Some mathematical results on three-way component analysis

PhD ceremony: Mr. J.N. Tendeiro, 16.15 uur, Academiegebouw (aula), Broerstraat 5, Groningen

Thesis: Some mathematical results on three-way component analysis

Promotor(s): prof. J.M.F ten Berge, prof. H.A.L Kiers

Faculty: Behavioural and Social Studies

 

Researchers often need to deal with data that fail to meet the common two-way structure “subjects × variables”. In some practical settings the data consist of sets of data matrices (collected over time, for example). Data with this structure is commonly referred to as multi-way data. The techniques used to analyze this type of data are multi-way techniques. Multi-way models are a natural extension of two-way techniques to deal with multi-way data. Its origins go back to the 1920’s (Hitchcock). In 1966 Tucker presented another three-way component analysis method. Carroll and Chang and Harshman, in 1970, rediscovered the method proposed by Hitchcock. Since then much has been done: research has been conducted to better understand the mathematical properties of multi-way models, and new models have been proposed. In this thesis we focused on three-way models. One of our goals was to provide a concise overview about some linear algebra properties of three-way arrays. We also studied properties of various statistical models for analyzing three-way data.