In this paper we suggest a new algorithm for the computation of a best rank one approximation of tensors, called alternating singular value decomposition. This method is based on the computation of maximal singular values and the corresponding singular vectors of matrices. We also introduce a modification for this method and the alternating least squares method, which ensures that alternating i...

prediction using pure standards is expected to be biased whenever the slope of the calibration is affected by the presence of sample matrix. moreover, in the presence of unknown spectral interferents, first-order algorithms like partial least squares cannot be used. in this study, a method for determination of carvedilol (car) in tablet and urine samples is proposed by excitation-emission fluor...

Pedomodels have become a popular topic in soil science and environmentalresearch. They are predictive functions of certain soil properties based on other easily orcheaply measured properties. The common method for fitting pedomodels is to use classicalregression analysis, based on the assumptions of data crispness and deterministic relationsamong variables. In modeling natural systems such as s...

The purpose of this thesis is to explore the methods to solve the tensor completion problem. Inspired by the matrix completion problem, the tensor completion problem is formulated as an unconstrained nonlinear optimization problem, which finds three factors that give a low-rank approximation. Various of iterative methods, including the gradient-based methods, stochastic gradient descent method ...

Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices and has been shown to be particularly useful in many applications, e.g., in text mining, image processing, computational biology, etc. In this paper, we explain how algorithms for NMF can be embedded into the framework of multilevel methods in order t...

Nonnegative matrix factorization (NMF) is a data analysis technique used in a great variety of applications such as text mining, image processing, hyperspectral data analysis, computational biology, and clustering. In this letter, we consider two well-known algorithms designed to solve NMF problems: the multiplicative updates of Lee and Seung and the hierarchical alternating least squares of Ci...