Orthogonalization

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Walter Thiel - One of the best experts on this subject based on the ideXlab platform.

  • semiempirical quantum chemical methods with Orthogonalization and dispersion corrections
    Journal of Chemical Theory and Computation, 2019
    Co-Authors: Pavlo O Dral, Xin Wu, Walter Thiel
    Abstract:

    We present two new semiempirical quantum-chemical methods with Orthogonalization and dispersion corrections: ODM2 and ODM3 (ODMx). They employ the same electronic structure model as the OM2 and OM3...

  • Orthogonalization corrections for semiempirical methods
    Theoretical Chemistry Accounts, 2000
    Co-Authors: Wolfgang Weber, Walter Thiel
    Abstract:

    Based on a general discussion of Orthogonalization effects, two new one-electron Orthogonalization corrections are derived to improve existing semiempirical models at the neglect of diatomic differential overlap level. The first one accounts for valence-shell Orthogonalization effects on the resonance integrals, while the second one includes the dominant repulsive core–valence interactions through an effective core potential. The corrections for the resonance integrals consist of three-center terms which incorporate stereodiscriminating properties into the two-center matrix elements of the core Hamiltonian. They provide a better description of conformational properties, which is rationalized qualitatively and demonstrated through numerical calculations on small model systems. The proposed corrections are part of a new general-purpose semiempirical method which will be described elsewhere.

Xiaohui Li - One of the best experts on this subject based on the ideXlab platform.

  • Channel Orthogonalization (CO) and its Combination with THP (CO-THP) for Multiuser MIMO Systems
    2012 IEEE 26th International Conference on Advanced Information Networking and Applications, 2012
    Co-Authors: Liang Zhou, Xiaohui Li
    Abstract:

    In this paper, a linear Channel Orthogonalization (CO) algorithm with low complexity is presented, which is applicable to systems with an arbitrary number of antennas and users. Unlike other conventional linear methods, CO obtains the orthonormal basis to achieve the precoding matrix by means of using Schmidt Orthogonalization method. Then, the algorithm (CO-THP) combining CO with Tomlinson-Harashima Precoding (THP) is proposed to eliminate the residual interference from any former user in CO. Different from the conventional THP algorithms, CO-THP eliminates all the Multi-User Interference (MUI) without amplifying the noise, which brings it better BER performance. And the combination with THP brings CO a higher capacity than linear scheme BD. Simulation results show the performance advantage obtained by the CO and CO-THP.

  • Channel Orthogonalization precoding algorithms for multiuser MIMO downlink systems
    2011 International Conference on Communications and Signal Processing, 2011
    Co-Authors: Liang Zhou, Xiaohui Li, Guanghui Yu
    Abstract:

    In this paper, two precoding algorithms based on channel Orthogonalization have been proposed for multi-user MIMO downlink systems. Unlike other conventional methods, the first scheme obtains the orthonormal basis to achieve the precoding matrix by means of using Schmidt Orthogonalization method. In this way, the co-channel interference can be eliminated to some degree. The second algorithm increases every user's receive SINR (Signal to Interference plus Noise Ratio) by taking noise into account to balance the multi-user interference and the noise for every user. Simulation results show that the performance of our proposed schemes is very close to the conventional iterative scheme but significantly reduce the complexity with one data stream per user. For systems with multiple data streams per user, the second algorithm achieves better BER performance compared with several other algorithms.

Alper T. Erdogan - One of the best experts on this subject based on the ideXlab platform.

  • ICASSP - On the convergence of ICA algorithms with symmetric Orthogonalization
    2008 IEEE International Conference on Acoustics Speech and Signal Processing, 2008
    Co-Authors: Alper T. Erdogan
    Abstract:

    We study the convergence behavior of independent component analysis (ICA) algorithms that are based on the contrast function maximization and that employ symmetric Orthogonalization method to guarantee the orthogonality property of the search matrix. In particular, the characterization of the critical points of the corresponding optimization problem and the stationary points of the conventional gradient ascent and fixed point algorithms are obtained. As an interesting and a useful feature of the symmetrical Orthogonalization method, we show that the use of symmetric Orthogonalization enables the monotonic convergence for the fixed point ICA algorithms that are based on the convex contrast functions.

  • On the convergence of ICA algorithms with symmetric Orthogonalization
    2008 IEEE International Conference on Acoustics Speech and Signal Processing, 2008
    Co-Authors: Alper T. Erdogan
    Abstract:

    We study the convergence behavior of independent component analysis (ICA) algorithms that are based on the contrast function maximization and that employ symmetric Orthogonalization method to guarantee the orthogonality property of the search matrix. In particular, the characterization of the critical points of the corresponding optimization problem and the stationary points of the conventional gradient ascent and fixed point algorithms are obtained. As an interesting and a useful feature of the symmetrical Orthogonalization method, we show that the use of symmetric Orthogonalization enables the monotonic convergence for the fixed point ICA algorithms that are based on the convex contrast functions.

Deqing Wang - One of the best experts on this subject based on the ideXlab platform.

  • unsupervised feature selection through gram schmidt Orthogonalization a word co occurrence perspective
    Neurocomputing, 2016
    Co-Authors: Deqing Wang, Hui Zhang, Jing Wang
    Abstract:

    Feature selection is a key step in many machine learning applications, such as categorization, and clustering. Especially for text data, the original document-term matrix is high-dimensional and sparse, which affects the performance of feature selection algorithms. Meanwhile, labeling training instance is time-consuming and expensive. So unsupervised feature selection algorithms have attracted more attention. In this paper, we propose an unsupervised feature selection algorithm through R ? andom P ? rojection and G ? ram- G ? chmidt O ? rthogonalization (RP-GSO) from the word co-occurrence matrix. The RP-GSO algorithm has three advantages: (1) it takes as input dense word co-occurrence matrix, avoiding the sparseness of original document-term matrix; (2) it selects "basis features" by Gram-Schmidt process, guaranteeing the Orthogonalization of feature space; and (3) it adopts random projection to speed up GS process. Extensive experimental results show our proposed RP-GSO approach achieves better performance comparing against supervised and unsupervised feature selection methods in text classification and clustering tasks.

  • GS-Orthogonalization Based "Basis Feature" Selection from Word Co-occurrence Matrix
    2015 IEEE International Conference on Data Mining, 2015
    Co-Authors: Deqing Wang, Hui Zhang
    Abstract:

    Feature selection plays an important role in machinelearning applications. Especially for text data, the highdimensionaland sparse characteristics will affect the performanceof feature selction. In this paper, an unsupervised feature selection algorithm through Random Projection and Gram-Schmidt Orthogonalization (RP-GSO) from the word co-occurrence matrix is proposed. The RP-GSO has three advantages: (1) it takes as input dense word co-occurrence matrix, avoiding the sparseness of original document-term matrix, (2) it selects "basis features" by Gram-Schmidt process, guaranteeing the Orthogonalization of feature space, and (3) it adopts random projection to speed upGS process. We did extensive experiments on two real-world textcorpora, and observed that RP-GSO achieves better performancecomparing against supervised and unsupervised methods in textclassification and clustering tasks.

Liang Zhou - One of the best experts on this subject based on the ideXlab platform.

  • Channel Orthogonalization (CO) and its Combination with THP (CO-THP) for Multiuser MIMO Systems
    2012 IEEE 26th International Conference on Advanced Information Networking and Applications, 2012
    Co-Authors: Liang Zhou, Xiaohui Li
    Abstract:

    In this paper, a linear Channel Orthogonalization (CO) algorithm with low complexity is presented, which is applicable to systems with an arbitrary number of antennas and users. Unlike other conventional linear methods, CO obtains the orthonormal basis to achieve the precoding matrix by means of using Schmidt Orthogonalization method. Then, the algorithm (CO-THP) combining CO with Tomlinson-Harashima Precoding (THP) is proposed to eliminate the residual interference from any former user in CO. Different from the conventional THP algorithms, CO-THP eliminates all the Multi-User Interference (MUI) without amplifying the noise, which brings it better BER performance. And the combination with THP brings CO a higher capacity than linear scheme BD. Simulation results show the performance advantage obtained by the CO and CO-THP.

  • Channel Orthogonalization precoding algorithms for multiuser MIMO downlink systems
    2011 International Conference on Communications and Signal Processing, 2011
    Co-Authors: Liang Zhou, Xiaohui Li, Guanghui Yu
    Abstract:

    In this paper, two precoding algorithms based on channel Orthogonalization have been proposed for multi-user MIMO downlink systems. Unlike other conventional methods, the first scheme obtains the orthonormal basis to achieve the precoding matrix by means of using Schmidt Orthogonalization method. In this way, the co-channel interference can be eliminated to some degree. The second algorithm increases every user's receive SINR (Signal to Interference plus Noise Ratio) by taking noise into account to balance the multi-user interference and the noise for every user. Simulation results show that the performance of our proposed schemes is very close to the conventional iterative scheme but significantly reduce the complexity with one data stream per user. For systems with multiple data streams per user, the second algorithm achieves better BER performance compared with several other algorithms.