Agnar Höskuldsson  

H-Methods in Applied Sciences

  New horizon in
A personal website  

Superior methods for multivariate data analysis

  industrial mathematics
         
Centre of Advanced
Data Analysis
 
H-methods
 
Mathematics of
H-methods
 
New mathematics
 

A new framework for mathematical modelling within applied sciences is presented on this website. 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 that are expected to perform a certain task. Optimisation procedures are used to obtain ‘the best’ solution at each step. At each step the optimisation is concerned with finding a balance between the estimation task and the prediction task. 

The name H-methods has been chosen because of close analogy with the Heisenberg uncertainty inequality. A similar situation is present in modelling data. The mathematical modelling stops, when the prediction aspect of the model can not be improved.

H-methods have been applied to wide range of fields within applied sciences. In each case the H-methods provide with superior solutions compared to the traditional ones. 

Examples of application areas: General linear models, non-linear models, multi-block methods, path modelling, multi-way data analysis, growth models, dynamic models and pattern recognition.

 

  A review of ideas and philosophy of the H-methods
    Graphic procedures for latent structures in multivariate models
    Maximum Likelihood methods have low prediction ability
    Presentation of results from methods in simple terms
    Important to test the solution of methods
    Confidence intervals of parameters based on observed data
    Basic issues in modelling data