# H‐methods in applied sciences

@article{Hskuldsson2008HmethodsIA, title={H‐methods in applied sciences}, author={Agnar H{\"o}skuldsson}, journal={Journal of Chemometrics}, year={2008}, volume={22} }

The author has developed a framework for mathematical modelling within applied sciences. It is characteristic for data from ‘nature and industry’ that they have reduced rank for inference. It means that full rank solutions normally do not give satisfactory solutions. The basic idea of H‐methods is to build up the mathematical model in steps by using weighing schemes. Each weighing scheme produces a score and/or a loading vector that are expected to perform a certain task. Optimisation…

## 17 Citations

Applications of the H-Principle of Mathematical Modelling

- Mathematics
- 2017

Traditional statistical test procedures are briefly reviewed. It is pointed out that significance testing may not always be reliable. The author has formulated a modelling procedure, the H-principle,…

Latent Structure Linear Regression

- Computer Science
- 2014

A general framework for linear regression is presented that includes most linear regression methods based on linear algebra and uses the H-principle of mathematical modelling, which uses the analogy between the modelling task and measurement situation in quantum mechanics.

Methods for estimation of intrinsic dimensionality

- Computer Science
- 2014

The main goal of this thesis is to develop algorithms for determining the intrinsic dimensions of recorded data sets in a nonlinear context, with special consideration given to recent developments in non–linear techniques, such as charted manifold and fractal–based methods.

Improved variable reduction in partial least squares modelling based on predictive-property-ranked variables and adaptation of partial least squares complexity.

- BusinessAnalytica chimica acta
- 2011

Predictive-property-ranked variable reduction in partial least squares modelling with final complexity adapted models: comparison of properties for ranking.

- BusinessAnalytica chimica acta
- 2013

Predictive-property-ranked variable reduction with final complexity adapted models in partial least squares modeling for multiple responses.

- ChemistryAnalytical chemistry
- 2013

The utility and effectiveness of four new predictor-variable properties, derived from the multiple response PLS2 regression coefficients, are studied for six data sets consisting of ultraviolet-visible (UV-vis) spectra, near-infrared (NIR) spectRA, NMR spectra and two simulated sets, one with correlated and one with uncorrelated responses.

Practical Considerations on Nonparametric Methods for Estimating Intrinsic Dimensions of Nonlinear Data Structures

- Computer ScienceInt. J. Pattern Recognit. Artif. Intell.
- 2020

This paper develops readily applicable methods for estimating the intrinsic dimension of multivariate datasets with performance generally in line with other dimension estimators, specifically noting that the correlation dimension variants perform favorably to the maximum likelihood method in terms of accuracy and computational efficiency.

Improved modelling for low-correlated multiple responses by common-subset-of-independent-variables partial-least-squares.

- BusinessTalanta
- 2021

Improved variable reduction in partial least squares modelling by Global-Minimum Error Uninformative-Variable Elimination.

- BusinessAnalytica chimica acta
- 2017

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