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In this paper we present two algorithms for handwritten digit classification based on the higher order singular value decomposition (HOSVD). The first algorithm uses HOSVD for construction of the class models and achieves classification results with error rate lower than 6%. The second algorithm uses the HOSVD for tensor approximation simultaneously in two… (More)

An orthogonal Procrustes problem on the Stiefel manifold is studied , where a matrix Q with orthonormal columns is to be found that minimizes kAQ ? Bk F for an l m matrix A and an l n matrix B with l m and m > n. Based on the normal and secular equations and the properties of the Stiefel manifold, necessary conditions for a global minimum, as well as… (More)

We derive a Newton method for computing the best rank-(r 1 , r 2 , r 3) approximation of a given J × K × L tensor A. The problem is formulated as an approximation problem on a product of Grassmann manifolds. Incorporating the manifold structure into Newton's method ensures that all iterates generated by the algorithm are points on the Grassmann manifolds.… (More)

- Haesun Park, Lars Elden, Lars Eldén
- 2003

Numerical techniques for data analysis and feature extraction are discussed using the framework of matrix rank reduction. The singular value decomposition (SVD) and its properties are reviewed, and the relation to Latent Semantic Indexing (LSI) and Principal Component Analysis (PCA) is described. Methods that approximate the SVD are reviewed. A few basic… (More)

- Berkant Savas, Lars Eldén
- 2009

A couple of generalizations of matrix Krylov subspace methods to tensors are presented. It is shown that a particular variant can be interpreted as a Krylov factorization of the tensor. A generalization to tensors of the Krylov-Schur method for computing matrix eigenvalues is proposed. The methods are intended for the computation of low-rank approximations… (More)

- Lars Eldén
- 2003

We consider an inverse heat conduction problem, the Sideways Heat Equation, which is a model of a problem, where one wants to determine the temperature on both sides of a thick wall, but where one side is inaccessible to measurements. Mathematically it is formulated as a Cauchy problem for the heat equation in a quarter plane, with data given along the line… (More)

We consider the problem of updating an invariant subspace of a Hermitian, large and struc-tured matrix when the matrix is modiied slightly. The problem can be formulated as that of computing stationary values of a certain function, with orthogonality constraints. The constraint is formulated as the requirement that the solution must be on the Grassmann… (More)