Tree Decomposition

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D S Weile - One of the best experts on this subject based on the ideXlab platform.

  • a finite difference delay modeling approach to the discretization of the time domain integral equations of electromagnetics
    IEEE Transactions on Antennas and Propagation, 2008
    Co-Authors: Xiaobo Wang, D S Weile, Raymond A Wildman, Peter Monk
    Abstract:

    A new method for solving the time-domain integral equations of electromagnetic scattering from conductors is introduced. This method, called finite difference delay modeling, appears to be completely stable and accurate when applied to arbitrary structures. The temporal discretization used is based on finite differences. Specifically, based on a mapping from the Laplace domain to the z-transform domain, first- and second-order unconditionally stable methods are derived. Spatial convergence is achieved using the higher-order divergence-conforming vector bases of Graglia et al. Low frequency instability problems are avoided with the loop-Tree Decomposition approach. Numerical results will illustrate the accuracy and stability of the technique.

  • robust solution of time domain integral equations using loop Tree Decomposition and bandlimited extrapolation
    IEEE Transactions on Antennas and Propagation, 2005
    Co-Authors: G Pisharody, D S Weile
    Abstract:

    A stabilization method that eradicates low frequency instabilities in the solution of the time-domain integral equations of electromagnetic scattering is presented. The method uses the loop-Tree Decomposition originally suggested for the solution of low frequency scattering problems via the method of moments. Specifically, a temporally differentiated form of the pertinent integral equation is tested using Tree basis functions, and the undifferentiated form is tested using solenoidal basis functions. The underlying solution method uses bandlimited interpolation functions (BLIFs) and the higher-order divergence-conforming vector bases of Graglia et al. for the temporal and spatial discretization of the integral equations, respectively. An extrapolation technique has been implemented to overcome the noncausality introduced into the system by the BLIFs. Numerical results will demonstrate the stability and accuracy of the proposed technique.

Peter Monk - One of the best experts on this subject based on the ideXlab platform.

  • a finite difference delay modeling approach to the discretization of the time domain integral equations of electromagnetics
    IEEE Transactions on Antennas and Propagation, 2008
    Co-Authors: Xiaobo Wang, D S Weile, Raymond A Wildman, Peter Monk
    Abstract:

    A new method for solving the time-domain integral equations of electromagnetic scattering from conductors is introduced. This method, called finite difference delay modeling, appears to be completely stable and accurate when applied to arbitrary structures. The temporal discretization used is based on finite differences. Specifically, based on a mapping from the Laplace domain to the z-transform domain, first- and second-order unconditionally stable methods are derived. Spatial convergence is achieved using the higher-order divergence-conforming vector bases of Graglia et al. Low frequency instability problems are avoided with the loop-Tree Decomposition approach. Numerical results will illustrate the accuracy and stability of the technique.

Shihfu Chang - One of the best experts on this subject based on the ideXlab platform.

  • quad Tree segmentation for texture based image query
    ACM Multimedia, 1994
    Co-Authors: John R Smith, Shihfu Chang
    Abstract:

    In this paper we propose a technique for segmenting images by texture content with application to indexing images in a large image database. Using quad-Tree Decomposition, texture features are extracted from spatial blocks at a hierarchy of scales in each image. The quad-Tree is grown by iteratively testing conditions for splitting parent blocks based on texture content of children blocks. While this approach does not achieve smooth identification of texture region borders, homogeneous blocks of texture are extracted which can be used in a database index. Furthermore, this technique performs the segmentation directly using image spatial-frequency data. In the segmentation reported here, texture features are extracted from the wavelet representation of the image. This method however, can use other subband Decompositions including Discrete Cosine Transform (DCT), which has been adopted by the JPEG standard for image coding. This makes our segmentation method extremely applicable to databases containing compressed image data. We show application of the texture segmentation towards providing a new method for searching for images in large image databases using “Query-by-texture.”

Xiaorong Lin - One of the best experts on this subject based on the ideXlab platform.

  • Tree Decomposition for large scale svm problems
    Journal of Machine Learning Research, 2010
    Co-Authors: Fu Chang, Chienyang Guo, Xiaorong Lin
    Abstract:

    To handle problems created by large data sets, we propose a method that uses a decision Tree to decompose a given data space and train SVMs on the decomposed regions. Although there are other means of decomposing a data space, we show that the decision Tree has several merits for large-scale SVM training. First, it can classify some data points by its own means, thereby reducing the cost of SVM training for the remaining data points. Second, it is efficient in determining the parameter values that maximize the validation accuracy, which helps maintain good test accuracy. Third, the Tree Decomposition method can derive a generalization error bound for the classifier. For data sets whose size can be handled by current non-linear, or kernel-based, SVM training techniques, the proposed method can speed up the training by a factor of thousands, and still achieve comparable test accuracy.

Philip S. Yu - One of the best experts on this subject based on the ideXlab platform.

  • Low-Density Cut Based Tree Decomposition for Large-Scale SVM Problems
    2014 IEEE International Conference on Data Mining, 2014
    Co-Authors: Lifang He, Hong-han Shuai, Xiangnan Kong, Xiaowei Yang, Philip S. Yu
    Abstract:

    The current trend of growth of information reveals that it is inevitable that large-scale learning problems become the norm. In this paper, we propose and analyze a novel Low-density Cut based Tree Decomposition method for large-scale SVM problems, called LCD-SVM. The basic idea here is divide and conquer: use a decision Tree to decompose the data space and train SVMs on the decomposed regions. Specifically, we demonstrate the application of low density separation principle to devise a splitting criterion for rapidly generating a high-quality Tree, thus maximizing the benefits of SVMs training. Extensive experiments on 14 real-world datasets show that our approach can provide a significant improvement in training time over state-of-the-art methods while keeps comparable test accuracy with other methods, especially for very large-scale datasets.