Generalizations of Tikhonov’s regularized method of least squares to non-Euclidean vector norms

Volkov, V. V.; Erokhin, V. I.; Kakaev, V. V.; Onufrei, A. Yu.

doi:10.1134/s0965542517090147

Cited by 2 publications

(1 citation statement)

References 3 publications

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“…It is well known that least-squares fitting is a common procedure to find the best fitting curve to a given set of data points by minimizing the sum of the squares of the data points from the curve ( [9,21,22]). The least-squares method is sensitive to small perturbations in data and, in those cases, regularization methods can be applied such as the regularized least-squares method (see [23]). Therefore, two experiments have been developed.…”

Section: Archimedean Spiral Curvementioning

confidence: 99%

Neural-Network-Based Curve Fitting Using Totally Positive Rational Bases

et al. 2020

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This paper proposes a method for learning the process of curve fitting through a general class of totally positive rational bases. The approximation is achieved by finding suitable weights and control points to fit the given set of data points using a neural network and a training algorithm, called AdaMax algorithm, which is a first-order gradient-based stochastic optimization. The neural network presented in this paper is novel and based on a recent generalization of rational curves which inherit geometric properties and algorithms of the traditional rational Bézier curves. The neural network has been applied to different kinds of datasets and it has been compared with the traditional least-squares method to test its performance. The obtained results show that our method can generate a satisfactory approximation.

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Section: Archimedean Spiral Curvementioning

confidence: 99%