Sökning: "Singular vectors"

Visar resultat 1 - 5 av 9 avhandlingar innehållade orden Singular vectors.

  1. 1. Principal Word Vectors

    Författare :Ali Basirat; Joakim Nivre; Hinrich Schütze; Uppsala universitet; []
    Nyckelord :HUMANITIES; HUMANIORA; NATURAL SCIENCES; NATURVETENSKAP; ENGINEERING AND TECHNOLOGY; TEKNIK OCH TEKNOLOGIER; NATURVETENSKAP; TEKNIK OCH TEKNOLOGIER; HUMANIORA; NATURAL SCIENCES; ENGINEERING AND TECHNOLOGY; HUMANITIES; word; context; word embedding; principal component analysis; PCA; sparse matrix; singular value decomposition; SVD; entropy;

    Sammanfattning : Word embedding is a technique for associating the words of a language with real-valued vectors, enabling us to use algebraic methods to reason about their semantic and grammatical properties. This thesis introduces a word embedding method called principal word embedding, which makes use of principal component analysis (PCA) to train a set of word embeddings for words of a language. LÄS MER

  2. 2. On Vertex Operator Algebras of Affine Type at Admissible Levels

    Författare :Thomas Edlund; Matematik (naturvetenskapliga fakulteten); []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Vertex operator algebras; Kac-Moody algebras; Ore localization; Admissible levels; Singular vectors; Intertwining operators;

    Sammanfattning : The main purpose of this thesis is the study of the structure and representation theory of simple vertex operator algebras (VOAs) of affine type at admissible levels. To do this, it is crucial to obtain knowledge of the singular vectors which generate the maximal submodules, with respect to which these VOAs appear as irreducible quotients, and therefore a substantial part of the text is devoted to this matter. LÄS MER

  3. 3. Topics on Harmonic analysis and Multilinear Algebra

    Författare :Mahdi Hormozi; Göteborgs universitet; Göteborgs universitet; Gothenburg University; []
    Nyckelord :Generalized bounded variation; Helly s theorem; Modulus of variation; Generalized Wiener classes; Symmetry classes of tensors; Orthogonal basis; Brauer symmetry classes of tensors; Multilinear singular integrals; weighted norm inequalities; weighted bounds; local mean oscillation; Lerner s formula; Brauer symmetry classes of tensors;

    Sammanfattning : The present thesis consists of six different papers. Indeed, they treat three different research areas: function spaces, singular integrals and multilinear algebra. In paper I, a characterization of continuity of the $p$-$\Lambda$-variation function is given and Helly's selection principle for $\Lambda BV^{(p)}$ functions is established. LÄS MER

  4. 4. On Methods for Solving Symmetric Systems of Linear Equations Arising in Optimization

    Författare :Tove Odland; Anders Forsgren; William W. Hager; KTH; []
    Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; symmetric system of linear equations; method of conjugate gradients; quasi-Newton method; unconstrained optimization; unconstrained quadratic optimiza- tion; Krylov subspace method; unnormalized Lanczos vectors; minimum-residual method; symmetriska linjära ekvationssystem; konjugerade gradientmetoden; kvasi- Newtonmetoder; optimering utan bivillkor; kvadratisk optimering utan bivillkor; Kry- lovunderrumsmetoder; icke-normaliserade Lanczosvektorer; minimum-residualmetoden; Matematik; Mathematics;

    Sammanfattning : In this thesis we present research on mathematical properties of methods for solv- ing symmetric systems of linear equations that arise in various optimization problem formulations and in methods for solving such problems.In the first and third paper (Paper A and Paper C), we consider the connection be- tween the method of conjugate gradients and quasi-Newton methods on strictly convex quadratic optimization problems or equivalently on a symmetric system of linear equa- tions with a positive definite matrix. LÄS MER

  5. 5. Algorithms in data mining using matrix and tensor methods

    Författare :Berkant Savas; Lars Eldén; Lieven De Lathauwer; Linköpings universitet; []
    Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; Volume; Minimization criterion; Determinant; Rank deficient matrix; Reduced rank regression; System identification; Rank reduction; Volume minimization; General algorithm; Handwritten digit classification; Tensors; Higher order singular value decomposition; Tensor approximation; Least squares; Tucker model; Multilinear algebra; Notation; Contraction; Tensor matricization; Newton s method; Grassmann manifolds; Product manifolds; Quasi-Newton algorithms; BFGS and L-BFGS; Symmetric tensor approximation; Local intrinsic coordinates; Global embedded coordinates; ; Numerical analysis; Numerisk analys;

    Sammanfattning : In many fields of science, engineering, and economics large amounts of data are stored and there is a need to analyze these data in order to extract information for various purposes. Data mining is a general concept involving different tools for performing this kind of analysis. LÄS MER