Weight Matrix ◽  
Block Bootstrap ◽  
Two Dimensional ◽  
Large Matrix ◽  
Specific Manner ◽  
Spatial Autoregressive ◽  
The Difference ◽  
Blurring Effect ◽  
Regular Texture

We apply the Bayesian Spatial Autoregressive, which is developed by Geweke and LeSage, for reducing the blurring effect in the image. This blurring effect, particularly comes from the synthesizing semi regular texture via, e.g., two dimensional block bootstrap. We model the error, i.e., the difference between the true image and the synthesis one, as the Bayesian Spatial Autoregressive (SAR). Moreover, the weight matrix is defined in a specific manner, such that the problem in the computational for a very large matrix can be avoided. Finally, we use the error estimate, as the result of Bayesian SAR modelling, for reducing the blurring effect in the synthesis image.

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