The traditional Hessian-related vessel filters often suffer from detecting complex structures like bifurcations due to an over-simplified cylindrical model. To solve this problem, we present a shape-tuned strain energy density function to measure vessel likelihood in 3D medical images. This method is initially inspired by established stress-strain principles in mechanics. By considering the Hes...

A local convergence theorem for calculating canonical low-rank tensor approximations (PARAFAC, CANDECOMP) by the alternating least squares algorithm is established. The main assumption is that the Hessian matrix of the problem is positive definite modulo the scaling indeterminacy. A discussion, whether this is realistic, and numerical illustrations are included. Also regularization is addressed.

*Correspondence: [email protected] 1Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany 2Department of Computational Science and Engineering, Yonsei University, Unter den Linden 6, 120-749, Seoul, Korea Abstract Background: The discretisation of degenerate convex minimisation problems experiences numerical difficulties with a singular or near...

In this paper we present one approach to build optimal meshes for P1 interpolation. Considering classical geometric error estimates based on the Hessian matrix of a solution, we show it is possible to generate optimal meshes in H 1 semi-norm via a simple minimization procedure.

Graph regularized nonnegative matrix factorization (GNMF) decomposes a nonnegative data matrix X[Symbol:see text]R(m x n) to the product of two lower-rank nonnegative factor matrices, i.e.,W[Symbol:see text]R(m x r) and H[Symbol:see text]R(r x n) (r < min {m,n}) and aims to preserve the local geometric structure of the dataset by minimizing squared Euclidean distance or Kullback-Leibler (KL) di...

Several attempts have been made to modify the quasi-Newton condition in order obtain rapid convergence with complete properties (symmetric and positive definite) of inverse Hessian matrix (second derivative objective function). There are many unconstrained optimization methods that do not generate definiteness matrix. One those is symmetric rank 1( H-version) update (SR1 update), where this sat...

Matrix factorization based methods have widely been used in data representation. Among them, Non-negative Matrix Factorization (NMF) is a promising technique owing to its psychological and physiological interpretation of spontaneously occurring data. On one hand, although traditional Laplacian regularization can enhance the performance of NMF, it still suffers from the problem of its weak extra...

The curvature matrix depends on the specific optimisation method and will often be only an estimate. For notational simplicity, the dependence of f̂ on θ is omitted. Setting C to the true Hessian matrix of f would make f̂ the exact secondorder Taylor expansion of the function around θ. However, when f is a nonlinear function, the Hessian can be indefinite, which leads to an ill-conditioned quadra...

Matrix factorization based methods have widely been used in data representation. Among them, Non-negative Matrix Factorization (NMF) is a promising technique owing to its psychological and physiological interpretation of spontaneously occurring data. On one hand, although traditional Laplacian regularization can enhance the performance of NMF, it still suffers from the problem of its weak extra...

Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example...