positive definite matrices

Convexity Conditions and the Legendre-Fenchel Transform for the Product of Finitely Many Positive Definite Quadratic Forms

  • Yun-Bin Zhao
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , ,

    While the product of finitely many convex functions has been investigated in the field of global optimization, some fundamental issues such as the convexity condition and the Legendre-Fenchel transform for the product function remain unresolved. Focusing on quadratic forms, this paper is aimed at addressing the question: \emph{When is the product of finitely many positive … Read more

    A Framework for Kernel Regularization with Applications to Protein Clustering

  • Sunduz Keles
  • Stephen Wright
  • Fan Lu
  • Grace Wahba
    • Categories Biomedical Applications, Linear, Cone and Semidefinite Programming, Statistics Tags , , , , , , ,

    We develop and apply a novel framework which is designed to extract information in the form of a positive definite kernel matrix from possibly crude, noisy, incomplete, inconsistent dissimilarity information between pairs of objects, obtainable in a variety of contexts. Any positive definite kernel defines a consistent set of distances, and the fitted kernel provides … Read more