The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform

Wataru Takahashi - One of the best experts on this subject based on the ideXlab platform.

Jun Zhang - One of the best experts on this subject based on the ideXlab platform.

  • vector valued reproducing kernel Banach Spaces with applications to multi task learning
    Journal of Complexity, 2013
    Co-Authors: Haizhang Zhang, Jun Zhang
    Abstract:

    Motivated by multi-task machine learning with Banach Spaces, we propose the notion of vector-valued reproducing kernel Banach Spaces (RKBSs). Basic properties of the Spaces and the associated reproducing kernels are investigated. We also present feature map constructions and several concrete examples of vector-valued RKBSs. The theory is then applied to multi-task machine learning. Especially, the representer theorem and characterization equations for the minimizer of regularized learning schemes in vector-valued RKBSs are established.

  • Reproducing kernel Banach Spaces for machine learning
    2009 International Joint Conference on Neural Networks, 2009
    Co-Authors: Haizhang Zhang, Yuesheng Xu, Jun Zhang
    Abstract:

    Reproducing kernel Hilbert space (RKHS) methods have become powerful tools in machine learning. However, their kernels, which measure similarity of inputs, are required to be symmetric, constraining certain applications in practice. Furthermore, the celebrated representer theorem only applies to regularizers induced by the norm of an RKHS. To remove these limitations, we introduce the notion of reproducing kernel Banach Spaces (RKBS) for pairs of reflexive Banach Spaces of functions by making use of semi-inner-products and the duality mapping. As applications, we develop the framework of RKBS standard learning schemes including minimal norm interpolation, regularization network, and support vector machines. In particular, existence, uniqueness and representer theorems are established.

Trygve Helgaker - One of the best experts on this subject based on the ideXlab platform.

  • generalized kohn sham iteration on Banach Spaces
    Journal of Chemical Physics, 2018
    Co-Authors: Andre Laestadius, Markus Penz, Erik I Tellgren, Michael Ruggenthaler, Simen Kvaal, Trygve Helgaker
    Abstract:

    A detailed account of the Kohn–Sham (KS) algorithm from quantum chemistry, formulated rigorously in the very general setting of convex analysis on Banach Spaces, is given here. Starting from a Levy–Lieb-type functional, its convex and lower semi-continuous extension is regularized to obtain differentiability. This extra layer allows us to rigorously introduce, in contrast to the common unregularized approach, a well-defined KS iteration scheme. Convergence in a weak sense is then proven. This generalized formulation is applicable to a wide range of different density-functional theories and possibly even to models outside of quantum mechanics.A detailed account of the Kohn–Sham (KS) algorithm from quantum chemistry, formulated rigorously in the very general setting of convex analysis on Banach Spaces, is given here. Starting from a Levy–Lieb-type functional, its convex and lower semi-continuous extension is regularized to obtain differentiability. This extra layer allows us to rigorously introduce, in contrast to the common unregularized approach, a well-defined KS iteration scheme. Convergence in a weak sense is then proven. This generalized formulation is applicable to a wide range of different density-functional theories and possibly even to models outside of quantum mechanics.

Shinya Matsushita - One of the best experts on this subject based on the ideXlab platform.

Erdal Karapinar - One of the best experts on this subject based on the ideXlab platform.

  • fixed point theorems in cone Banach Spaces
    Fixed Point Theory and Applications, 2009
    Co-Authors: Erdal Karapinar
    Abstract:

    In this manuscript, a class of self-mappings on cone Banach Spaces which have at least one fixed point is considered. More precisely, for a closed and convex subset of a cone Banach space with the norm , if there exist , , and satisfies the conditions and for all , then has at least one Fixed point.